Zeroth and second laws of thermodynamics simultaneously questioned in the quantum microworld

Abstract

A new and rather trivial model is suggested with mechanism that implies simultaneous violation of the zeroth and the second laws of thermodynamics. Mathematically rigorous quantum theory reduces to a trivial application of the Golden rule formula. It yields exciton on-energy-shell diffusion caused by bath-nonassisted excitation hopping between tails of different exciton site levels ε1 < ε2 broadened by bath-assisted finite life-time effects. The elastic character of the hopping implies 1 ↔ 2-symmetric transfer rate W. Thus the net diffusion exciton flow W(P 1 - P 2) and also, as argued, the net energy flow are possible due to different near-to-equilibrium exciton populations P 1 > P 2. As the sites are provided with two different baths, the population imbalance and the flows survive even for slightly different local bath temperatures T 1 < T 2 < T 1ε2/ε1. Thus spontaneous exciton and also energy flows against temperature step become possible, in contradiction with the Clausius form of the second law. Violations of both the laws disappear in the high-temperature, i.e. classical limit