Global passivity in microscopic thermodynamics

TL;DR

This paper introduces global passivity as a new framework to extend thermodynamic inequalities, like the Clausius inequality, to small quantum systems with initial correlations, providing practical bounds and detection methods for heat leaks and feedback.

Contribution

The authors develop the concept of global passivity, extending thermodynamic inequalities to correlated quantum systems and offering new bounds and detection tools beyond traditional Clausius inequality.

Findings

Global passivity recovers the Clausius inequality for uncorrelated environments.

It provides valid thermodynamic bounds even with strong initial correlations.

It can detect heat leaks and feedback operations that Clausius inequality misses.

Abstract

The main thread that links classical thermodynamics and the thermodynamics of small quantum systems is the celebrated Clausius inequality form of the second law. However, its application to small quantum systems suffers from two cardinal problems: (i) The Clausius inequality does not hold when the system and environment are initially correlated - a commonly encountered scenario in microscopic setups. (ii) In some other cases, the Clausius inequality does not provide any useful information (e.g. in dephasing scenarios). We address these deficiencies by developing the notion of global passivity and employing it as a tool for deriving thermodynamic inequalities on observables. For initially uncorrelated thermal environments the global passivity framework recovers the Clausius inequality. More generally, global passivity provides an extension of the Clausius inequality that holds even in the presences of strong initial system-environment correlations. Crucially, the present framework provides additional thermodynamic bounds on expectation values. To illustrate the role of the additional bounds we use them to detect unaccounted heat leaks and weak feedback operations ("Maxwell's demons") that the Clausius inequality cannot detect. In addition, it is shown that global passivity can put practical upper and lower bounds on the buildup of system-environment correlation for dephasing interactions. Our findings are highly relevant for experiments in various systems such as ion traps, superconducting circuits, atoms in optical cavities and more.