Student or educator? Sign up with your school email and get 6 months of Pro free.
CoChat
Sign Up
Cited by 337

The DOI matches its Crossref record; 68 of the 68 references it cites were found in a registry or an index.

Three faces of the second law. I. Master equation formulation

Open access
Esposito, Massimiliano, Van den Broeck, Christian·2010·Physical Review E
DOI 10.1103/physreve.82.011143
Open this paper in CoChat — free account

Abstract

We propose a formulation of stochastic thermodynamics for systems subjected to nonequilibrium constraints (i.e. broken detailed balance at steady state) and furthermore driven by external time-dependent forces. A splitting of the second law occurs in this description leading to three second-law-like relations. The general results are illustrated on specific solvable models. The present paper uses a master equation based approach.

Overview

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Integrity signals

Registry

Crossref · 10.1103/physreve.82.011143

Cites

68 of 68 references verified0 citation errors · 0 not checkable

Statistics

Verification

Claims the paper makes

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

The self-check needs the paper’s full text.

Citations

Cites

Show all 68 references

Cited by

See all 337

Metadata

Authors
Esposito, M., & Van den Broeck, C.
Venue
Physical Review E
Publisher
American Physical Society (APS)
Published
2010-07-30
Volume
82
Issue
1
Pages
011143-011143
ISSN
  • 1539-3755 (ISSN-L)
  • 1550-2376
DOI
10.1103/physreve.82.011143
OpenAlex
W2091965271
Cited by
337
References
68
FWCI
12.94
Type
journal article
Language
en
Open access
bronze

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review

How to cite

Cite CoChat for the checks on this page, and the paper for its own findings.

This page
CoChat. (2026). Citation check: Three faces of the second law. I. Master equation formulation. https://app.cochat.ai/papers/10.1103/physreve.82.011143
The paper
Esposito, M., & Van den Broeck, C. (2010). Three faces of the second law. I. Master equation formulation. Physical Review E. https://doi.org/10.1103/physreve.82.011143

Data sources

Bibliographic data: Semantic Scholar, OpenAlex, Crossref.

Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).

Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.