The second law of thermodynamics in the quantum Brownian oscillator at an arbitrary temperature

TL;DR

This paper proves that in quantum systems, the work required to couple a linear oscillator to a bath always exceeds or equals the work obtainable upon decoupling, confirming the second law of thermodynamics at any temperature.

Contribution

It analytically demonstrates that the quantum second law holds for a linear oscillator coupled to a bath at any temperature, extending previous zero-temperature results.

Findings

Work needed to couple the oscillator is never less than the work obtainable upon decoupling.

The quantum second law is valid at arbitrary temperatures.

Classical behavior is recovered in the high-temperature limit.

Abstract

In the classical limit no work is needed to couple a system to a bath with sufficiently weak coupling strength (or with arbitrarily finite coupling strength for a linear system) at the same temperature. In the quantum domain this may be expected to change due to system-bath entanglement. Here we show analytically that the work needed to couple a single linear oscillator with finite strength to a bath cannot be less than the work obtainable from the oscillator when it decouples from the bath. Therefore, the quantum second law holds for an arbitrary temperature. This is a generalization of the previous results for zero temperature [1,2]; in the high temperature limit we recover the classical behavior.