Quantum Brownian motion and its conflict with the second law

TL;DR

This paper demonstrates that quantum Brownian motion at low temperatures can violate classical thermodynamic laws, showing non-Gibbsian states and the possibility of work extraction from a quantum bath.

Contribution

It reveals how quantum entanglement leads to violations of the second law in quantum Brownian motion, challenging classical thermodynamic assumptions.

Findings

Clausius inequality can be violated at low temperatures.

Negative entropy production occurs during relaxation after potential changes.

Work can be cyclically extracted from the quantum bath, suggesting a quantum perpetuum mobile.

Abstract

The Brownian motion of a harmonically bound quantum particle and coupled to a harmonic quantum bath is exactly solvable. At low enough temperatures the stationary state is non-Gibbsian due to an entanglement with the bath. This happens when a cloud of bath modes around the particle is formed. Equilibrium thermodynamics for particle plus bath together, does not imply standard thermodynamics for the particle itself at low T. Various formulations of the second law are then invalid. First, the Clausius inequality can be violated. Second, when the width of the confining potential is suddenly changed, there occurs a relaxation to equilibrium during which the rate of entropy production is partly negative. Third, for non-adiabatic changes of system parameters the rate of energy dissipation can be negative, and, out of equilibrium, cyclic processes are possible which extract work from the bath. Conditions are put forward under which perpetuum mobile of the second kind, having several work extraction cycles, enter the realm of condensed matter physics.