Unified thermodynamic uncertainty relations in linear response

TL;DR

This paper derives unified thermodynamic uncertainty relations within linear response theory, extending their applicability to systems lacking time reversal symmetry and connecting them to fluctuation theorems beyond linear response.

Contribution

It introduces a unified framework for TURs using linear response theory, applicable to a broader class of nonequilibrium systems including driven and quantum systems.

Findings

Bounds on uncertainty depend on dissipation and asymmetry parameters.

The approach applies to ballistic transport and periodically driven systems.

Connections between TURs and fluctuation theorems are established beyond linear response.

Abstract

Thermodynamic uncertainty relations (TURs) are recently established relations between the relative uncertainty of time-integrated currents and entropy production in nonequilibrium systems. For small perturbations away from equilibrium, linear response (LR) theory provides the natural framework to study generic nonequilibrium processes. Here we use LR to derive TURs in a straightforward and unified way. Our approach allows us to generalize TURs to systems without local time reversal symmetry, including, for example, ballistic transport, and periodically driven classical and quantum systems. We find that for broken time reversal, the bounds on the relative uncertainty are controlled both by dissipation and by a parameter encoding the asymmetry of the Onsager matrix. We illustrate our results with an example from mesoscopic physics. We also extend our approach beyond linear response: for Markovian dynamics it reveals a connection between the TUR and current fluctuation theorems.