Thermodynamic uncertainty relations from exchange fluctuation theorems

TL;DR

This paper derives the tightest matrix-valued thermodynamic uncertainty relation from exchange fluctuation theorems, applicable to quantum and classical systems, providing bounds on fluctuations and correlations in nanoscale thermodynamic processes.

Contribution

It introduces the most comprehensive matrix-valued TUR derived from exchange fluctuation theorems, applicable to complex non-Markovian and non-stationary systems, including quantum and classical regimes.

Findings

Derived the tightest matrix-valued TUR from exchange fluctuation theorems.

Applicable to quantum and classical systems with non-Markovian dynamics.

Provided bounds on heat-work correlations in a two-qubit Otto cycle.

Abstract

Thermodynamic uncertainty relations (TURs) place strict bounds on the fluctuations of thermodynamic quantities in terms of the associated entropy production. In this work we identify the tightest (and saturable) matrix-valued TUR that can be derived from the exchange fluctuation theorems describing the statistics of heat and particle flow between multiple systems. Our result holds for both quantum and classical systems, undergoing general non-Markovian and non-stationary processes. Moreover, it provides bounds not only for the variances, but also for the correlations between thermodynamic quantities. To demonstrate the relevance of TURs to the design of nanoscale machines, we consider the operation of a two-qubit SWAP engine undergoing an Otto cycle and show how our results can be used to place strict bounds on the correlations between heat and work.