Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-16T04:59:47.653143Z
Paper Citation Record · LEDGER
As of 17 August 2026, this Paper Citation Record lists 72 of 72 outbound references and 1 inbound Pith citation observation for arXiv:2505.00188.
A citation records a reference. It does not transfer a finding from one paper to another.
Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-16T04:59:47.653143Z
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-08-03T22:35:20.605577Z
A source-named dated measurement, never combined with another source.
Source: cited_works
72 of 72 outbound references displayed
External citation measurements
No source-named external measurement is stored.
Observation 25400ade-d011-420a-8937-91438f7899de · outbound
Thermodynamic potentials from a probabilistic view on the system-environment interaction energy (2) By substituting ⟨⟨exp (−βV SE )⟩E0⟩S with ⟨exp (−βV SE )⟩S+E we will ultimately eliminate the free energy’s dependence on the HMF
Reference 1
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 8bf84b2a-ee39-460e-b066-5a05a4738e67 · outbound
Thermodynamic potentials from a probabilistic view on the system-environment interaction energy Unresolved cited work
Reference 2
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 2d9b461c-5df3-41ce-a5e3-d68ae0bb13a4 · outbound
Thermodynamic potentials from a probabilistic view on the system-environment interaction energy ( 9), we obtain after simplification ZS+E Z ∗ ZE = ⟨exp(−2βV SE )⟩E0 ⟨exp(−βV SE )⟩2 E|S
Reference 3
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation bbd3274d-a63c-4e00-b970-450e62ef59c7 · outbound
Thermodynamic potentials from a probabilistic view on the system-environment interaction energy Failure of the work-Hamiltonian connection for free-energy calculations
Reference 4
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 43895248-e71d-426c-8d5a-d4056b158eb2 · outbound
Thermodynamic potentials from a probabilistic view on the system-environment interaction energy (16) In the above expression, the function M (xE ) can be rewritten using Eq
Reference 5
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 5e9dc520-8537-4c37-8476-6f4d950d4741 · outbound
Thermodynamic potentials from a probabilistic view on the system-environment interaction energy Sekimoto, Langevin equation and thermodynamics, Prog
Reference 6
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation a757bdb6-24f9-4c01-83d2-50cf7cdb19f2 · outbound
Thermodynamic potentials from a probabilistic view on the system-environment interaction energy Zhang, H
Reference 7
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation caf72770-9fc9-421a-8293-1b40a2dd1974 · outbound
Thermodynamic potentials from a probabilistic view on the system-environment interaction energy Van den Broeck and M
Reference 8
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 69c27fee-20f4-4964-801b-79d1af5fa89c · outbound
Thermodynamic potentials from a probabilistic view on the system-environment interaction energy (10) By multiplying both sides of the above equation by Pβ (xS )/ ZE , substituting P (xE |xS ) Pβ (xS ) on the right- hand side with P (xS , x E ), and by using Eq
Reference 9
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation c8f4def3-bb94-42a7-84e1-0f0d77d89cd4 · outbound
Thermodynamic potentials from a probabilistic view on the system-environment interaction energy Seifert, First and second law of thermodynamics at strong coupling, Phys
Reference 10
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation fc1adbf6-0a71-4e2f-b891-f895602313e8 · outbound
Thermodynamic potentials from a probabilistic view on the system-environment interaction energy Unresolved cited work
Reference 11
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation d94d9351-0d95-4d71-9048-0f2802e562a0 · outbound
Thermodynamic potentials from a probabilistic view on the system-environment interaction energy In terms of importance, it gives a com- plementary view of how free energy changes
Reference 12
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 05b3856e-91f2-4fa7-981e-9d900a398610 · outbound
Thermodynamic potentials from a probabilistic view on the system-environment interaction energy With this in mind, we combine or result with the JE and arrive at ⟨ e− β ∆ Hβ (x)⟩ S 1 + χ 2 (Pβ ‖ PS0 ) = ⟨e− βW ⟩
Reference 13
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation ca71d8f6-8037-481d-b882-92a860410348 · outbound
Thermodynamic potentials from a probabilistic view on the system-environment interaction energy Campa, T
Reference 14
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 634de3ce-97a1-4a8f-a4f0-ccc93a1df12d · outbound
Thermodynamic potentials from a probabilistic view on the system-environment interaction energy In this way, one arrives at US = ⟨HS⟩S + ⟨VSE ⟩ for calculating internal energy
Reference 15
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 39bf1356-47b3-4a86-979c-71adf3dd56c2 · outbound
Thermodynamic potentials from a probabilistic view on the system-environment interaction energy Jarzynski, Stochastic and macroscopic thermodynam- ics of strongly coupled systems, Phys
Reference 16
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation fefe0bac-6f0e-4c31-8fd8-c81086466afd · outbound
Thermodynamic potentials from a probabilistic view on the system-environment interaction energy Unresolved cited work
Reference 17
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 31a80440-3929-49af-8c63-1e7ee65bfd2b · outbound
Thermodynamic potentials from a probabilistic view on the system-environment interaction energy Unresolved cited work
Reference 18
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation ec970a99-7491-4332-be40-eb13d4920be9 · outbound
Thermodynamic potentials from a probabilistic view on the system-environment interaction energy Failure of the work-Hamiltonian connection for free-energy calcula- tions
Reference 19
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation e0672cfe-deb5-4ec8-b531-16841e1e999e · outbound
Thermodynamic potentials from a probabilistic view on the system-environment interaction energy Seifert, Stochastic thermodynamics, fluctuation the- orems and molecular machines, Rep
Reference 20
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation a7ba696c-c152-469e-82e5-6c7206560c5f · outbound
Thermodynamic potentials from a probabilistic view on the system-environment interaction energy Unresolved cited work
Reference 21
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 8fe0347f-6cef-436f-91d2-efcb34e8d846 · outbound
Thermodynamic potentials from a probabilistic view on the system-environment interaction energy Hilfer, Foundations of statistical mechanics for unsta- ble interactions, Phys
Reference 22
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation f1212994-1600-44af-aad9-432ebcf0e9f7 · outbound
Thermodynamic potentials from a probabilistic view on the system-environment interaction energy Unresolved cited work
Reference 23
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 4a393f34-e36f-42d9-ab1d-36648e06803b · outbound
Thermodynamic potentials from a probabilistic view on the system-environment interaction energy Esposito, K
Reference 24
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation d6c5ad56-d179-4e74-9ff8-cfad41ef494a · outbound
Thermodynamic potentials from a probabilistic view on the system-environment interaction energy Talkner and P
Reference 25
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 08fac0fc-9608-4cad-935e-669d2cc6f839 · outbound
Thermodynamic potentials from a probabilistic view on the system-environment interaction energy Unresolved cited work
Reference 26
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 7b1b17c4-c530-4175-8cce-388cee5d288e · outbound
Thermodynamic potentials from a probabilistic view on the system-environment interaction energy Goldstein, D
Reference 27
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 38a46cd9-8aa7-420f-bd07-8416f4c4fbc7 · outbound
Thermodynamic potentials from a probabilistic view on the system-environment interaction energy Anto-Sztrikacs, A
Reference 28
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 15bb43d4-b4cf-4ac8-961f-d3c5a7c23cdc · outbound
Thermodynamic potentials from a probabilistic view on the system-environment interaction energy Unresolved cited work
Reference 29
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation d0b7460c-da85-472e-a394-52efd36aa421 · outbound
Thermodynamic potentials from a probabilistic view on the system-environment interaction energy Binder, L
Reference 30
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 00c8191b-1791-4e80-92a3-224043124f3d · outbound
Thermodynamic potentials from a probabilistic view on the system-environment interaction energy In the cases discussed above where Var E0 (e− βV SE ) = 0 holds, by placing the result of Eq
Reference 31
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 8d6f6817-cf83-4567-9b0e-42083078eee2 · outbound
Thermodynamic potentials from a probabilistic view on the system-environment interaction energy Talkner and P
Reference 32
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation d4ead28b-ca4d-4642-af3f-64e0e67cec71 · outbound
Thermodynamic potentials from a probabilistic view on the system-environment interaction energy Thirring, H
Reference 33
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 367cc845-bddf-40e1-af46-da7f4c16c2ef · outbound
Thermodynamic potentials from a probabilistic view on the system-environment interaction energy H¨ anggi, P
Reference 34
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 898e2e63-7074-4c79-9e93-71ec38e0c7a6 · outbound
Thermodynamic potentials from a probabilistic view on the system-environment interaction energy Unresolved cited work
Reference 35
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation f4c6eb93-5540-4867-8838-6f4c57137336 · outbound
Thermodynamic potentials from a probabilistic view on the system-environment interaction energy Chipot and A
Reference 36
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 2fa11448-f7c2-41f2-b701-e240e73c9920 · outbound
Thermodynamic potentials from a probabilistic view on the system-environment interaction energy These relations imply that the variance of VSE is invariant upon coupling (i.e
Reference 37
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 3298c1c1-640d-465f-ae7a-e40291e60232 · outbound
Thermodynamic potentials from a probabilistic view on the system-environment interaction energy Campisi, P
Reference 38
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation bed3be0d-19d4-4814-b5ff-bc85ee8de5dc · outbound
Thermodynamic potentials from a probabilistic view on the system-environment interaction energy Unresolved cited work
Reference 39
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation a769359e-9ceb-4eb9-a6d5-2ffc878c8f6e · outbound
Thermodynamic potentials from a probabilistic view on the system-environment interaction energy (41) Now, finally with Eq
Reference 40
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation ebab0a88-f140-4a4c-9303-c3ebf6101138 · outbound
Thermodynamic potentials from a probabilistic view on the system-environment interaction energy Unresolved cited work
Reference 41
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation cfdc37ab-ff68-4c0c-a20b-1bedfd53d41e · outbound
Thermodynamic potentials from a probabilistic view on the system-environment interaction energy Roux and T
Reference 42
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation f92d775d-e33f-49a0-91ed-e45355bc9528 · outbound
Thermodynamic potentials from a probabilistic view on the system-environment interaction energy Unresolved cited work
Reference 43
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 0cf3b272-2643-4e68-8d47-b9cbe9535dd7 · outbound
Thermodynamic potentials from a probabilistic view on the system-environment interaction energy Strasberg and M
Reference 44
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation c4d7c948-8df7-4eba-81a1-94b93312b040 · outbound
Thermodynamic potentials from a probabilistic view on the system-environment interaction energy Xing and M
Reference 45
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 270b4427-cdad-4de5-a77b-54b7bba7c02e · outbound
Thermodynamic potentials from a probabilistic view on the system-environment interaction energy Colla, F
Reference 46
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation f4ab0b22-76c2-41ba-91f2-430ea4643ee4 · outbound
Thermodynamic potentials from a probabilistic view on the system-environment interaction energy Mondal, S
Reference 47
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 58041e53-df9f-4d32-aa12-c6012e196dba · outbound
Thermodynamic potentials from a probabilistic view on the system-environment interaction energy Unresolved cited work
Reference 48
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 0a75af62-0ba5-41a4-bcdd-59a2a478c6c4 · outbound
Thermodynamic potentials from a probabilistic view on the system-environment interaction energy Unresolved cited work
Reference 49
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 3c95c682-1c6b-43d5-b240-f29d64590b99 · outbound
Thermodynamic potentials from a probabilistic view on the system-environment interaction energy Unresolved cited work
Reference 50
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 57150103-36e3-4541-a2a2-4ebbb5e989ed · outbound
Thermodynamic potentials from a probabilistic view on the system-environment interaction energy Rahbar and C
Reference 51
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation ba95ff9c-ddd4-4daa-906c-ed3637a5666c · outbound
Thermodynamic potentials from a probabilistic view on the system-environment interaction energy Unresolved cited work
Reference 52
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation b00589dc-0ebe-4d9d-b075-0550dd728982 · outbound
Thermodynamic potentials from a probabilistic view on the system-environment interaction energy Zhang, The application of the Gibbs-Bogoliubov- Feynman inequality in mean field calculations for Markov random fields, IEEE Trans
Reference 53
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 76a055eb-be21-49f0-bb37-a6798fcefdb5 · outbound
Thermodynamic potentials from a probabilistic view on the system-environment interaction energy Faussurier and M
Reference 54
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 780899bf-5ed9-4792-b4fe-9ff939d1c68e · outbound
Thermodynamic potentials from a probabilistic view on the system-environment interaction energy Unresolved cited work
Reference 55
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 3be274a8-3c15-463e-901e-fefe4390fccf · outbound
Thermodynamic potentials from a probabilistic view on the system-environment interaction energy Unresolved cited work
Reference 56
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 45665628-f212-4415-a4ca-d4463f34669e · outbound
Thermodynamic potentials from a probabilistic view on the system-environment interaction energy Unresolved cited work
Reference 57
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 4d1b34cc-2334-4b15-bc71-e1f214dac713 · outbound
Thermodynamic potentials from a probabilistic view on the system-environment interaction energy Delle Site, G
Reference 58
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 34b78d48-851b-4761-87e6-5c616195f9f8 · outbound
Thermodynamic potentials from a probabilistic view on the system-environment interaction energy H¨ older, Ueber einen Mittelwerthssatz, Nachrichten von der K¨ onigl
Reference 59
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation cdafe8a7-13a1-4b99-85e5-8b3e7d5e89c5 · outbound
Thermodynamic potentials from a probabilistic view on the system-environment interaction energy Nishiyama and I
Reference 60
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 2e759f8f-bb5d-4188-ae91-f9217138a702 · outbound
Thermodynamic potentials from a probabilistic view on the system-environment interaction energy Huang and W.-M
Reference 61
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation f065b1fa-a818-40a3-85ee-4e8ea2d5f0a4 · outbound
Thermodynamic potentials from a probabilistic view on the system-environment interaction energy Naleem, E
Reference 62
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 947c38da-179d-4b06-b955-de596cb229ec · outbound
Thermodynamic potentials from a probabilistic view on the system-environment interaction energy Park and K
Reference 63
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 9fe7822d-3d00-4efd-855b-e03d884eb85a · outbound
Thermodynamic potentials from a probabilistic view on the system-environment interaction energy Unresolved cited work
Reference 64
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation aa61aa0f-21dd-4cd7-8045-2fa83752a072 · outbound
Thermodynamic potentials from a probabilistic view on the system-environment interaction energy Gupta, C
Reference 65
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 2a544603-4c9a-49e4-a87b-4860d735f868 · outbound
Thermodynamic potentials from a probabilistic view on the system-environment interaction energy Jarzynski, Nonequilibrium equality for free energy dif- ferences, Phys
Reference 66
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 3fb36537-44ad-41bc-8357-455c4b5e0de5 · outbound
Thermodynamic potentials from a probabilistic view on the system-environment interaction energy Cohen and D
Reference 67
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 59b4c495-7cd5-43ed-89a1-8cee887f407d · outbound
Thermodynamic potentials from a probabilistic view on the system-environment interaction energy Collin, F
Reference 68
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 0bccd805-3c17-474a-b2e6-ba4b9b83d8d7 · outbound
Thermodynamic potentials from a probabilistic view on the system-environment interaction energy An, J.-N
Reference 69
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 2c007f25-fde5-4cf6-a7a5-db168479c9e9 · outbound
Thermodynamic potentials from a probabilistic view on the system-environment interaction energy Unresolved cited work
Reference 70
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 5fe5ab30-3f75-4c45-ac8f-bc75ffac0911 · outbound
Thermodynamic potentials from a probabilistic view on the system-environment interaction energy Jarzynski, Nonequilibrium work theorem for a sys- tem strongly coupled to a thermal environment, J
Reference 71
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 8980a4b2-e3d0-445b-b4f9-4c1656cd0a04 · outbound
Thermodynamic potentials from a probabilistic view on the system-environment interaction energy Jarzynski, Equalities and inequalities: Irreversibili ty and the second law of thermodynamics at the nanoscale, in Time: Poincar´ e Seminar 2010 (Springer, 2012) pp
Reference 72
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 3ed4d2bd-40db-48e3-9bc8-ec2998408ba8 · inbound
Exact and variational identities for free energy differences in strongly coupled open systems Thermodynamic potentials from a probabilistic view on the system-environment interaction energy
Reference 52
Source-reported events for the cited work
Unavailable: canonical work link unavailable.