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Paper Citation Record · LEDGER

Mori-Zwanzig formalism: An existence proof for weak solutions of the orthogonal dynamics equation

As of 12 August 2026, this Paper Citation Record lists 54 of 54 outbound references and 1 inbound Pith citation observation for arXiv:2607.25855.

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2607.25855 v1

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measured 54 of 54 reference resolution

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Source: paper_references, paper_reference_links, observed 2026-08-01T01:38:15.783121Z

measured 55 of 55 standing notices

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Source: pith, observed 2026-08-12T00:12:48.578387Z

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54 of 54 outbound references displayed

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Outbound references

Observation d76c08db-cd16-41f5-b475-4d9524ebb6e1 · outbound

This paper cites On quantum theory of transport phenomena: Steady diffusion.Progress of Theoretical Physics, 20(6):948–959, 12 1958.

Mori-Zwanzig formalism: An existence proof for weak solutions of the orthogonal dynamics equation On quantum theory of transport phenomena: Steady diffusion.Progress of Theoretical Physics, 20(6):948–959, 12 1958

Reference 1

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Observation 5dc06b48-c12a-4479-97d1-83f43fbbe00e · outbound

This paper cites Ensemble method in the theory of irreversibility.The Journal of Chemical Physics, 33(5):1338–1341, 11 1960.

Mori-Zwanzig formalism: An existence proof for weak solutions of the orthogonal dynamics equation Ensemble method in the theory of irreversibility.The Journal of Chemical Physics, 33(5):1338–1341, 11 1960

Reference 2

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Observation d44a7b30-7d3b-4544-a701-fdbce89991eb · outbound

This paper cites Memory effects in irreversible thermodynamics.Phys.

Mori-Zwanzig formalism: An existence proof for weak solutions of the orthogonal dynamics equation Memory effects in irreversible thermodynamics.Phys

Reference 3

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Observation 07f6160b-2deb-422f-ac00-78443fe9ccf8 · outbound

This paper cites Transport, collective motion, and Brownian motion.Progress of theoretical physics, 33(3):423–455, 1965.

Mori-Zwanzig formalism: An existence proof for weak solutions of the orthogonal dynamics equation Transport, collective motion, and Brownian motion.Progress of theoretical physics, 33(3):423–455, 1965

Reference 4

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Observation 1b7c9e7e-59ca-4851-ac69-4576b5fde467 · outbound

This paper cites Simple derivations of generalized linear and nonlinear Langevin equations.Jour- nal of Physics A: Mathematical, Nuclear and General, 6(9):1289, sep 1973.

Mori-Zwanzig formalism: An existence proof for weak solutions of the orthogonal dynamics equation Simple derivations of generalized linear and nonlinear Langevin equations.Jour- nal of Physics A: Mathematical, Nuclear and General, 6(9):1289, sep 1973

Reference 5

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Observation 99b53e31-d9db-4f7e-8cae-e4331c7aa732 · outbound

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Mori-Zwanzig formalism: An existence proof for weak solutions of the orthogonal dynamics equation Unresolved cited work

Reference 6

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source=pdf_text observed=2026-08-01T01:38:15.636282Z digest=sha256:490ad275f6839a079a63c734e5e1b7c9d820d5ef36cd0d2f4ea558f5e3a84df3

Observation 5f23ad93-c1d2-4587-b09a-41808841fdea · outbound

This paper cites Study of Langevin type equations by means of a new projection operator method in nonequilibrium states.Progress of Theoretical Physics, 62(1):70–90, 07 1979.

Mori-Zwanzig formalism: An existence proof for weak solutions of the orthogonal dynamics equation Study of Langevin type equations by means of a new projection operator method in nonequilibrium states.Progress of Theoretical Physics, 62(1):70–90, 07 1979

Reference 7

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Observation 7cba7e62-a467-4bde-9878-37ac1e55d49c · outbound

This paper cites Computing generalized Langevin equations and generalized Fokker–Planck equations.Proceedings of the National Academy of Sciences, 106(27):10884–10889, 2009.

Mori-Zwanzig formalism: An existence proof for weak solutions of the orthogonal dynamics equation Computing generalized Langevin equations and generalized Fokker–Planck equations.Proceedings of the National Academy of Sciences, 106(27):10884–10889, 2009

Reference 8

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This paper cites Derivation of the generalized Langevin equation in nonstationary environments.The Journal of Chemical Physics, 134(11):114523, 03 2011.

Mori-Zwanzig formalism: An existence proof for weak solutions of the orthogonal dynamics equation Derivation of the generalized Langevin equation in nonstationary environments.The Journal of Chemical Physics, 134(11):114523, 03 2011

Reference 9

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Observation dc3bfc0d-6223-44df-80e7-282dc124f97f · outbound

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Mori-Zwanzig formalism: An existence proof for weak solutions of the orthogonal dynamics equation Unresolved cited work

Reference 10

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Observation ce3660b7-1088-4135-955c-f9104d92a516 · outbound

This paper cites On the non-stationary generalized Langevin equation.The Journal of Chemical Physics, 147(21):214110, 12 2017.

Mori-Zwanzig formalism: An existence proof for weak solutions of the orthogonal dynamics equation On the non-stationary generalized Langevin equation.The Journal of Chemical Physics, 147(21):214110, 12 2017

Reference 11

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Observation 20e2f677-76f3-4418-967d-3fee892049dc · outbound

This paper cites Mori-Zwanzig projection operator formalism for far-from-equilibrium systems with time-dependent Hamiltonians.Phys.

Mori-Zwanzig formalism: An existence proof for weak solutions of the orthogonal dynamics equation Mori-Zwanzig projection operator formalism for far-from-equilibrium systems with time-dependent Hamiltonians.Phys

Reference 12

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Observation 629b3ca7-3873-4ef4-ac5a-ea5434588054 · outbound

This paper cites Microscopic derivation of coarse-grained, energy-conserving generalized Langevin dynamics.The Journal of Chemical Physics, 151(10):104109, 09 2019.

Mori-Zwanzig formalism: An existence proof for weak solutions of the orthogonal dynamics equation Microscopic derivation of coarse-grained, energy-conserving generalized Langevin dynamics.The Journal of Chemical Physics, 151(10):104109, 09 2019

Reference 13

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Observation 7a97b3f5-4a95-4179-8101-6fdb4c4848cf · outbound

This paper cites Dalton, and Roland R.

Mori-Zwanzig formalism: An existence proof for weak solutions of the orthogonal dynamics equation Dalton, and Roland R

Reference 14

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Observation 83d9ee25-57b2-4631-8102-c1c143ae8804 · outbound

This paper cites On the derivation of the generalized Langevin equation and the fluctuation-dissipation theorem.Europhysics Letters, 140(6):62003, dec 2022.

Mori-Zwanzig formalism: An existence proof for weak solutions of the orthogonal dynamics equation On the derivation of the generalized Langevin equation and the fluctuation-dissipation theorem.Europhysics Letters, 140(6):62003, dec 2022

Reference 15

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Observation b1198cb5-ed31-4035-a7dd-f6cb15c078ca · outbound

This paper cites Nonequilibrium solvent response force: What happens if you push a Brownian particle.Phys.

Mori-Zwanzig formalism: An existence proof for weak solutions of the orthogonal dynamics equation Nonequilibrium solvent response force: What happens if you push a Brownian particle.Phys

Reference 16

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Observation bbc86634-2796-4482-8db9-4173ae66dad4 · outbound

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Mori-Zwanzig formalism: An existence proof for weak solutions of the orthogonal dynamics equation Unresolved cited work

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Observation 4bbc8e97-b47d-473b-b9d3-29de30184fd7 · outbound

This paper cites Derivation of a generalized Langevin equation from a generic time-dependent Hamiltonian.Journal of Physics A: Mathematical and Theoretical, 57(50):505003, nov 2024.

Mori-Zwanzig formalism: An existence proof for weak solutions of the orthogonal dynamics equation Derivation of a generalized Langevin equation from a generic time-dependent Hamiltonian.Journal of Physics A: Mathematical and Theoretical, 57(50):505003, nov 2024

Reference 18

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Observation d40b0f76-5621-4f47-a61d-2bc5e5b2c634 · outbound

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Mori-Zwanzig formalism: An existence proof for weak solutions of the orthogonal dynamics equation Unresolved cited work

Reference 19

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Observation ec81724a-af27-460d-b621-d88e151208e1 · outbound

This paper cites Berkowitz, J.

Mori-Zwanzig formalism: An existence proof for weak solutions of the orthogonal dynamics equation Berkowitz, J

Reference 20

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Observation 2035b9e2-f9cb-49ac-9045-be8f773adde2 · outbound

This paper cites Incorporation of memory effects in coarse-grained modeling via the Mori-Zwanzig formalism.The Journal of Chemical Physics, 143(24):243128, 11 2015.

Mori-Zwanzig formalism: An existence proof for weak solutions of the orthogonal dynamics equation Incorporation of memory effects in coarse-grained modeling via the Mori-Zwanzig formalism.The Journal of Chemical Physics, 143(24):243128, 11 2015

Reference 21

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Observation dc23dd30-fc9e-4139-b5cd-89ce42848611 · outbound

This paper cites Introducing memory in coarse-grained molecular simulations.The Journal of Physical Chemistry B, 125(19):4931–4954, 2021.

Mori-Zwanzig formalism: An existence proof for weak solutions of the orthogonal dynamics equation Introducing memory in coarse-grained molecular simulations.The Journal of Physical Chemistry B, 125(19):4931–4954, 2021

Reference 22

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Observation 4f53fca5-3849-4769-8582-ab40b0f5b643 · outbound

This paper cites Elsevier, 2006.

Mori-Zwanzig formalism: An existence proof for weak solutions of the orthogonal dynamics equation Elsevier, 2006

Reference 23

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Observation e5102911-3d07-44c2-afb1-ce3dc1ad08b9 · outbound

This paper cites A coarse-grained molecular dynamics model for crystalline solids.International Journal for Numerical Methods in Engineering, 83(8-9):986–997, 2010.

Mori-Zwanzig formalism: An existence proof for weak solutions of the orthogonal dynamics equation A coarse-grained molecular dynamics model for crystalline solids.International Journal for Numerical Methods in Engineering, 83(8-9):986–997, 2010

Reference 24

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Observation e89ce2b4-4e6f-4d1e-9e61-bea4cc84c861 · outbound

This paper cites Mode- coupling theory of the glass transition for a liquid in a periodic potential.Phys.

Mori-Zwanzig formalism: An existence proof for weak solutions of the orthogonal dynamics equation Mode- coupling theory of the glass transition for a liquid in a periodic potential.Phys

Reference 25

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Observation 80ff2d02-763b-4b76-b076-f2d9c337811e · outbound

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Mori-Zwanzig formalism: An existence proof for weak solutions of the orthogonal dynamics equation Unresolved cited work

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Observation eb666c4f-b7b5-4b6d-932a-e6d541f5482f · outbound

This paper cites Hansen and I.R.

Mori-Zwanzig formalism: An existence proof for weak solutions of the orthogonal dynamics equation Hansen and I.R

Reference 27

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Observation 7feb6627-9482-4569-961a-2afd9962b985 · outbound

This paper cites OUP Oxford, 2002.

Mori-Zwanzig formalism: An existence proof for weak solutions of the orthogonal dynamics equation OUP Oxford, 2002

Reference 28

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Observation 575d5810-8454-410b-8ab7-b24b6c9a8071 · outbound

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Mori-Zwanzig formalism: An existence proof for weak solutions of the orthogonal dynamics equation Unresolved cited work

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Observation c70aa7ac-205f-40f1-9ed5-0615bf05e0ef · outbound

This paper cites Derivation of dynamical density functional theory using the projection operator technique.The Journal of chemical physics, 131(24), 2009.

Mori-Zwanzig formalism: An existence proof for weak solutions of the orthogonal dynamics equation Derivation of dynamical density functional theory using the projection operator technique.The Journal of chemical physics, 131(24), 2009

Reference 30

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Observation 4f7eb932-3c2f-43a2-94eb-9caf02cd78d0 · outbound

This paper cites Graduate Texts in Mathematics.

Mori-Zwanzig formalism: An existence proof for weak solutions of the orthogonal dynamics equation Graduate Texts in Mathematics

Reference 31

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Observation 1b455ccf-580a-4b8b-8a60-714cd91e70ab · outbound

This paper cites Addendum: On the generalized Langevin equation and the Mori projection operator technique (2025 J.

Mori-Zwanzig formalism: An existence proof for weak solutions of the orthogonal dynamics equation Addendum: On the generalized Langevin equation and the Mori projection operator technique (2025 J

Reference 32

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Observation 818f67da-38b0-4dbe-8071-6ee8e2da3073 · outbound

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Mori-Zwanzig formalism: An existence proof for weak solutions of the orthogonal dynamics equation Unresolved cited work

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Observation 618a9b88-e4d4-42f6-a045-a4a78905a911 · outbound

This paper cites Dominy, and Daniele Venturi.

Mori-Zwanzig formalism: An existence proof for weak solutions of the orthogonal dynamics equation Dominy, and Daniele Venturi

Reference 34

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This paper cites Springer, 2006.

Mori-Zwanzig formalism: An existence proof for weak solutions of the orthogonal dynamics equation Springer, 2006

Reference 35

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Observation afdfe9fc-bb64-4337-a6b9-96718d896a49 · outbound

This paper cites Oxford University Press, 2001.

Mori-Zwanzig formalism: An existence proof for weak solutions of the orthogonal dynamics equation Oxford University Press, 2001

Reference 36

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Observation f0d0968a-25a1-4ee0-b585-cb74569490c7 · outbound

This paper cites Coarse-grained modelling out of equilibrium.Physics Reports, 972:1–45, 2022.

Mori-Zwanzig formalism: An existence proof for weak solutions of the orthogonal dynamics equation Coarse-grained modelling out of equilibrium.Physics Reports, 972:1–45, 2022

Reference 37

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Observation 67f8115d-62ea-4501-91d0-e5fc61a2a33e · outbound

This paper cites Optimal prediction and the Mori– Zwanzig representation of irreversible processes.Proceedings of the National Academy of Sciences, 97(7):2968–2973, 2000.

Mori-Zwanzig formalism: An existence proof for weak solutions of the orthogonal dynamics equation Optimal prediction and the Mori– Zwanzig representation of irreversible processes.Proceedings of the National Academy of Sciences, 97(7):2968–2973, 2000

Reference 38

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Observation f56b2370-6631-4d58-be5d-a0c67052272b · outbound

This paper cites Generalised Langevin dynamics: Significance and limitations of the projection operator formalism, 2026.

Mori-Zwanzig formalism: An existence proof for weak solutions of the orthogonal dynamics equation Generalised Langevin dynamics: Significance and limitations of the projection operator formalism, 2026

Reference 39

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Observation 9405d763-1e1a-4135-9c2a-fe36af6db4aa · outbound

This paper cites an unresolved cited work.

Mori-Zwanzig formalism: An existence proof for weak solutions of the orthogonal dynamics equation Unresolved cited work

Reference 40

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Observation 60fa7bb1-af4c-407e-8235-3dca68b7c794 · outbound

This paper cites Vector-valued Laplace transforms and Cauchy problems.Israel Journal of Mathematics, 59(3):327–352, Oct 1987.

Mori-Zwanzig formalism: An existence proof for weak solutions of the orthogonal dynamics equation Vector-valued Laplace transforms and Cauchy problems.Israel Journal of Mathematics, 59(3):327–352, Oct 1987

Reference 41

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source=pdf_text observed=2026-08-01T01:38:15.749268Z digest=sha256:566887b8fba242a30d63b7e5fef7035059715a31d90986ec6dfba3ae9d743ffd

Observation 950fa994-d8aa-4605-8fb0-59657f391b90 · outbound

This paper cites Volterra integral equations in a Banach space.Funkcialaj Ekvacioj, 18(2):163–193, 1975.

Mori-Zwanzig formalism: An existence proof for weak solutions of the orthogonal dynamics equation Volterra integral equations in a Banach space.Funkcialaj Ekvacioj, 18(2):163–193, 1975

Reference 42

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Observation 31726b38-abc6-4a27-a839-7dbe3ecce3e9 · outbound

This paper cites Grimmer and J.

Mori-Zwanzig formalism: An existence proof for weak solutions of the orthogonal dynamics equation Grimmer and J

Reference 43

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Observation 19996269-8729-43ce-b009-0bd8b4d1667d · outbound

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Mori-Zwanzig formalism: An existence proof for weak solutions of the orthogonal dynamics equation Unresolved cited work

Reference 44

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Observation 25ac845d-2610-4d95-99cf-0c9b045ad520 · outbound

This paper cites Evans.Partial Differential Equations.

Mori-Zwanzig formalism: An existence proof for weak solutions of the orthogonal dynamics equation Evans.Partial Differential Equations

Reference 45

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Observation e01e53ae-1585-4e31-b289-1c796c1e5213 · outbound

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Mori-Zwanzig formalism: An existence proof for weak solutions of the orthogonal dynamics equation Unresolved cited work

Reference 46

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Observation 606e92b4-8076-4350-8f79-2cf2612523e6 · outbound

This paper cites Springer New York, New York, NY, 2011.

Mori-Zwanzig formalism: An existence proof for weak solutions of the orthogonal dynamics equation Springer New York, New York, NY, 2011

Reference 47

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Observation 807d9203-22ba-48d8-acd4-e6231fde0616 · outbound

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Mori-Zwanzig formalism: An existence proof for weak solutions of the orthogonal dynamics equation Unresolved cited work

Reference 48

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Observation 2b9ed922-be74-41ef-9912-5c0d6156c322 · outbound

This paper cites Rudin.Functional Analysis.

Mori-Zwanzig formalism: An existence proof for weak solutions of the orthogonal dynamics equation Rudin.Functional Analysis

Reference 49

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Observation c706a137-ed26-453c-aebe-6299e5e33647 · outbound

This paper cites Reed and B.

Mori-Zwanzig formalism: An existence proof for weak solutions of the orthogonal dynamics equation Reed and B

Reference 50

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Observation 37f0050e-2e6a-4c42-b74f-41bf79f1caf0 · outbound

This paper cites Springer Berlin Heidelberg, Berlin, Heidelberg, 1992.

Mori-Zwanzig formalism: An existence proof for weak solutions of the orthogonal dynamics equation Springer Berlin Heidelberg, Berlin, Heidelberg, 1992

Reference 51

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Observation 748322e8-09d0-483c-a342-9ba37214d35f · outbound

This paper cites On the generalized Langevin equation and the Mori projection operator technique.Journal of Physics A: Mathematical and Theoretical, 58(40):405001, sep 2025.

Mori-Zwanzig formalism: An existence proof for weak solutions of the orthogonal dynamics equation On the generalized Langevin equation and the Mori projection operator technique.Journal of Physics A: Mathematical and Theoretical, 58(40):405001, sep 2025

Reference 52

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Observation cece8ce1-9c31-4450-91f1-846bfd574d25 · outbound

This paper cites Folland.Real Analysis - Modern Techniques and Their Applications - Second Edi- tion.

Mori-Zwanzig formalism: An existence proof for weak solutions of the orthogonal dynamics equation Folland.Real Analysis - Modern Techniques and Their Applications - Second Edi- tion

Reference 53

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Observation 95e0967c-d2f3-4b35-8f0f-3c1888041def · outbound

This paper cites an unresolved cited work.

Mori-Zwanzig formalism: An existence proof for weak solutions of the orthogonal dynamics equation Unresolved cited work

Reference 143

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Pith citing papers

Observation 95b1fb35-b00f-48ed-935f-50dbba5f64eb · inbound

A Shared Observation Shields Collective Fluctuations while Preserving Local Independence cites this paper.

A Shared Observation Shields Collective Fluctuations while Preserving Local Independence Mori-Zwanzig formalism: An existence proof for weak solutions of the orthogonal dynamics equation

Reference 72

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source=arxiv_source observed=2026-08-12T00:12:47.284624Z digest=sha256:2a6882bb8edfedd6e130309fa992be81bd95e5e4ea52919ff816811ce7480a56