Generalized uncertainty relation between thermodynamic variables in quantum thermodynamics

TL;DR

This paper derives a generalized thermodynamic uncertainty relation applicable across all coupling regimes in quantum thermodynamics, highlighting how quantum fluctuations influence the precision of thermodynamic variables.

Contribution

It introduces a unified uncertainty relation for thermodynamic variables valid at all coupling strengths using quantum estimation theory and the generalized Gibbs ensemble.

Findings

Lower bound on uncertainty increases with quantum fluctuations.

Uncertainty relations are consistent across different ensembles.

Method demonstrates versatility in various quantum thermodynamic scenarios.

Abstract

Macroscopic thermodynamics, via the weak coupling approximation, assumes that the equi?librium properties of a system are not affected by interactions with its environment. However, this assumption may not hold for quantum systems, where the strength of interaction between the system and the environment may become non-negligible in a strong coupling regime. In such a regime, the equilibrium properties of the system depend on the interaction energy and the system state is no longer of the Gibbs form. Regarding such interactions, using tools from the quantum estimation theory, we derive the thermodynamic uncertainty relation between intensive and exten?sive variables valid at all coupling regimes through the generalized Gibbs ensemble (GGE). Where we demonstrate the lower bound on the uncertainty of intensive variables increases in presence of quantum fluctuations. Also, we calculate the general uncertainty relations for several ensembles to corroborate the literature results, thus showing the versatility of our method.