A. N. Gorban, I. V. Karlin
Geometry of irreversibility: The film of nonequilibrium states
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ABSTRACT. A general geometrical framework of nonequilibrium thermodynamics is developed. The notion of macroscopically definable ensembles is developed. The thesis about macroscopically definable
ensembles is suggested. This thesis should play the same role in the nonequilibrium thermodynamics,
as the Church-Turing thesis in the theory of computability. The primitive macroscopically
definable ensembles are described. These are ensembles with macroscopically prepared initial states.
The method for computing trajectories of primitive macroscopically definable nonequilibrium ensembles
is elaborated. These trajectories are represented as sequences of deformed equilibrium ensembles and
simple quadratic models between them. The primitive macroscopically definable ensembles form the
manifold in the space of ensembles. We call this manifold the film of nonequilibrium states.
The equation for the film and the equation for the ensemble motion on the film are written down. The
notion of the invariant film of non-equilibrium states, and the method of its approximate
construction transform the the problem of nonequilibrium kinetics into a series of problems of
equilibrium statistical physics. The developed methods allow us to solve the problem of
macro-kinetics even when there are no autonomous equations of macro-kinetics.