Fluctuations and Irreversible Thermodynamics

Publisher Website
Google Scholar
Abstract
The time-dependent theory of fluctuations is based on a combined application of the phenomenological theory of dissipation and the stochastic theory of random processes. The traditional method of joining these theories into a uniform scheme proceeds by adding a random perturbation to the differential equation of the phenomenological kinetic theory (the Langevin equation in case of Brownian motion). In the present approach the problem is considered as an essentially statistical one. The role of the differential equation is to fix the form of the distribution function over the manifold of fluctuation paths in function space. The solutions of the equation constitute the most probable region in function space and the fluctuations appear with their appropriate probabilities. The connection between the phenomenological equation and the distribution function is stipulated by means of a postulate, the essential ingredient of which is the auxiliary function recently introduced by Onsager and Machlup. Heuristically this postulate was suggested by the kinetic analog of Boltzmann's principle established by these authors. In the present logical structure it is sufficient to join this postulate to the standard assumptions of the phenomenological and the stochastic theories for the derivation of the entire time-dependent fluctuation theory. A number of statements usually postulated appear as theorems in this presentation. The reversible and irreversible aspects of time play an essential part in the argument. The calculation of fluctuations is carried out in the temporal and the spectral descriptions. The relation of the two schemes is discussed along with the scope and limitations of the theory.