Thermodynamic length and work optimisation for Gaussian quantum states

TL;DR

This paper investigates thermodynamic lengths in Gaussian quantum states to optimize work and fluctuations, deriving general formulas and computing optimal protocols for driven systems with multiple controls.

Contribution

It introduces general expressions for two quantum thermodynamic lengths and applies them to find optimal protocols in Gaussian quantum systems.

Findings

Derived formulas for thermodynamic lengths in Gaussian states.

Computed optimal protocols for driven Gaussian systems.

Analyzed the trade-off between work and fluctuations in quantum thermodynamics.

Abstract

Constructing optimal thermodynamic processes in quantum systems relies on managing the balance between the average excess work and its stochastic fluctuations. Recently it has been shown that two different quantum generalisations of thermodynamic length can be utilised to determine protocols with either minimal excess work or minimal work variance. These lengths measure the distance between points on a manifold of control parameters, and optimal protocols are achieved by following the relevant geodesic paths given some fixed boundary conditions. Here we explore this problem in the context of Gaussian quantum states that are weakly coupled to an environment and derive general expressions for these two forms of thermodynamic length. We then use this to compute optimal thermodynamic protocols for various examples of externally driven Gaussian systems with multiple control parameters.