Imperfect Thermalizations Allow for Optimal Thermodynamic Processes

TL;DR

This paper demonstrates that near-optimal thermodynamic processes can be achieved despite finite-time, uncontrolled partial thermalizations, by increasing the number of steps, thus showing robustness to practical imperfections.

Contribution

It introduces a framework for achieving optimal thermodynamic processes with partial thermalizations, expanding the understanding of robustness in quantum thermodynamics.

Findings

Optimal processes are achievable with partial thermalizations by increasing steps.

Tradeoff between the degree of thermalization and number of operations is characterized.

Results are applicable in collision models and controlled Hamiltonian systems.

Abstract

Optimal (reversible) processes in thermodynamics can be modelled as step-by-step processes, where the system is successively thermalized with respect to different Hamiltonians by an external thermal bath. However, in practice interactions between system and thermal bath will take finite time, and precise control of their interaction is usually out of reach. Motivated by this observation, we consider finite-time and uncontrolled operations between system and bath, which result in thermalizations that are only partial in each step. We show that optimal processes can still be achieved for any non-trivial partial thermalizations at the price of increasing the number of operations, and characterise the corresponding tradeoff. We focus on work extraction protocols and show our results in two different frameworks: A collision model and a model where the Hamiltonian of the working system is controlled over time and the system can be brought into contact with a heat bath. Our results show that optimal processes are robust to noise and imperfections in small quantum systems, and can be achieved by a large set of interactions between system and bath.