Universal Relation between Entropy and Kinetics

Benjamin Sorkin, Haim Diamant, Gil Ariel

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


Relating thermodynamic and kinetic properties is a conceptual challenge with many practical benefits. Here, based on first principles, we derive a rigorous inequality relating the entropy and the dynamic propagator of particle configurations. It is universal and applicable to steady states arbitrarily far from thermodynamic equilibrium. Applying the general relation to diffusive dynamics yields a relation between the entropy and the (normal or anomalous) diffusion coefficient. The relation can be used to obtain useful bounds for the late-time diffusion coefficient from the calculated steady-state entropy or, conversely, to estimate the entropy based on measured diffusion coefficients. We demonstrate the validity and usefulness of the relation through several examples and discuss its broad range of applications, in particular, for systems far from equilibrium.

Original languageEnglish
Article number147101
JournalPhysical Review Letters
Issue number14
StatePublished - 6 Oct 2023

Bibliographical note

Publisher Copyright:
© 2023 American Physical Society.


We thank David Dean, Ofek Lauber Bonomo, Oren Raz, Shlomi Reuveni, and Tom Witten for illuminating discussions. The research has been supported by the Israel Science Foundation (Grant No. 986/18).

FundersFunder number
Israel Science Foundation986/18


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