Operational typicality of the nonequilibrium states: a thermodynamic lower bound of the deviation from equilibrium

TL;DR

This paper derives a universal thermodynamic lower bound on the deviation from equilibrium for nonequilibrium states, linking external forcing and entropy production to the distance from canonical states in high-dimensional quantum systems.

Contribution

It introduces a universal thermodynamic expression for the lower bound of deviation from equilibrium based on external forcing and entropy production.

Findings

Lower bound expressed by external forcing and entropy production.

Deviation from equilibrium quantified by Hilbert-Schmidt distance.

Applicable to high-dimensional quantum systems under external forces.

Abstract

The typicality of the canonical state shows that majority of the states are indistinguishable from equilibrium, and thus the nonequilibrium states are exceptionally rare in the extremely high-dimensional Hilbert space. On the contrary, we can easily apply an external force acting on the system, and then the actual density matrix quantitatively deviates from the canonical state specified by the system Hamiltonian at each instance. To express how the external forcing amounts to the deviation from equilibrium, we give a universal thermodynamic expression of the lower bound of Hilbert-Schmidt distance between the actual nonequilibrium and corresponding canonical states. The lower bound is expressed only by the amount of forcing and its consequent entropy production rate.