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.
Highlights
A central task in finite-time thermodynamics is to design protocols that maximise the extracted work while minimising the dissipation during the process
The geometry of quantum equilibrium Gibbs states has been characterised in [16,17,18,19,20]; the resulting metric does not take into account dynamical features of the dissipation, which are of crucial importance in finitetime protocols
Kubo linear-response theory allows for describing dissipation near equilibrium [23,24,25], which in turn allows for defining a notion of thermodynamic metric [24, 26]
Summary
A central task in finite-time thermodynamics is to design protocols that maximise the extracted work while minimising the dissipation during the process. In the slow driving regime, a powerful approach consists in equipping the space of thermodynamic states with a metric whose geodesics correspond to minimally dissipative processes This geometrical construction was first developed in the 80s for macroscopic endoreversible thermodynamics in a series of seminal papers [1,2,3,4,5,6,7,8], and more recently it was extended to the microscopic regime [9,10,11,12], leading to several applications in, e.g., molecular motors [13] and small-scale information processing [14, 15]. This geometrical approach is used to find minimally dissipating protocols of a slowly driven Ising chain in a transverse field, and of a qubit in contact with a bosonic bath with different spectral densities
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