Geometric optimisation of quantum thermodynamic processes

TL;DR

This paper explores the use of differential geometry to optimize quantum thermodynamic processes, introducing a quantum thermodynamic length and bounds on entropy production, with principles for process optimization in linear response.

Contribution

It develops a geometric framework for quantum thermodynamics, including a quantum entropy production bound and optimization principles for finite-time processes.

Findings

Quantum thermodynamic length generalizes classical concepts.

A lower bound on entropy production in quantum systems is established.

Optimization strategies for quantum heat engines are proposed.

Abstract

Differential geometry offers a powerful framework for optimising and characterising finite-time thermodynamic processes, both classical and quantum. Here, we start by a pedagogical introduction to the notion of thermodynamic length. We review and connect different frameworks where it emerges in the quantum regime: adiabatically driven closed systems, time-dependent Lindblad master equations, and discrete processes. A geometric lower bound on entropy production in finitetime is then presented, which represents a quantum generalisation of the original classical bound. Following this, we review and develop some general principles for the optimisation of thermodynamic processes in the linear-response regime. These include constant speed of control variation according to the thermodynamic metric, absence of quantum coherence, and optimality of small cycles around the point of maximal ratio between heat capacity and relaxation time for Carnot engines.