Kubo formula and the time-irreversibility of fluctuations

Interrelationship of classical and quantum fluctuations is discussed. With energy dissipation being taken into account, fluctuations are shown to be i rreversible even in the case of classical systems. Classical systems are tr eated as the Limiting case of relevant quantum systems for h --> 0. The irr eversibility of classical fluctuations should be interpreted in the sense t hat though correlation functions of time-reversed fluctuations are equal fo r h --> 0, the derivatives over the quantity h --> 0 of correlation functio ns of time-reversed fluctuations differ, and just this difference determine s the linear response of the system. An analogue of Kubo relation for class ical fluctuations is derived. Fluctuations in both equilibrium and nonequil ibrium (though stationary) states of the system are considered. (C) 2001 El sevier Science B.V. All rights reserved.