New interpretations of equilibrium and reversibility

In order to clearly explain the possibilities of describing nonequlibrium irreversible processes in terms of equilibrium it is certainly necessary to define quite accurately the notions of equilibrium and reversibility, nonequilibrium and irreversibility. It is clear that their interpretation, as well as the interpretation of other scientific notions, changes with the development of respective theories, models, and methods. Since the work touches upon the issues of interrelations between the competing models in a historical profile it is desirable that the appropriateness of various interpretations of the said notions be assessed in this profile. Making no pretence of the systematic presentation of the issue we will only touch upon some points that are important for understanding the text1 below. 

Mechanics emerged as a science studying reversible processes that are symmetrical relative to time. Euler, in his thesis on the least action 

A rich materia] for the comprehension of the evolution of basic notions in the course of development of variational principles and principles of equilibrium and extremality in physics can be found in remarkable books by L.S. Polak (1987, 1960). 

However, the presented interpretation of equilibrium processes turns out to be unsatisfactory for the analysis of possibility to use equilibrium descriptions for irreversible phenomena. The interpretation of interrelations between equilibrium and reversibility that was given by 

Gorban et al. in their works (Gorban, 2007 Gorban et al., 2001,2006) seems to be more comprehensive for our discussion. The works unfolded the idea of the Ehrenfests (1959) on the isolated system tending toward the Boltzmann equilibrium trajectory as a result of agitations.  

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