Nonlinear nonequilibrium thermodynamics I. Linear and nonlinear fluctuation-dissipation theorems (Q1202182)

This volume belongs to a series devoted to a field that falls between different spheres of interest and thus might be, unfortunately, overlooked. Synergetics is concerned with cooperation of different parts of a system that produces macroscopic structures. The reviewer, whose main interest is continuum thermomechanics, regrets particularly the relatively scarce attention paid by his community to the field. This first volume could be a good introduction to the subfield which the author calls nonlinear nonequilibrium and fluctuation-dissipative thermodynamics (advanced problems are considered in the second volume). The six chapters are devoted respectively to: Preliminary concepts; Essential aspects of probability theory; Systems without after-effect: Generating equation and consequences; Systems where after-effect is allowed: Theory and applications. The level of rigour is that generally accepted in theoretical physics; if the mathematical reader feels impelled to improve and enlarge, the book will achieve one of its aims. The reviewer recommends it to the attention of many, though the specificity of the title will deter some. Notice that the references are mainly to papers in Russian, apart some books and contributions to the Rev. Mod. Phys.