Thermodynamic uncertainty relations under arbitrary control protocols

TL;DR

This paper derives universal thermodynamic uncertainty relations for Langevin systems under arbitrary control protocols, linking observable fluctuations to entropy production and kinetic terms, applicable to diverse systems.

Contribution

It introduces a general framework for thermodynamic uncertainty relations under arbitrary time-dependent protocols using information-theoretic methods.

Findings

Derived bounds for both current and noncurrent observables.

Applicable to overdamped and underdamped Langevin systems.

Validated with examples: Brownian particle, gyrator, heat engine.

Abstract

Thermodynamic uncertainty relations quantifying a trade-off between current fluctuation and entropy production have been found in various stochastic systems. Herein, we study the thermodynamic uncertainty relations for Langevin systems driven by an external control protocol. Using information-theoretic techniques, we derive the uncertainty relations for arbitrary observables satisfying a scaling condition in both overdamped and underdamped regimes. We prove that the observable fluctuation is constrained by both entropy production and a kinetic term. The derived bounds are applicable to both current and noncurrent observables, and hold for arbitrary time-dependent protocols, thus, providing a wide range of applicability. We illustrate our universal bounds with the help of three systems: a dragged Brownian particle, a Brownian gyrator, and a stochastic underdamped heat engine.