Thermodynamics

Download Nonlinear Nonequilibrium Thermodynamics I: Linear and by Rouslan L. Stratonovich PDF

By Rouslan L. Stratonovich

This ebook supplies the 1st specified coherent therapy of a comparatively younger department of statistical physics - nonlinear nonequilibrium and fluctuation-dissipative thermo­ dynamics. This quarter of study has taken form rather lately: its improvement begun in 1959. the sooner concept -linear nonequilibrium thermodynamics - is in precept an easy precise case of the recent idea. although the name of this publication contains the notice "nonlinear", it additionally covers the result of linear nonequilibrium thermodynamics. The presentation of the linear and nonlinear theories is completed inside of a standard theoretical framework that isn't topic to the linearity situation. the writer hopes that the reader will understand the intrinsic team spirit of this self-discipline, and the uniformity and generality of its constituent components. This concept has a large choice of purposes in numerous domain names of physics and actual chemistry, allowing one to calculate thermal fluctuations in numerous nonlinear platforms. The e-book is split into volumes. Fluctuation-dissipation theorems (or kinfolk) of assorted forms (linear, quadratic and cubic, classical and quantum) are thought of within the first quantity. right here one encounters the Markov and non-Markov fluctuation-dissipation theorems (FDTs), theorems of the 1st, moment and 3rd types. Nonlinear FDTs are much less renowned than their linear counterparts.

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Extra info for Nonlinear Nonequilibrium Thermodynamics I: Linear and Nonlinear Fluctuation-Dissipation Theorems

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Here we use the fact that K1 (B) is nothing but the average derivative

19) . 14-16) are significantly simpler in the case of Gaussian random variables. 3 Moments and Correlators in Quantum Theory The above formulas are valid in the nonquantum case. However, it should be noted that random variables become operators in the quantum case and, generally speaking, they are noncommutative. Therefore, products with different order of multipliers are distinct in the quantum case. All of them correspond to the same nonquantum product. Hence, moments and, consequently, cumulants may be defined in various ways in the quantum case.

1 Moments and the Characteristic Function Suppose we have random variables ~ 1, . . , ~n (n is arbitrary), which have the joint probability density w( ~ 1, . . , ~n)' The mean value f <~~l ... ~~n) = ~~l ... ~~nW(~l' ... , ~n)d~l ... 1) is called the moment. The characteristic function e(iu 1, ... • , iun ) = (exPCt1 f iU~~~) ) = eXPCt1 iu~~~ )W(~l" .. , ~n )d~l ... 1,2), we easily verify that the moments can be expressed in terms of the characteristic function: ): ... _m[ame(iU1, ... , iUn)] <"~l 1 Here U = °means that U1 aU~l ...

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