A quantum system consisting of a regular chain of elementary subsystems with nearest neighbor interactions was considered and it was assumed that the total system is in a canonical state with temperature T. The conditions under which the state factors into a product of canonical density matrices with respect to groups of n subsystems each, and when these groups have the same temperature T, were analyzed. A quantitative estimate of the minimal length scale on which temperature can exist was given by the approach for the harmonic chain, which successfully describes thermal properties of insulating solids. It was found that this length scale is constant for temperatures above the Debye temperature and proportional to T-3 below.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics