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The fourth law of thermodynamics: steepest entropy ascent

As of 15 August 2026, this Paper Citation Record lists 100 of 115 outbound references and 0 inbound Pith citation observations for arXiv:1908.05768.

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pith.paper-citation-record.v1
1908.05768 v2

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100 of 115 outbound references displayed

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Outbound references

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

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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

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This paper cites 2005Thermodynamics: Foundations and applications.

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

Reference 3

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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

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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

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

Reference 6

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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

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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

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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

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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

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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

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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

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

Reference 13

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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

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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

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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

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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

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

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

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

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

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

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

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

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

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

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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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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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

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

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

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

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

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

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

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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

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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

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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

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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.

source=pdf_text observed=2026-08-14T13:10:26.493302Z digest=sha256:b45ac6963fa551ce63906dc78b33d6d444208189a2242982c9265bbb01b35178

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

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

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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

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source=pdf_text observed=2026-08-14T13:10:26.502395Z digest=sha256:db492adbbe67d6ef0c88cd4e23e229f6e113ece0a4bb0615bf3292115e3e3056

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

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source=pdf_text observed=2026-08-14T13:10:26.507341Z digest=sha256:e6ebd1297f96215d59615545fc4db271f7c68bd4d0570d381d3f8d496979da50

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

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source=pdf_text observed=2026-08-14T13:10:26.511989Z digest=sha256:a45f1d6a41519fcbf422c06c2aa70f0a3c840de6381301f0353c76cb0ed7d819

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

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source=pdf_text observed=2026-08-14T13:10:26.516442Z digest=sha256:b84e40ec58f333d636e56e6004622fea97d57796b20f6f7c19948f64c4347c12

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

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source=pdf_text observed=2026-08-14T13:10:26.521851Z digest=sha256:5ed2233426d5c1d438e3e64f6d13b6dbbfd168493c6ba1559cfc01d46e5736bd

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

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

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

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

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

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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

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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

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

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

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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

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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

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source=pdf_text observed=2026-08-14T13:10:26.559566Z digest=sha256:6899ca02e3a8649ba3ed064b65d6fa50f8b2a81e4cded438e7705f91d280f79d

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

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

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

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

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

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

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

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

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source=pdf_text observed=2026-08-14T13:10:26.588118Z digest=sha256:14d39b46b065fde35a6364b05c67ce2d3407b59e251e92da10a68e24f7bf9d12

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

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source=pdf_text observed=2026-08-14T13:10:26.595424Z digest=sha256:f41d39e73c5d0051774e5103df483b7bc8e748e35b5fb72b350e18d0251ebba7

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

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source=pdf_text observed=2026-08-14T13:10:26.599887Z digest=sha256:6f0885d9bd322190be895232c4b568b4763735569b0ed3545cdac379c86e3b85

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

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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

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source=pdf_text observed=2026-08-14T13:10:26.605183Z digest=sha256:9be6adb2a68549be825c06b6d139effc8220a1466c1128323bb36ac70fe261a0

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

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source=pdf_text observed=2026-08-14T13:10:26.610719Z digest=sha256:94e5be997f7d0b53020df8e54193ea11d023e542e23eb29cc03eb9281c234951

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

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

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source=pdf_text observed=2026-08-14T13:10:26.615152Z digest=sha256:0348c72cfb353991209af422657934cabf09640d979f6e957efb822d9dbedb02

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

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

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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

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source=pdf_text observed=2026-08-14T13:10:26.625294Z digest=sha256:f08cbed5ce122d40b68214088b195005c07a88ce2024fad3dee2e7a7bb5ac209

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

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

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

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

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

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

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source=pdf_text observed=2026-08-14T13:10:26.640075Z digest=sha256:9c1d3782e8008375ec1fa9833b9a0c48c1bab4275d5a17c743eb7d83cc8d77dd

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

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source=pdf_text observed=2026-08-14T13:10:26.644544Z digest=sha256:2602e754b6db637fd54dc9fdae5985a30b1612d88a3a54ae22361409db81258f

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

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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

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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

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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

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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

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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

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

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

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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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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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

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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

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

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

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

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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

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

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

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

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

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

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

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source=pdf_text observed=2026-08-14T13:10:26.754606Z digest=sha256:f3f2ae974a59dfb40dc991a1c822d71b8cb28d4311d76bc5ff9e94fa71a650de

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

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

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

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

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