Statistical physics: Some basic principles of fluctuation and noise theory

Models have traditionally played a significant role in statistical mechanics. In view of the complexity of the system which statistical mechanics attempt to describe, this is not at all surprising. The study of simplified models has frequently revealed the underlying mathematical structure of many physical questions and in so doing the study of models has contributed directly to a clarification of several paradoxes which beset statistical mechanics.In this paper some of the models which appear to be useful for the discussion of non-equilibrium phenomena are examined in some detail. As usual these models are extremely simplified versions of the actual situations. It is, finally, as well to stress that although the models are mathematically simpler, the actual discussion is still sometimes quite complicated.“Mathematics is often regarded as the bread and butter of science. If the butter is omitted, the results is indigestion, loss of appetite, or both. The purpose of this book is to suggest some ways of buttering the bread. The human mind can seldom accept completely abstract ideas; they must be derived from, or illustrated by, concrete examples. Here the reader will find ways of providing for himself tangible objects which will bring that necessary contact with reality into the symbolic world of mathematics.”(Cundy and Rollett, 1961)