Kubo formula and the time-irreversibility of fluctuations

Abstract

Interrelationship of classical and quantum fluctuations is discussed. With energy dissipation being taken into account, fluctuations are shown to be irreversible even in the case of classical systems. Classical systems are treated as the limiting case of relevant quantum systems for ℏ→0. The irreversibility of classical fluctuations should be interpreted in the sense that though correlation functions of time-reversed fluctuations are equal for ℏ→0, the derivatives over the quantity ℏ→0 of correlation functions of time-reversed fluctuations differ, and just this difference determines the linear response of the system. An analogue of Kubo relation for classical fluctuations is derived. Fluctuations in both equilibrium and nonequilibrium (though stationary) states of the system are considered.