Dynamics and Equations of Motion in Physico-Chemical Systems

2 Dynamics and Equations of Motion in Physico-Chemical Systems 

It is now one of the fundamental problems of statistical physics and synergetics to derive the properties of physico-chemical multi-component systems on the macroscopic level from their constituent components on the elementary microscopic level. Part of the problem is to explain which macrovariables (including order parameters) may be relevant under given circumstances and to describe their dynamics by appropriate equations of motion [1.49, 50]. 

General concepts have been developed to establish relevant macrovariables and to derive formally exact equations of motion for the macrovariables from a fundtoental standpoint [1.29, 30]. 

On the other hand, phenomenological derivations of such equations are possible by making some approximations and plausible assumptions about the system. Simple but intuitively plausible forms for these equations will now be discussed. Exact equations of motion for macrovariables contain the interactions between the macrovariables as well as the rapidly fluctuating random forces due to the influence of the microvariables [1.31-33, 51-53]. 

The simplest type of such equations for macrovariables either derived phenomenologically or from fundamental dynamics is that of the Langevin equations , a set of first-order differential equations in the time variable t 

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