Entropy Production by Underdamped Langevin Dynamics

TL;DR

This paper introduces a modified thermodynamic uncertainty relation for underdamped Langevin systems, enabling entropy production estimation with limited dynamic knowledge, validated through numerical examples.

Contribution

It develops a new TUR-based method to estimate entropy production in underdamped Langevin dynamics using only limited system parameters.

Findings

The method accurately estimates entropy production in various underdamped systems.

It requires only damping-coefficient to mass ratio and diffusion constant, simplifying experimental access.

The approach applies to both steady-state and nonsteady-state scenarios.

Abstract

Entropy production (EP) is a central quantity in nonequilibrium physics as it monitors energy dissipation, irreversibility, and free energy differences during thermodynamic transformations. Estimating EP, however, is challenging both theoretically and experimentally due to limited access to the system dynamics. For overdamped Langevin dynamics and Markov jump processes it was recently proposed that, from thermodynamic uncertainty relations (TUR), short-time cumulant currents can be used to estimate EP without knowledge of the dynamics. Yet, estimation of EP in underdamped Langevin systems remains an active challenge. To address this, we derive a modified TUR that relates the statistics of two specific novel currents -- one cumulant current and one stochastic current -- to a system's EP. These two distinct but related currents are used to constrain EP in the modified TUR. One highlight is that there always exists a family of currents such that the uncertainty relations saturate, even for long-time averages and in nonsteady-state scenarios. Another is that our method only requires limited knowledge of the dynamics -- specifically, the damping-coefficient to mass ratio and the diffusion constant. This uncertainty relation allows estimating EP for both overdamped and underdamped Langevin dynamics. We validate the method numerically, through applications to several underdamped systems, to underscore the flexibility in obtaining EP in nonequilibrium Langevin systems.