Thermodynamic length for far from equilibrium quantum systems

TL;DR

This paper introduces a thermodynamic length based on the Bures angle for quantum systems driven far from equilibrium, providing a lower bound on entropy production applicable to arbitrary protocols.

Contribution

It derives a new thermodynamic length measure using the Bures angle, valid far from equilibrium, and applies it analytically to a driven harmonic oscillator.

Findings

Lower bound on entropy production in quantum systems.

Analytic expressions for driven harmonic oscillator.

Thermodynamic length applicable far from equilibrium.

Abstract

We consider a closed quantum system, initially at thermal equilibrium, driven by arbitrary external parameters. We derive a lower bound on the entropy production which we express in terms of the Bures angle between the nonequilibrium and the corresponding equilibrium state of the system. The Bures angle is an angle between mixed quantum states and defines a thermodynamic length valid arbitrarily far from equilibrium. As an illustration, we treat the case of a time-dependent harmonic oscillator for which we obtain analytic expressions for generic driving protocols.