By Yu.L. Klimontovich
Let us commence by means of quoting from the Preface to the author's Statistical Physics (Moscow, Nauka 1982; additionally released in English through Harwood in 1986): '''My God! one more e-book on statistical physics! there isn't any room on my bookshelves left!' Such emotionsare rather comprehensible. Beforejumping to conclusions, although, it might be helpful to learn the creation and glance through the desk of contents. Then the reader will locate that this e-book is completely diversified from the prevailing classes, primary and concise. ... we don't use the traditional department into statistical theories ofequilibrium and nonequilibrium states. instead of that, the speculation ofnonequilibrium country is the root and the spine oftheentirecourse. ... This technique permits us to enhance a unified procedure for statistical description ofa very broadclassofsystems. ... the writer definitely doesn't desire to exaggerate some great benefits of the ebook, contemplating it asjustthe first attemptto create a textbookofa new kind." your next step during this path was once the author's Turbulent movement and the constitution of Chaos (Moscow, Nauka 1990; Kluwer educational Publishers 1991). This ebook is subtitled a brand new method of the Statistical conception of Open structures. evidently, the "new procedure" isn't intended to defy the constant and effective tools of the traditional statistical concept; itshould be considered as auseful reinforcementofsuch methods.
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Additional info for Statistical Theory of Open Systems: Volume 1: A Unified Approach to Kinetic Description of Processes in Active Systems
The right-hand side of the kinetic equation contains two dissipative terms. The first of these, f(v)(r,p,t), accounts for dissipation due to the redistribution of particle velocities (hence the subscript "v") - for instance, because of collisions between the particles. In general, f(v) is the Boltzmann collision integral. 11)), however, a much simpler expression can be used for this dissipative term (see Ch. 13). The second dissipative term on the right-hand side of the kinetic equation is due to the redistribution of particle coordinates.
In case of open systems the situation is even more complicated, because in the course of evolution towards equilibrium the value of mean energy or the relevant effective energy (effective Hamilton function) is not conserved. Nevertheless, the Boltzmann - Gibbs - Shannon entropy can be used as the measure of the relative degree of order of different states of open systems in the course of evolution of both in time and in the space of controlling parameters. First, however, let us discuss a general result obtained by Gibbs without any constraints being imposed on the nature of interaction between the elements of the system in question.
4) to FKPP equation is possible in the approximation which neglects this internal noise (D(X) == 0, and the distribution function f(X,R,t) only depends on X(R,t): INTRODUCTION f(X,R,t) =c5(X - X(R,t»), and, therefore, (X) =X(R,t) . 2). Possible is also the other limiting case, when spatial diffusion is a "fast" process, so that a uniform distribution over space is established within 'rD < 1/lal. 4) reduces to an equation for distribution function f(X,t) in internal variableX. 5), which corresponds to FKPP equation, is entirely determined by the first moment, (X) =X(R,t).
Statistical Theory of Open Systems: Volume 1: A Unified Approach to Kinetic Description of Processes in Active Systems by Yu.L. Klimontovich