Lower bound of entropy production at short time scales for noise-driven stochastic systems

TL;DR

This paper investigates the lower bounds of entropy production at short time scales in noise-driven stochastic systems by analyzing trajectory divergences, revealing how local fluctuations differ from global behavior and depend on noise types.

Contribution

It introduces a method to measure the lower bound of entropy production at short time scales using Kullback-Leibler divergence, highlighting the significance of local fluctuations and noise types.

Findings

Short time scale entropy production bounds depend on noise type.

Local fluctuations reveal distinctions not visible at larger scales.

Analysis of trajectory divergence informs nonequilibrium dynamics.

Abstract

The second law of thermodynamics governs that nonequilibrium systems evolve towards states of higher entropy over time. However, it does not specify the rate of this evolution and the role of fluctuations that impact the system's dynamics. Entropy production quantifies how far a system is driven away from equilibrium and provides a measure of irreversibility. In stochastic systems, entropy production becomes essential for understanding the approach to nonequilibrium states. While macroscopic observations provide valuable insights, they often overlook the local behaviors of the system, governed by fluctuations. In this study, we focus on measuring the lower bound of entropy production at short time scales for generalized stochastic systems by calculating the Kullback-Leibler divergence (KLD) between the probability density functions of forward and backward trajectories. By analysing the entropy production across sliding time scales, we uncover patterns that reveal distinctions between local, small-scale dynamics and the global, macroscopic behavior, offering deeper insights into the system's departure from equilibrium. We also analysed the effects of switching to different types of noise or fluctuations and found that the observations at larger time scales provide no distinction between the different forms of noise while at short time scales, the distinction is significant.