A Universal Trade-off Relation Between Dissipation and Relaxation Timescale and An Inverse Speed Limit in Thermal Relaxation

Ruicheng Bao, Zhonghuai Hou

Published 2023-03-11Version 1

A general lower bound for the entropy production rate based on the Kullback-Leibler divergence and the Logarithmic-Sobolev constant characterizing the time-scale of relaxation is established, which can be regarded as an enhanced second law of thermodynamics. As a crucial application, we find a universal trade-off relation between the dissipation rate and relaxation time-scale in thermal relaxation processes. Importantly, we show that a thermodynamic upper bound of the relaxation time between two given states follows directly from the trade-off relation, serving as an inverse speed limit taking effect in the whole time region. Our results unveil some hidden universal behaviors of thermal relaxation processes. Moreover, they can be generalized to open quantum systems.