Quantum Brownian motion and the Third Law of thermodynamics

TL;DR

This paper explores how quantum dissipation influences the thermodynamic behavior of small quantum systems, demonstrating that it enforces the Third Law by causing specific heat to vanish at low temperatures.

Contribution

It shows that finite quantum dissipation restores the Third Law in quantum systems, altering low-temperature specific heat behavior in a novel way.

Findings

Finite damping changes exponential suppression to power-law in quantum oscillators.

Quantum dissipation causes the specific heat of a free quantum Brownian particle to vanish proportionally to temperature.

Thermodynamic functions depend on dissipation strength and the chosen definition prescription.

Abstract

The quantum thermodynamic behavior of small systems is investigated in presence of finite quantum dissipation. We consider the archetype cases of a damped harmonic oscillator and a free quantum Brownian particle. A main finding is that quantum dissipation helps to ensure the validity of the Third Law. For the quantum oscillator, finite damping replaces the zero-coupling result of an exponential suppression of the specific heat at low temperatures by a power-law behavior. Rather intriguing is the behavior of the free quantum Brownian particle. In this case, quantum dissipation is able to restore the Third Law: Instead of being constant down to zero temperature, the specific heat now vanishes proportional to temperature with an amplitude that is inversely proportional to the ohmic dissipation strength. A distinct subtlety of finite quantum dissipation is the result that the various thermodynamic functions of the sub-system do not only depend on the dissipation strength but depend as well on the prescription employed in their definition.