Quantum dissipative Brownian motion and the Casimir effect

TL;DR

This paper investigates the thermodynamics of dissipative quantum particles and their analogy to the Casimir effect, revealing nonmonotonic entropy behavior and noncontinuous limits related to dissipation and conductivity.

Contribution

It establishes a novel analogy between dissipative quantum particles and electromagnetic Casimir effects, highlighting quantum effects at low temperatures and noncontinuous limits.

Findings

Entropy can be nonmonotonic with temperature.

Quantum effects ensure correct low-temperature behavior.

Limits of dissipation and conductivity are noncontinuous.

Abstract

We explore an analogy between the thermodynamics of a free dissipative quantum particle and that of an electromagnetic field between two mirrors of finite conductivity. While a free particle isolated from its environment will effectively be in the high-temperature limit for any nonvanishing temperature, a finite coupling to the environment leads to quantum effects ensuring the correct low-temperature behavior. Even then, it is found that under appropriate circumstances the entropy can be a nonmonotonic function of the temperature. Such a scenario with its specific dependence on the ratio of temperature and damping constant also appears for the transverse electric mode in the Casimir effect. The limits of vanishing dissipation for the quantum particle and of infinite conductivity of the mirrors in the Casimir effect both turn out to be noncontinuous.