A Novel Dissipation Property of the Master Equation

TL;DR

This paper establishes new nonzero lower bounds for entropy-related quantities in master equations, revealing stronger dissipative properties in nonequilibrium processes and providing insights into their long-term behavior.

Contribution

It introduces novel nonzero lower bounds for entropy and dissipation rates in master equations, extending to Tsallis statistics and offering new constraints on thermodynamic relations.

Findings

Nonzero lower bounds for relative entropy and dissipation rates.

Stronger dissipative properties than the second law of thermodynamics.

Implications for the long-time behavior of master equations.

Abstract

Recent studies have shown that the entropy production rate for the master equation consists of two nonnegative terms: the adiabatic and non-adiabatic parts, where the non-adiabatic part is also known as the dissipation rate of a Boltzmann-Shannon relative entropy. In this paper, we provide some nonzero lower bounds for the relative entropy, the entropy production rate, and its adiabatic and non-adiabatic parts. These nonzero lower bounds not only reveal some novel dissipative properties for general nonequilibrium processes which are much stronger than the second law of thermodynamics, but also impose some new constraints on thermodynamic constitutive relations. Moreover, we also provide a mathematical application of these nonzero lower bounds by studying the long-time behavior of the master equation. Extensions to the Tsallis statistics are also discussed, including the nonzero lower bounds for the Tsallis-type relative entropy and its dissipation rate.