Gauge field and geometric control of quantum-thermodynamic engine

TL;DR

This paper introduces a gauge-theoretic framework for analyzing work extraction in quantum thermodynamic systems driven by slowly changing parameters, linking geometric phases to nonequilibrium states and power output.

Contribution

It develops a novel gauge field formalism for quantum thermodynamics, connecting geometric control with work extraction and power optimization in cyclic processes.

Findings

Gauge field vanishes in equilibrium states

Nonvanishing field indicates nonequilibrium quasi-stationary states

Maximum power discussed for finite-time cyclic processes

Abstract

The problem of extracting the work from a quantum-thermodynamic system driven by slowly varying external parameters is discussed. It is shown that there naturally emerges a gauge-theoretic structure. The field strength identically vanishes if the system is in an equilibrium state, i.e., the nonvanishing field strength implies that the system is in a nonequilibrium quasi-stationary state. The work done through a cyclic process in the parameter space is given in terms of the flux of the field. This general formalism is applied to an example of a single spin in a varying magnetic field, and the maximum power output is discussed in a given finite-time cyclic process.