Universal Relation between Entropy and Kinetics

TL;DR

This paper derives a universal inequality linking entropy and kinetic properties of particle systems, applicable even far from equilibrium, enabling bounds and estimates for diffusion coefficients and entropy based on measurable quantities.

Contribution

It introduces a rigorous, universal relation between entropy and the dynamic propagator, applicable to steady states far from equilibrium, bridging thermodynamics and kinetics.

Findings

Derived a universal inequality relating entropy and the propagator.

Validated the relation through multiple examples.

Provided bounds for diffusion coefficients from entropy measurements.

Abstract

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 thermal 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.