Uncertainty Principle Consequences at Thermal Equilibrium

Abstract

Contrary to the conventional wisdom that deviations from standard thermodynamics originate from the strong coupling to the bath, it is shown that these deviations are intimately linked to the power spectrum of the thermal bath. Specifically, it is shown that the lower bound of the dispersion of the total energy of the system, imposed by the uncertainty principle, is dominated by the bath power spectrum and therefore, quantum mechanics inhibits the system thermal-equilibriun-state from being described by the canonical Boltzrhann's distribution. This is in sharp contrast to the classical case, for which the thermal equilibrium distribution of a system interacting via central forces with pairwise-self-interacting environment, irrespective of the interaction strength, is shown to be eractly characterized by the canonical Boltzmann distribution. As a consequence of this analysis we define an effective coupling to the environment that depends on all energy scales in the system and reservoir interaction. Sample computations in regimes predicted by this effective coupling are demonstrated. For example, for the case of strong effective coupling, deviations from standard thermodynamics are present and, for the case of weak effective coupling, quantum features such as stationary entanglement are possible at high temperatures.