Thermodynamics of quantum informational systems - Hamiltonian description

TL;DR

This paper rigorously derives the formula for work extraction from a quantum system and heat bath using Hamiltonian dynamics, confirming the thermodynamic limits and linking quantum correlations to work.

Contribution

It provides a Hamiltonian-based proof of work extraction limits from quantum systems, extending previous heuristic arguments and connecting to quantum correlations.

Findings

Proves the work extraction formula within Hamiltonian framework.

Derives Landauer principle from the second law in this model.

Establishes a physical scenario for extracting work from quantum correlations.

Abstract

It is often claimed, that from a quantum system of d levels, and entropy S and heat bath of temperature T one can draw kT(ln d -S) amount of work. However, the usual arguments based on Szilard engine are not fully rigorous. Here we prove the formula within Hamiltonian description of drawing work from a quantum system and a heat bath, at a cost of entropy of the system. We base on the derivation of thermodynamical laws and quantities in [R. Alicki, J. Phys. A, 12, L103 (1979)] within a weak coupling limit. Our result provides fully physical scenario for extracting thermodynamical work from quantum correlations [J. Oppenheim et al. Phys. Rev. Lett. 89, 180402 (2002)]. We also derive Landauer principle as a consquence of second law within the considered model.