1205.4386 (Pei Wang)

The breakdown of the zeroth law of thermodynamics and the definition of
temperature in small quantum systems    [PDF]

Pei Wang

We find that the zeroth law of thermodynamics is broken in small quantum systems. We study two small quantum systems coupled to the same Fermi sea which is in thermal equilibrium. We find that the two systems are not in thermal equilibrium with each other, because the electrons in the two systems will redistribute themselves after the two systems contact with each other. The traditional way of defining temperature fails in small quantum systems due to the breakdown of the transitive relation of thermal equilibrium. Then we show a new method of defining temperature by attaching an auxiliary site, which plays the role of a thermometer, to the system. Our method is indifferent to whether or not the density matrix of the system is a canonical one.

View original: http://arxiv.org/abs/1205.4386