Measuring Nonequilibrium Temperature of Forced Oscillators

TL;DR

This paper investigates how temperature can be defined and measured in nonequilibrium systems using a forced harmonic oscillator, revealing that effective temperatures depend on the measurement interaction.

Contribution

It introduces a concrete thermometer model to test nonequilibrium temperatures and shows the dependence of measured temperature on system-thermometer interaction.

Findings

Measured temperature varies with interaction form

Effective temperatures for position and momentum differ

Zeroth law does not straightforwardly extend to nonequilibrium

Abstract

The meaning of temperature in nonequilibrium thermodynamics is considered by using a forced harmonic oscillator in a heat bath, where we have two effective temperatures for the position and the momentum, respectively. We invent a concrete model of a thermometer to testify the validity of these different temperatures from the operational point of view. It is found that the measured temperature depends on a specific form of interaction between the system and a thermometer, which means the zeroth law of thermodynamics cannot be immediately extended to nonequilibrium cases.