Thermodynamic length in open quantum systems

TL;DR

This paper extends the concept of thermodynamic length to open quantum systems by deriving a metric from Lindblad equations, enabling analysis of dissipation in quantum thermodynamic processes.

Contribution

It introduces a method to derive the thermodynamic metric for open quantum systems from Lindblad dynamics, generalizing previous equilibrium-based approaches.

Findings

Derived the thermodynamic metric for Lindblad systems.

Applied the framework to an Ising chain and a two-level system.

Showed how dissipation relates to geodesic trajectories in quantum state space.

Abstract

The dissipation generated during a quasistatic thermodynamic process can be characterised by introducing a metric on the space of Gibbs states, in such a way that minimally-dissipating protocols correspond to geodesic trajectories. Here, we show how to generalize this approach to open quantum systems by finding the thermodynamic metric associated to a given Lindblad master equation. The obtained metric can be understood as a perturbation over the background geometry of equilibrium Gibbs states, which is induced by the Kubo-Mori-Bogoliubov (KMB) inner product. We illustrate this construction on two paradigmatic examples: an Ising chain and a two-level system interacting with a bosonic bath with different spectral densities.