Contribution to the general theory of thermal fluctuations in nonlinear systems

A method is proposed for investigating the thermal fluctuations in an arbitrary system subjected to the influence of a dynamic perturbation (and in contact with a thermostat). An exact formula is obtained for the characteristic functional of the fluctuations of the macroscopic variables. The formula contains all the most general consequences of the basic postulates of statistical mechanics regarding the macroscopic variables. An infinite set of relations between the moment and cumulant functions of the equilibrium and nonequilibrium fluctuations (in particular, the Onsager reciprocity relations and the fluctuation-dissipation theorems) follows from the formula. The consequences of the additional assumption that the macroscopic variables are Markovian are also considered.