Minimal length scales for the existence of local temperature

TL;DR

This paper reviews a method to determine the minimal spatial scales where local temperature can be defined, based on analyzing equilibrium states in particle chains, with implications for experiments and real materials.

Contribution

It introduces a precise approach to identify the minimal length scales for local temperature existence in homogeneous particle chains in thermal equilibrium.

Findings

Estimates for minimal length scales in real materials.

Discussion on the physical relevance of local temperature.

Possibility of experimental detection of local thermal states.

Abstract

We review a recent approach to determine the minimal spatial length scales on which local temperature exists. After mentioning an experiment where such considerations are of relevance, we first discuss the precise definition of the existence of local temperature and its physical relevance. The approach to calculate the length scales in question considers homogenous chains of particles with nearest neighbor interactions. The entire chain is assumed to be in a thermal equilibrium state and it is analyzed when such an equilibrium state at the same time exists for a local part of it. The result yields estimates for real materials, the liability of which is discussed in the sequel. We finally consider a possibility to detect the existence or non-existence of a local thermal state in experiment.