Existence of temperature on the nanoscale

Abstract

We consider a regular chain of quantum particles with nearest neighbour interactions in a canonical state with temperature $T$. We analyse the conditions under which the state factors into a product of canonical density matrices with respect to groups of $n$ particles each and under which these groups have the same temperature $T$. In quantum mechanics the minimum group size $n_{min}$ depends on the temperature $T$, contrary to the classical case. We apply our analysis to a harmonic chain and find that $n_{min}=const.$ for temperatures above the Debye temperature and $n_{min}\propto T^{-3}$ below.

Version that appeared in PRL

References in corpus (2)

• Fourier's Law confirmed for a class of small quantum systems
• Entanglement Energetics at Zero Temperature

Cited by in corpus (3)

• Ground State Entanglement Energetics
• Global and local relaxation of a spin-chain under exact Schroedinger and master-equation dynamics
• Nanothermodynamics:a generic approach to material properties at nanoscale