Entropy production and nonequilibrium stationarity in quantum dynamical systems

Abstract

In statistical physics, Kubo's linear response theory is well known as the most effective method, in the linear-approximation regimes, of calculating transport coefficients which describe dissipative aspects in the macroscopic manifestations of microscopic quantum systems. From the viewpoint of the mutual relationship between the microscopic and macroscopic levels, it is clear that the response theory is essentially concerned with the information-theoretical problems. For lack of such key-concepts as entropy and/or entropy production, however, this theory has long been taken in physics merely as a calculational device, without the deep understanding of the reason for its general validity.

In this report, it is shown that the notion of entropy production as a generating function of various transport coefficients can be defined in a natural way with the aid of relative entropy. We carefully examine the nonlinear responses of quantum dynamical systems against almost-periodic perturbations with (countably) many frequencies in the general algebraic framework which is applicable to the systems with infinite degrees of freedom without the limitations of standard linear response theory. Then, the positivity of (time-averaged) entropy production expressing the dissipativity is proved on a general ground, and also the basis for the validity of linear approximation is clarified on the basis of time-scale change controlled by van Hove limit. By virtue of the methods of dilation/coarse graining, the parallelism becomes clear between the response theory in statistical physics and the theory of quantum measurements as well as of communication channels.