Multiscale equilibrium thermodynamics systems

The review is organized as follows In Section 2 we present the multiscale equilibrium thermodynamics in the setting of contact geometry. The time evolution (multiscale nonequilibrium thermodynamics) representing approach of a mesoscopic level LmeSoi to the level of equilibrium thermodynamics Leth is discussed in Section 3. A generalization in which the level Leth is replaced by another mesoscopic level LmesoZ is considered in Section 4. The notion of multiscale thermodynamics of systems arises in the analysis of this type of time evolution. 

The simplest one-constant limitation concept cannot be applied to all systems. There is another very simple case based on exclusion of "fast equilibria" A Ay. In this limit, the ratio of reaction constants Kij — kij/kji is bounded, 0equilibrium constant", even if there is no relevant thermodynamics.) Ray (1983) discussed that case systematically for some real examples. Of course, it is possible to create the theory for that case very similarly to the theory presented above. This should be done, but it is worth to mention now that the limitation concept can be applied to any modular structure of reaction network. Let for the reaction network if the set of elementary reactions is partitioned on some modules — U j. We can consider the related multiscale ensemble of reaction constants let the ratio of any two-rate constants inside each module be bounded (and separated from zero, of course), but the ratios between modules form a well-separated ensemble. This can be formalized by multiplication of rate constants of each module on a timescale coefficient fc,. If we assume that In fc, are uniformly and independently distributed on a real line (or fc, are independently and log-uniformly distributed on a sufficiently large interval) then we come to the problem of modular limitation. The problem is quite general describe the typical behavior of multiscale ensembles for systems with given modular structure each module has its own timescale and these time scales are well separated. 

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