Universal trade-off between irreversibility and intrinsic timescale in thermal relaxation with applications to thermodynamic inference

TL;DR

This paper derives a universal lower bound on entropy production rate linked to relaxation timescales, revealing a fundamental trade-off in thermal relaxation that applies to classical and quantum systems, with implications for thermodynamic inference.

Contribution

It introduces a universal trade-off relation between dissipation and relaxation timescale, extending to quantum and non-Markovian systems, and provides bounds useful for thermodynamic inference.

Findings

Established a lower bound for entropy production rate based on divergence and relaxation timescale.

Discovered a universal trade-off relation between dissipation rate and relaxation time.

Derived a quantum version of the relaxation time bound, tighter than the classical one.

Abstract

We establish a general lower bound for the entropy production rate (EPR) based on the Kullback-Leibler divergence and the Logarithmic-Sobolev constant that characterizes the time-scale of relaxation. This bound can be considered as an enhanced second law of thermodynamics. When applied to thermal relaxation, it reveals a universal trade-off relation between the dissipation rate and the intrinsic relaxation timescale. From this relation, a thermodynamic upper bound on the relaxation time between two given states emerges, acting as an inverse speed limit over the entire time region. We also obtain a quantum version of this upper bound, which is always tighter than its classical counterpart, incorporating an additional term due to decoherence. Remarkably, we further demonstrate that the trade-off relation remains valid for any generally non-Markovian coarse-grained relaxation dynamics, highlighting its significant applications in thermodynamic inference. This trade-off relation is a new tool in inferring EPRs in molecular dynamics simulations and practical experiments.