Work extraction and thermodynamics for individual quantum systems

TL;DR

This paper develops a framework extending thermodynamics to individual quantum systems, demonstrating the second law, optimal work extraction, and the construction of a quantum Carnot engine.

Contribution

It introduces a new approach to quantum thermodynamics that applies to single systems, including non-equilibrium states, and establishes protocols for optimal work extraction.

Findings

Second law holds for individual quantum systems

Optimal work equals change in free energy

Quantum Carnot engine can be constructed

Abstract

Thermodynamics is traditionally concerned with systems comprised of a large number of particles. Here we present a framework for extending thermodynamics to individual quantum systems, including explicitly a thermal bath and work-storage device (essentially a `weight' that can be raised or lowered). We prove that the second law of thermodynamics holds in our framework, and give a simple protocol to extract the optimal amount of work from the system, equal to its change in free energy. Our results apply to any quantum system in an arbitrary initial state, in particular including non-equilibrium situations. The optimal protocol is essentially reversible, similar to classical Carnot cycles, and indeed, we show that it can be used it to construct a quantum Carnot engine.