Quantum thermodynamics of general quantum processes

TL;DR

This paper develops an operational framework for quantum thermodynamics applicable to general quantum processes, establishing a first law consistent with the second law and linking heat and entropy changes through majorisation.

Contribution

It introduces a new operational approach to quantum thermodynamics for open systems undergoing general quantum processes, deriving a first law and connecting heat and entropy via majorisation.

Findings

Heat is positive when input majorises output state.

Entropy change is positive under the same majorisation condition.

The framework ensures consistency with the second law of thermodynamics.

Abstract

Accurately describing work extraction from a quantum system is a central objective for the extension of thermodynamics to individual quantum systems. The concepts of work and heat are surprisingly subtle when generalizations are made to arbitrary quantum states. We formulate an operational thermodynamics suitable for application to an open quantum system undergoing quantum evolution under a general quantum process by which we mean a completely-positive and trace-preserving map. We derive an operational first law of thermodynamics for such processes and show consistency with the second law. We show that heat, from the first law, is positive when the input state of the map majorises the output state. Moreover, the change in entropy is also positive for the same majorisation condition. This makes a strong connection between the two operational laws of thermodynamics.