Fundamental work cost of quantum processes

TL;DR

This paper establishes a fundamental lower bound on the work cost of quantum processes using a new information measure called coherent relative entropy, extending thermodynamics to quantum and nanoscale systems.

Contribution

It introduces the coherent relative entropy as a universal measure for quantum thermodynamic processes, applicable at any scale and with arbitrary Hamiltonians.

Findings

Derives a lower bound on work cost for quantum processes.

Shows how classical thermodynamics laws emerge in the macroscopic limit.

Provides a criterion for the applicability of thermodynamic laws at different scales.

Abstract

Information-theoretic approaches provide a promising avenue for extending the laws of thermodynamics to the nanoscale. Here, we provide a general fundamental lower limit, valid for systems with an arbitrary Hamiltonian and in contact with any thermodynamic bath, on the work cost for the implementation of any logical process. This limit is given by a new information measure---the coherent relative entropy---which accounts for the Gibbs weight of each microstate. The coherent relative entropy enjoys a collection of natural properties justifying its interpretation as a measure of information, and can be understood as a generalization of a quantum relative entropy difference. As an application, we show that the standard first and second laws of thermodynamics emerge from our microscopic picture in the macroscopic limit. Finally, our results have an impact on understanding the role of the observer in thermodynamics: Our approach may be applied at any level of knowledge---for instance at the microscopic, mesoscopic or macroscopic scales---thus providing a formulation of thermodynamics that is inherently relative to the observer. We obtain a precise criterion for when the laws of thermodynamics can be applied, thus making a step forward in determining the exact extent of the universality of thermodynamics and enabling a systematic treatment of Maxwell-demon-like situations.