Quantum heat-up operation and violation of the second law of thermodynamics

TL;DR

This paper introduces a quantum heat-up operation that models irreversible thermalization, revealing potential violations of the second law of thermodynamics in quantum systems.

Contribution

It explicitly constructs a quantum heat-up operator and analyzes its implications, including entropy changes and potential second law violations.

Findings

Repeated application leads to high-temperature equilibrium

Entropy can decrease, violating the second law

Operation induces irreversible thermalization in quantum states

Abstract

Toward the formulation of the operational approach to quantum thermodynamics, the heat-up operator is explicitly constructed. This quantum operation generates for a generic system an irreversible transformation from a pure ground state at zero temperature to a state at finite temperature. The fixed point analysis shows that repeated applications of the operation map from an arbitrary state to the completely random state realized in the high-temperature limit. The change of the von Neumann entropy is evaluated for a simple bipartite spin-1/2 system. It is shown that remarkably, the second law of thermodynamics may be violated along processes generated by the present quantum operation.