A principle in dynamic coarse graining–Onsager principle and its applications
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Dynamic coarse graining is a procedure to map a dynamical system with large degrees of freedom to a system with smaller degrees of freedom by properly choosing coarse grained variables. This procedure has been conducted mainly by empiricisms. In this paper, I will discuss a theoretical principle which may be useful for this procedure. I will discuss how to choose coarse grained variables (or slow variables), and how to set up their evolution equations. To this end, I will review the classical example of dynamic coarse graining, i.e., the Brownian motion theory, and show a variational principle for the evolution of the slow variables. The principle, called the Onsager principle, is useful not only to derive the evolution equations, but also to solve the problems.
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