The fourth law of thermodynamics: steepest entropy ascent | Paper Citation Record

Observation cf99ab60-c2d5-4573-b536-6e9f3c000346 · outbound

This paper cites The Character of Physical Law.

The fourth law of thermodynamics: steepest entropy ascent The Character of Physical Law

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-14T13:10:26.236653Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 47f45264-b7a6-4f15-9b51-d0d687869039 · outbound

This paper cites 1950 The nature of physical reality: A philosophy of modern physics.

The fourth law of thermodynamics: steepest entropy ascent 1950 The nature of physical reality: A philosophy of modern physics

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-14T13:10:26.241342Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f0295161-178b-4fea-9b1b-daa0538350cc · outbound

This paper cites 2005Thermodynamics: Foundations and applications.

The fourth law of thermodynamics: steepest entropy ascent 2005Thermodynamics: Foundations and applications

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-14T13:10:26.245663Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation dad521e7-e739-4dd3-8ed1-5a8b14ed330c · outbound

This paper cites 1976 A uniﬁed quantum theory of mechanics and thermodynamics.

The fourth law of thermodynamics: steepest entropy ascent 1976 A uniﬁed quantum theory of mechanics and thermodynamics

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-14T13:10:26.251173Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 354b785d-29a7-4ef9-8a9f-faac8542b700 · outbound

This paper cites 2014 Recent progress in the deﬁnition of thermodynamic entropy.Entropy 16 1547–1570.

The fourth law of thermodynamics: steepest entropy ascent 2014 Recent progress in the deﬁnition of thermodynamic entropy.Entropy 16 1547–1570

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-14T13:10:26.256046Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b6b50d2b-9c67-4318-baa4-81acb54e1856 · outbound

This paper cites an unresolved cited work.

The fourth law of thermodynamics: steepest entropy ascent Unresolved cited work

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-14T13:10:26.263233Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation dc13b8c1-6287-4dc4-9cbd-1994df460f18 · outbound

This paper cites 1998 General projection operator formalism for the dynamics and thermodynamics of complex ﬂuids.Phys.

The fourth law of thermodynamics: steepest entropy ascent 1998 General projection operator formalism for the dynamics and thermodynamics of complex ﬂuids.Phys

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-14T13:10:26.269592Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b1c8baf1-af94-473a-955a-4b815b7820d4 · outbound

This paper cites 2014 Contact geometry of mesoscopic thermodynamics and dynamics.Entropy 161652-1686.

The fourth law of thermodynamics: steepest entropy ascent 2014 Contact geometry of mesoscopic thermodynamics and dynamics.Entropy 161652-1686

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-14T13:10:26.276201Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7f3f68d2-bd56-4fb8-936a-1d7a82638190 · outbound

This paper cites 2014 Time reversal in nonequilibrium thermodynamics.Phys.

The fourth law of thermodynamics: steepest entropy ascent 2014 Time reversal in nonequilibrium thermodynamics.Phys

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-14T13:10:26.280368Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 21f26088-afbc-4aa0-86a1-8f0f912ff376 · outbound

This paper cites Coarse-graining via the fluctuation-dissipation theorem and large-deviation theory.

The fourth law of thermodynamics: steepest entropy ascent Coarse-graining via the fluctuation-dissipation theorem and large-deviation theory

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-14T13:10:26.286056Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 398db7a4-84fd-4d86-a5d6-f91bee551329 · outbound

This paper cites 2007 Comparison of invariant manifolds for model reduction in chemical kinetics.Commun.

The fourth law of thermodynamics: steepest entropy ascent 2007 Comparison of invariant manifolds for model reduction in chemical kinetics.Commun

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-14T13:10:26.292480Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a4dfad03-7102-4f9c-8dba-2bc1db973857 · outbound

This paper cites 2010 Minimal curvature trajectories: Riemannian geometry concepts for slow manifold computation in chemical kinetics.

The fourth law of thermodynamics: steepest entropy ascent 2010 Minimal curvature trajectories: Riemannian geometry concepts for slow manifold computation in chemical kinetics

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-14T13:10:26.299041Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b98bcef8-33f7-4ef8-abcf-37eb3948d295 · outbound

This paper cites an unresolved cited work.

The fourth law of thermodynamics: steepest entropy ascent Unresolved cited work

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-14T13:10:26.303255Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 459a1948-9033-40c6-81b8-8b04cef0a048 · outbound

This paper cites 2018 Systematic constraint selection strategy for rate-controlled constrained-equilibrium modeling of complex nonequilibrium chemical kinetics.

The fourth law of thermodynamics: steepest entropy ascent 2018 Systematic constraint selection strategy for rate-controlled constrained-equilibrium modeling of complex nonequilibrium chemical kinetics

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-14T13:10:26.308248Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7ce6b73f-bdc7-464d-a0ae-a24446826c14 · outbound

This paper cites 1976 A uniﬁed quantum theory of mechanics and thermodynamics.

The fourth law of thermodynamics: steepest entropy ascent 1976 A uniﬁed quantum theory of mechanics and thermodynamics

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-14T13:10:26.312244Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bdb7d9d2-c0e7-4878-9242-7e458b6cbd63 · outbound

This paper cites 1976 A uniﬁed quantum theory of mechanics and thermodynamics.

The fourth law of thermodynamics: steepest entropy ascent 1976 A uniﬁed quantum theory of mechanics and thermodynamics

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-14T13:10:26.317120Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 747a426c-b666-406c-b7b6-99336bd92048 · outbound

This paper cites 1976 A uniﬁed quantum theory of mechanics and thermodynamics.

The fourth law of thermodynamics: steepest entropy ascent 1976 A uniﬁed quantum theory of mechanics and thermodynamics

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-14T13:10:26.326401Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7d229260-82a4-4fbc-9659-ef9ca1f317f0 · outbound

This paper cites 1999 The physics and mathematics of the second law of thermodynamics.Phys.

The fourth law of thermodynamics: steepest entropy ascent 1999 The physics and mathematics of the second law of thermodynamics.Phys

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-14T13:10:26.331097Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e7ba075d-35dc-44ae-95db-cb74c8a6c3e5 · outbound

This paper cites 2013 The entropy concept for nonequilibrium states.Proc.

The fourth law of thermodynamics: steepest entropy ascent 2013 The entropy concept for nonequilibrium states.Proc

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-14T13:10:26.338090Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation be1fbd5b-915b-4ba4-9402-235938074ffd · outbound

This paper cites 2014 Entropy meters and the entropy of non-extensive systems.Proc.

The fourth law of thermodynamics: steepest entropy ascent 2014 Entropy meters and the entropy of non-extensive systems.Proc

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-14T13:10:26.342313Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d318d4dc-611b-4982-bc83-cdfaac7a07cf · outbound

This paper cites 2015 What is the second law? ASME Journal of Energy Resources Technology 137 021003.

The fourth law of thermodynamics: steepest entropy ascent 2015 What is the second law? ASME Journal of Energy Resources Technology 137 021003

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-14T13:10:26.346830Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ea7d818f-73a9-4d36-a1cb-da47f7955817 · outbound

This paper cites 2015 The second laws of quantum thermodynamics.

The fourth law of thermodynamics: steepest entropy ascent 2015 The second laws of quantum thermodynamics

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-14T13:10:26.352166Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 788a655e-1639-4224-91a1-5d1a2bdc46af · outbound

This paper cites 2016 Axiomatic relation between thermodynamic and information-theoretic entropies.Phys.

The fourth law of thermodynamics: steepest entropy ascent 2016 Axiomatic relation between thermodynamic and information-theoretic entropies.Phys

Reference 23

Resolution: verified exact; doi, observed 2026-08-14T13:10:28.180533Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 3fd0f09f-589e-4f1d-8c9f-d5328957c638 · outbound

This paper cites 2008 Where is the entropy challenge?AIP Conf.

The fourth law of thermodynamics: steepest entropy ascent 2008 Where is the entropy challenge?AIP Conf

Reference 24

Resolution: verified exact; doi, observed 2026-08-14T13:10:28.163455Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation b49f9c6e-902d-4305-b411-6fe0ad22f38d · outbound

This paper cites 1965Principles of general thermodynamics.

The fourth law of thermodynamics: steepest entropy ascent 1965Principles of general thermodynamics

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-14T13:10:26.366572Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7a8e92aa-ef83-44cd-810f-b679c18e75c8 · outbound

This paper cites 1979Thermionic Energy Conversion, Vol.

The fourth law of thermodynamics: steepest entropy ascent 1979Thermionic Energy Conversion, Vol

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-14T13:10:26.371378Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ae10e774-9008-42a0-9e1f-9434b3c60dff · outbound

This paper cites 2005Thermodynamics: Fundamentals for applications.

The fourth law of thermodynamics: steepest entropy ascent 2005Thermodynamics: Fundamentals for applications

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-14T13:10:26.376774Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 357c459b-0fc7-4bec-9417-a251824d2c87 · outbound

This paper cites 2005 Statistical Thermodynamics and Stochastic Theory of Nonequilibrium Systems.

The fourth law of thermodynamics: steepest entropy ascent 2005 Statistical Thermodynamics and Stochastic Theory of Nonequilibrium Systems

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-14T13:10:26.381821Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c2f4dc3f-12b3-4657-8211-415f6aaf90fe · outbound

This paper cites 2008Understanding non-equilibrium thermodynamics.

The fourth law of thermodynamics: steepest entropy ascent 2008Understanding non-equilibrium thermodynamics

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-14T13:10:26.386417Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 52c79263-d43f-4c70-8cf9-1bdf5f1a0180 · outbound

This paper cites 2008Non-equilibrium thermodynamics of heterogeneous systems.

The fourth law of thermodynamics: steepest entropy ascent 2008Non-equilibrium thermodynamics of heterogeneous systems

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-14T13:10:26.391259Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e9360937-b31b-4b8b-bd62-691ff70beca7 · outbound

This paper cites 2015 What is heat?ASME Journal of Energy Resources Technology137 021006.

The fourth law of thermodynamics: steepest entropy ascent 2015 What is heat?ASME Journal of Energy Resources Technology137 021006

Reference 31

Resolution: verified exact; doi, observed 2026-08-14T13:10:28.147929Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 38051494-56be-4a2b-87e4-85f490021a31 · outbound

This paper cites 2008 Local eﬀective dynamics of quantum systems: A generalized approach to work and heat.EPL, Europhys.

The fourth law of thermodynamics: steepest entropy ascent 2008 Local eﬀective dynamics of quantum systems: A generalized approach to work and heat.EPL, Europhys

Reference 32

Resolution: malformed identifier; no resolver link, observed 2026-08-14T13:10:26.409807Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7046cfeb-e3d2-4441-97e0-1c0cf13240b0 · outbound

This paper cites 2012 Quantum refrigerators and the third law of thermodynamics.Phys.

The fourth law of thermodynamics: steepest entropy ascent 2012 Quantum refrigerators and the third law of thermodynamics.Phys

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-14T13:10:26.415710Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation af925f60-5e1f-4b00-8b75-8ea92f296340 · outbound

This paper cites 2014 Work extraction and thermodynamics for individual quantum systems.

The fourth law of thermodynamics: steepest entropy ascent 2014 Work extraction and thermodynamics for individual quantum systems

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-14T13:10:26.421479Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d6124026-f4e9-4d4b-86be-af7c1eb83784 · outbound

This paper cites 2015 Quantum thermodynamics of general quantum processes.

The fourth law of thermodynamics: steepest entropy ascent 2015 Quantum thermodynamics of general quantum processes

Reference 35

Resolution: verified exact; doi, observed 2026-08-14T13:10:28.102540Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation a99a6647-8725-419f-af03-1215725e9f2c · outbound

This paper cites 2015 Nature of heat in strongly coupled open quantum systems.

The fourth law of thermodynamics: steepest entropy ascent 2015 Nature of heat in strongly coupled open quantum systems

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-14T13:10:26.434518Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 58384d78-7fbb-4707-804c-ecdd4753678a · outbound

This paper cites 2017 Resource theory for work and heat.Phys.

The fourth law of thermodynamics: steepest entropy ascent 2017 Resource theory for work and heat.Phys

Reference 37

Resolution: verified exact; doi, observed 2026-08-14T13:10:28.077602Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation f166f864-9949-40d7-a938-77c0bf63458c · outbound

This paper cites 2013 Resource theory of quantum states out of thermal equilibrium.Phys.

The fourth law of thermodynamics: steepest entropy ascent 2013 Resource theory of quantum states out of thermal equilibrium.Phys

Reference 38

Resolution: unresolved; no resolver link, observed 2026-08-14T13:10:26.444954Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 185fbf79-f9d1-4a42-ab3f-29fffd9b1274 · outbound

This paper cites 2016 Beyond heat baths: Generalized resource theories for small-scale thermodynamics.

The fourth law of thermodynamics: steepest entropy ascent 2016 Beyond heat baths: Generalized resource theories for small-scale thermodynamics

Reference 39

Resolution: verified exact; doi, observed 2026-08-14T13:10:28.051554Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 32cafa41-49a8-48f0-8bf2-ba28332ef5ac · outbound

This paper cites 2002 Entropy and temperature of a quantum Carnot engine.Proc.

The fourth law of thermodynamics: steepest entropy ascent 2002 Entropy and temperature of a quantum Carnot engine.Proc

Reference 40

Resolution: unresolved; no resolver link, observed 2026-08-14T13:10:26.453326Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e0ef57b2-5f44-4bf7-9f23-b3ce69673f10 · outbound

This paper cites 2011 Entropy of isolated quantum systems after a quench.Phys.

The fourth law of thermodynamics: steepest entropy ascent 2011 Entropy of isolated quantum systems after a quench.Phys

Reference 41

Resolution: unresolved; no resolver link, observed 2026-08-14T13:10:26.457369Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 62cf5c9a-1719-49e8-a342-e85c917df5c8 · outbound

This paper cites 2011 Rigorous and general deﬁnition of thermodynamic entropy in thermodynamics.

The fourth law of thermodynamics: steepest entropy ascent 2011 Rigorous and general deﬁnition of thermodynamic entropy in thermodynamics

Reference 42

Resolution: malformed identifier; doi_truncated, observed 2026-08-14T13:10:28.027605Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 78240455-9ee0-4679-94a5-b0ebc1fd8ed2 · outbound

This paper cites 2015 What is a simple system? ASME Journal of Energy Resources Technology 137 021007.

The fourth law of thermodynamics: steepest entropy ascent 2015 What is a simple system? ASME Journal of Energy Resources Technology 137 021007

Reference 43

Resolution: verified exact; doi, observed 2026-08-14T13:10:28.010219Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation d00b0f00-35ab-44b1-a887-365fc7e4c5b4 · outbound

This paper cites 2015 Thermal equilibrium of a macroscopic quantum system in a pure state.Phys.

The fourth law of thermodynamics: steepest entropy ascent 2015 Thermal equilibrium of a macroscopic quantum system in a pure state.Phys

Reference 44

Resolution: verified exact; doi, observed 2026-08-14T13:10:27.992924Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation b0ad15e5-566c-45e1-9cfd-23da0fd0c76e · outbound

This paper cites 2017 Stochastic and macroscopic thermodynamics of strongly coupled systems.Phys.

The fourth law of thermodynamics: steepest entropy ascent 2017 Stochastic and macroscopic thermodynamics of strongly coupled systems.Phys

Reference 45

Resolution: verified exact; doi, observed 2026-08-14T13:10:27.974838Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 1fb1c842-e2be-4ca7-9fdb-67f1332e1caa · outbound

This paper cites an unresolved cited work.

The fourth law of thermodynamics: steepest entropy ascent Unresolved cited work

Reference 46

Resolution: verified exact; doi, observed 2026-08-14T13:10:27.958114Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 070b72e5-84a4-43f5-a52e-18c1296cd1ce · outbound

This paper cites 1988 Thermodynamics: energy of closed and open systems.

The fourth law of thermodynamics: steepest entropy ascent 1988 Thermodynamics: energy of closed and open systems

Reference 47

Resolution: verified exact; doi, observed 2026-08-14T13:10:27.941943Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation d25f908b-5905-4297-99a6-a66c6c87f28b · outbound

This paper cites 1992 Thermodynamics: energy of nonsimple systems and second postulate.

The fourth law of thermodynamics: steepest entropy ascent 1992 Thermodynamics: energy of nonsimple systems and second postulate

Reference 48

Resolution: verified exact; doi, observed 2026-08-14T13:10:27.925211Z

Source-reported events for the cited work

correction dated 2007-12-18. Source: crossref record 10.1007/bf02728573->10.1007/bf02722911:correction, observed 2026-07-11T03:09:18.279813+00:00. This notice travels one citation hop only.

Observation e936600c-37b9-4433-b709-3ce7dd0a5ffe · outbound

This paper cites 1971 General state changes in quantum theory.Ann.

The fourth law of thermodynamics: steepest entropy ascent 1971 General state changes in quantum theory.Ann

Reference 49

Resolution: unresolved; no resolver link, observed 2026-08-14T13:10:26.498444Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2fe07d70-cc05-4405-916a-257ade55e2a3 · outbound

This paper cites 1972 On quantum statistical mechanics of non-Hamiltonian systems.Rep.

The fourth law of thermodynamics: steepest entropy ascent 1972 On quantum statistical mechanics of non-Hamiltonian systems.Rep

Reference 50

Resolution: unresolved; no resolver link, observed 2026-08-14T13:10:26.502395Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8ace3e33-60d8-4a16-b382-7c6957e1a5d7 · outbound

This paper cites 1975 On the connection of nonequilibrium information thermodynamics with non-Hamiltonian quantum mechanics of open systems.Ann.

The fourth law of thermodynamics: steepest entropy ascent 1975 On the connection of nonequilibrium information thermodynamics with non-Hamiltonian quantum mechanics of open systems.Ann

Reference 51

Resolution: malformed identifier; no resolver link, observed 2026-08-14T13:10:26.507341Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 48d50598-32c5-4611-bb92-50151cc15dbb · outbound

This paper cites 1976 On the generators of quantum dynamical semigroups.Commun.

The fourth law of thermodynamics: steepest entropy ascent 1976 On the generators of quantum dynamical semigroups.Commun

Reference 52

Resolution: unresolved; no resolver link, observed 2026-08-14T13:10:26.511989Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 55eeb1b8-7ed8-4ab8-be74-f48873aa552b · outbound

This paper cites 1976 Completely positive dynamical semigroups of N-level systems.

The fourth law of thermodynamics: steepest entropy ascent 1976 Completely positive dynamical semigroups of N-level systems

Reference 53

Resolution: unresolved; no resolver link, observed 2026-08-14T13:10:26.516442Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4a4339f7-5089-4a95-83f1-8c6a809ff653 · outbound

This paper cites an unresolved cited work.

The fourth law of thermodynamics: steepest entropy ascent Unresolved cited work

Reference 54

Resolution: unresolved; no resolver link, observed 2026-08-14T13:10:26.521851Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b8f6d831-cd95-4485-855f-45160dfb8a41 · outbound

This paper cites 2010 Maximum entropy production rate in quantum thermodynamics.J.

The fourth law of thermodynamics: steepest entropy ascent 2010 Maximum entropy production rate in quantum thermodynamics.J

Reference 55

Resolution: verified exact; doi, observed 2026-08-14T13:10:27.826739Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 5ef8218a-c4ea-4414-94b1-536e0115ca65 · outbound

This paper cites 2007 Well-behaved nonlinear evolution equation for steepest-entropy-ascent dissipative quantum dynamics.Int.

The fourth law of thermodynamics: steepest entropy ascent 2007 Well-behaved nonlinear evolution equation for steepest-entropy-ascent dissipative quantum dynamics.Int

Reference 56

Resolution: verified exact; doi, observed 2026-08-14T13:10:27.808929Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation ffc83c4b-8d66-4c2b-bc53-e00db895f3dd · outbound

This paper cites 2015 Steepest-entropy-ascent quantum thermodyna- mic modeling of decoherence in two diﬀerent microscopic composite systems.Phys.

The fourth law of thermodynamics: steepest entropy ascent 2015 Steepest-entropy-ascent quantum thermodyna- mic modeling of decoherence in two diﬀerent microscopic composite systems.Phys

Reference 57

Resolution: verified exact; doi, observed 2026-08-14T13:10:27.791761Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 30ec32b7-6eae-4ded-8af8-c2bfda41c20f · outbound

This paper cites an unresolved cited work.

The fourth law of thermodynamics: steepest entropy ascent Unresolved cited work

Reference 58

Resolution: verified exact; doi, observed 2026-08-14T13:10:27.771917Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation d0e46d33-808f-468d-b181-ac656310c290 · outbound

This paper cites 1985 Quantum thermodynamics.

The fourth law of thermodynamics: steepest entropy ascent 1985 Quantum thermodynamics

Reference 59

Resolution: unresolved; no resolver link, observed 2026-08-14T13:10:26.549274Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3e45b13e-e942-47c9-aed5-f612a2d9bff1 · outbound

This paper cites 2009 Nonlinear quantum evolution equations to model irreversible adiabatic relaxation with maximal entropy production and other nonunitary processes.

The fourth law of thermodynamics: steepest entropy ascent 2009 Nonlinear quantum evolution equations to model irreversible adiabatic relaxation with maximal entropy production and other nonunitary processes

Reference 60

Resolution: unresolved; no resolver link, observed 2026-08-14T13:10:26.554094Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1f4b7262-7b7c-4e4c-8f1e-6c3f8515b639 · outbound

This paper cites 1873 A method of geometrical representation of the thermodynamic properties by means of surfaces.

The fourth law of thermodynamics: steepest entropy ascent 1873 A method of geometrical representation of the thermodynamic properties by means of surfaces

Reference 61

Resolution: unresolved; no resolver link, observed 2026-08-14T13:10:26.559566Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9652229d-ac39-4a8d-a8cd-e3f2493c9095 · outbound

This paper cites 1980Statistical Physics, Part I.

The fourth law of thermodynamics: steepest entropy ascent 1980Statistical Physics, Part I

Reference 62

Resolution: unresolved; no resolver link, observed 2026-08-14T13:10:26.568479Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0f83dd15-a399-4748-931e-7f0303a478e5 · outbound

This paper cites 2013 Non-equilibrium thermodynamics in multiphase ﬂows New York, NY: Springer.

The fourth law of thermodynamics: steepest entropy ascent 2013 Non-equilibrium thermodynamics in multiphase ﬂows New York, NY: Springer

Reference 63

Resolution: verified exact; doi, observed 2026-08-14T13:10:27.745950Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 30b55139-daf0-4891-8cb7-8c7f552caa87 · outbound

This paper cites 2015 What is the third law? ASME Journal of Energy Resources Technology 137 021004.

The fourth law of thermodynamics: steepest entropy ascent 2015 What is the third law? ASME Journal of Energy Resources Technology 137 021004

Reference 64

Resolution: verified exact; doi, observed 2026-08-14T13:10:27.730797Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation d24130e4-88cf-4fce-8a3e-b83a3f69daf4 · outbound

This paper cites 2014 Steepest Entropy Ascent Model for Far-Non-Equilibrium Thermodynamics.

The fourth law of thermodynamics: steepest entropy ascent 2014 Steepest Entropy Ascent Model for Far-Non-Equilibrium Thermodynamics

Reference 65

Resolution: unresolved; no resolver link, observed 2026-08-14T13:10:26.588118Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bf2af013-6b98-44ec-b1a3-980d51d35072 · outbound

This paper cites 1971 Rate-controlled partial-equilibrium method for treating reacting gas mixtures.

The fourth law of thermodynamics: steepest entropy ascent 1971 Rate-controlled partial-equilibrium method for treating reacting gas mixtures

Reference 66

Resolution: unresolved; no resolver link, observed 2026-08-14T13:10:26.595424Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation dac2e27e-c8c9-4b3f-a33c-189453c450ab · outbound

This paper cites 1990 Rate-controlled constrained-equilibrium theory of chemical reactions in complex systems.

The fourth law of thermodynamics: steepest entropy ascent 1990 Rate-controlled constrained-equilibrium theory of chemical reactions in complex systems

Reference 67

Resolution: unresolved; no resolver link, observed 2026-08-14T13:10:26.599887Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1d75cb64-7978-4dc1-bdf1-880a252ec0a4 · outbound

This paper cites 2012 The Rate-controlled constrained-equilibrium approach to far-from-local-equilibrium thermodynamics.Entropy 14 92–130.

The fourth law of thermodynamics: steepest entropy ascent 2012 The Rate-controlled constrained-equilibrium approach to far-from-local-equilibrium thermodynamics.Entropy 14 92–130

Reference 68

Resolution: verified exact; doi, observed 2026-08-14T13:10:27.678987Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 60b60ccb-8b10-4604-b5b1-d57bdfbb529d · outbound

This paper cites 2001 Corrections and enhancements of quasi-equilibrium states J.

The fourth law of thermodynamics: steepest entropy ascent 2001 Corrections and enhancements of quasi-equilibrium states J

Reference 69

Resolution: unresolved; no resolver link, observed 2026-08-14T13:10:26.610719Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0a53c226-5431-44fb-911b-bd78fb62d5aa · outbound

This paper cites 1964 On the macroscopic description of kinetic processes (in russian).Dokl.

The fourth law of thermodynamics: steepest entropy ascent 1964 On the macroscopic description of kinetic processes (in russian).Dokl

Reference 70

Resolution: unresolved; no resolver link, observed 2026-08-14T13:10:26.615152Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1fe10a7d-7b36-40e9-be60-2c7c5df6642a · outbound

This paper cites 2019 Dynamic maximum entropy reductionEntropy 21 715.

The fourth law of thermodynamics: steepest entropy ascent 2019 Dynamic maximum entropy reductionEntropy 21 715

Reference 71

Resolution: verified exact; doi, observed 2026-08-14T13:10:27.646543Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 98f4d82f-2058-4a8d-8bcc-8f81107c5695 · outbound

This paper cites an unresolved cited work.

The fourth law of thermodynamics: steepest entropy ascent Unresolved cited work

Reference 72

Resolution: unresolved; no resolver link, observed 2026-08-14T13:10:26.625294Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6c3f59c2-3793-4578-9800-fcf803ccb463 · outbound

This paper cites 2005 Maximum entropy production and the ﬂuctuation theorem.J.

The fourth law of thermodynamics: steepest entropy ascent 2005 Maximum entropy production and the ﬂuctuation theorem.J

Reference 73

Resolution: verified exact; doi, observed 2026-08-14T13:10:27.621959Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation dfe83921-61c0-4110-905b-a8d9ca2a7556 · outbound

This paper cites 2013 Entropy and entropy production: Old misconceptions and new breakthroughs.

The fourth law of thermodynamics: steepest entropy ascent 2013 Entropy and entropy production: Old misconceptions and new breakthroughs

Reference 74

Resolution: verified exact; doi, observed 2026-08-14T13:10:27.604370Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation d759d939-7bf9-41a2-a2db-768251fc3e0b · outbound

This paper cites 1980 The Maxwell-Vlasov equations as a continuous Hamiltonian system.Phys.

The fourth law of thermodynamics: steepest entropy ascent 1980 The Maxwell-Vlasov equations as a continuous Hamiltonian system.Phys

Reference 75

Resolution: unresolved; no resolver link, observed 2026-08-14T13:10:26.640075Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ea09e9e9-d691-461c-969c-45a21d4b1af4 · outbound

This paper cites 1982 The Hamiltonian structure of the Maxwell-Vlasov equations.Physica D 4 394–406.

The fourth law of thermodynamics: steepest entropy ascent 1982 The Hamiltonian structure of the Maxwell-Vlasov equations.Physica D 4 394–406

Reference 76

Resolution: unresolved; no resolver link, observed 2026-08-14T13:10:26.644544Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4252a738-7a95-40d9-a51d-a559fb88b589 · outbound

This paper cites 1984 Dissipative hamiltonian systems: A unifying principle.Phys.

The fourth law of thermodynamics: steepest entropy ascent 1984 Dissipative hamiltonian systems: A unifying principle.Phys

Reference 77

Resolution: verified exact; doi, observed 2026-08-14T13:10:27.553721Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation dddc5c0d-7138-4d5d-b736-e2c08da05ea5 · outbound

This paper cites 1984 Bracket formulation for irreversible classical ﬁelds.Phys.

The fourth law of thermodynamics: steepest entropy ascent 1984 Bracket formulation for irreversible classical ﬁelds.Phys

Reference 78

Resolution: unresolved; no resolver link, observed 2026-08-14T13:10:26.654721Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c6737bd4-602a-43db-9326-d4a4853ce3c0 · outbound

This paper cites 1984 Bracket formulation of dissipative ﬂuid mechanics equations.Phys.

The fourth law of thermodynamics: steepest entropy ascent 1984 Bracket formulation of dissipative ﬂuid mechanics equations.Phys

Reference 79

Resolution: unresolved; no resolver link, observed 2026-08-14T13:10:26.658926Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 62c26223-3ab0-4d52-9955-b2d25da117c4 · outbound

This paper cites 1987 Steepest entropy ascent in quantum thermodynamics.Lecture Notes in Physics278 441–443.

The fourth law of thermodynamics: steepest entropy ascent 1987 Steepest entropy ascent in quantum thermodynamics.Lecture Notes in Physics278 441–443

Reference 80

Resolution: verified exact; doi, observed 2026-08-14T13:10:27.503810Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 641d6830-ac95-49c7-8fe1-358bc0e12296 · outbound

This paper cites 1985 Entropy and irreversibility for a single isolated two-level system.

The fourth law of thermodynamics: steepest entropy ascent 1985 Entropy and irreversibility for a single isolated two-level system

Reference 81

Resolution: verified exact; doi, observed 2026-08-14T13:10:27.482329Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 8bfded19-6ad6-4608-9db7-243b56244d3f · outbound

This paper cites 1984 A general nonlinear evolution equation for irreversible conservative approach to stable equilibrium.

The fourth law of thermodynamics: steepest entropy ascent 1984 A general nonlinear evolution equation for irreversible conservative approach to stable equilibrium

Reference 82

Resolution: verified exact; doi, observed 2026-08-14T13:10:27.460157Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation cd3fc7e5-4e56-49fe-87a3-820fc47cef93 · outbound

This paper cites 1986 A paradigm for joined Hamiltonian and dissipative systems.Physica D 18 410–419.

The fourth law of thermodynamics: steepest entropy ascent 1986 A paradigm for joined Hamiltonian and dissipative systems.Physica D 18 410–419

Reference 83

Resolution: unresolved; no resolver link, observed 2026-08-14T13:10:26.682247Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8dc94989-faff-4e40-9514-55549407eeaa · outbound

This paper cites 2007 Metriplectic structure, Leibniz dynamics and dissipative systems.J.

The fourth law of thermodynamics: steepest entropy ascent 2007 Metriplectic structure, Leibniz dynamics and dissipative systems.J

Reference 84

Resolution: verified exact; doi, observed 2026-08-14T13:10:27.422387Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 81567080-d579-4d62-95c5-9546bc806044 · outbound

This paper cites Entropy 18 304.

The fourth law of thermodynamics: steepest entropy ascent Entropy 18 304

Reference 85

Resolution: verified exact; doi, observed 2026-08-14T13:10:27.400448Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 9a3ba284-1b4d-4012-b984-d23e58eb9d1f · outbound

This paper cites 1997 Dynamics and thermodynamics of complex ﬂuids.

The fourth law of thermodynamics: steepest entropy ascent 1997 Dynamics and thermodynamics of complex ﬂuids

Reference 86

Resolution: unresolved; no resolver link, observed 2026-08-14T13:10:26.696287Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0d81e894-b4ff-4250-a1a4-dec84f7beb80 · outbound

This paper cites an unresolved cited work.

The fourth law of thermodynamics: steepest entropy ascent Unresolved cited work

Reference 87

Resolution: verified exact; doi, observed 2026-08-14T13:10:27.359302Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 0b7504d4-81bb-4e0a-afc1-87f5df13ff7c · outbound

This paper cites 1998 The variational formulation of the Fokker–Planck equation.

The fourth law of thermodynamics: steepest entropy ascent 1998 The variational formulation of the Fokker–Planck equation

Reference 88

Resolution: unresolved; no resolver link, observed 2026-08-14T13:10:26.705573Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 164f2dde-e39a-4436-b2cb-d42e00678add · outbound

This paper cites 2001 The geometry of dissipative evolution equations: The porous medium equation.Commun.

The fourth law of thermodynamics: steepest entropy ascent 2001 The geometry of dissipative evolution equations: The porous medium equation.Commun

Reference 89

Resolution: unresolved; no resolver link, observed 2026-08-14T13:10:26.710622Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 416ef18c-9215-4cf4-8a5a-ac170a4a7f5e · outbound

This paper cites 2011 A gradient structure for reaction–diﬀusion systems and for energy-drift-diﬀusion systems.

The fourth law of thermodynamics: steepest entropy ascent 2011 A gradient structure for reaction–diﬀusion systems and for energy-drift-diﬀusion systems

Reference 90

Resolution: unresolved; no resolver link, observed 2026-08-14T13:10:26.715289Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation dd40fad6-9e2f-43b5-90df-8eca784555c9 · outbound

This paper cites Peletier MA, Johannes Zimmer J.

The fourth law of thermodynamics: steepest entropy ascent Peletier MA, Johannes Zimmer J

Reference 91

Resolution: unresolved; no resolver link, observed 2026-08-14T13:10:26.719711Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation dcd65faf-9f88-43ef-bd5d-8419f65f3828 · outbound

This paper cites 2014 On the relation between gradient ﬂows and the large- deviation principle, with applications to Markov chains and diﬀusion.Potential Anal.

The fourth law of thermodynamics: steepest entropy ascent 2014 On the relation between gradient ﬂows and the large- deviation principle, with applications to Markov chains and diﬀusion.Potential Anal

Reference 92

Resolution: unresolved; no resolver link, observed 2026-08-14T13:10:26.723611Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 027643b7-aa3f-4d5f-96e4-25b5d08c5281 · outbound

This paper cites 2015 Entropy production and the geometry of dissipative evolution equations.Phys.

The fourth law of thermodynamics: steepest entropy ascent 2015 Entropy production and the geometry of dissipative evolution equations.Phys

Reference 93

Resolution: verified exact; doi, observed 2026-08-14T13:10:27.262647Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 884c7ab4-29e4-43df-9f03-3c277e45b703 · outbound

This paper cites 2018 Computing diﬀusivities from particle models out of equili- brium.

The fourth law of thermodynamics: steepest entropy ascent 2018 Computing diﬀusivities from particle models out of equili- brium

Reference 94

Resolution: unresolved; no resolver link, observed 2026-08-14T13:10:26.731843Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 87c57a54-2900-4df4-b196-a134abc46c11 · outbound

This paper cites 2016 Microcanonical and resource-theoretic deri- vations of the thermal state of a quantum system with noncommuting charges.Nat.

The fourth law of thermodynamics: steepest entropy ascent 2016 Microcanonical and resource-theoretic deri- vations of the thermal state of a quantum system with noncommuting charges.Nat

Reference 95

Resolution: unresolved; no resolver link, observed 2026-08-14T13:10:26.739766Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2150c824-b1dc-41fe-827d-c85ecbb20d5d · outbound

This paper cites 1984 Quantum thermodynamics.

The fourth law of thermodynamics: steepest entropy ascent 1984 Quantum thermodynamics

Reference 96

Resolution: verified exact; doi, observed 2026-08-14T13:10:27.223934Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 56ddcc2e-1bd2-4ff4-9704-a3cbd8554c2a · outbound

This paper cites 2001 Nonlinear quantum evolution with maximal entropy productionPhys.

The fourth law of thermodynamics: steepest entropy ascent 2001 Nonlinear quantum evolution with maximal entropy productionPhys

Reference 97

Resolution: unresolved; no resolver link, observed 2026-08-14T13:10:26.749750Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 98688a76-05a7-4aa2-a0b7-8ac5182b67db · outbound

This paper cites Nonlinear quantum evolution with maximal entropy production.

The fourth law of thermodynamics: steepest entropy ascent Nonlinear quantum evolution with maximal entropy production

Reference 98

Resolution: unresolved; no resolver link, observed 2026-08-14T13:10:26.754606Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7755abcf-146e-4d9a-9467-6b26edc482ec · outbound

This paper cites 1996 Microscale theory of surface tension.

The fourth law of thermodynamics: steepest entropy ascent 1996 Microscale theory of surface tension

Reference 99

Resolution: verified exact; doi, observed 2026-08-14T13:10:27.165217Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 591e86ff-b5fc-487a-9e89-2ba1e45145b0 · outbound

This paper cites 2001 Weakly nonlocal irreversible thermodynamics—the Guyer–Krumhansl and the Cahn–Hilliard equations.Phys.

The fourth law of thermodynamics: steepest entropy ascent 2001 Weakly nonlocal irreversible thermodynamics—the Guyer–Krumhansl and the Cahn–Hilliard equations.Phys

Reference 100

Resolution: verified exact; doi, observed 2026-08-14T13:10:27.144614Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Coverage vector

Reference resolution

Outbound references

Pith citing papers