Thermodynamic model of nonequilibrium phase transitions

Abstract

Within the scope of a thermodynamic description using the maximum entropy production principle, transitions from one nonequilibrium (kinetic) regime to another are considered. It is shown that in the case when power-law dependencies of thermodynamic flux on force are similar for two regimes, only a transition accompanied by a positive jump of thermodynamic flux is possible between them. It is found that the difference in powers of the dependencies of thermodynamic fluxes on forces results in a number of interesting nonequilibrium transitions between kinetic regimes, including the reentrant one with a negative jump of thermodynamic flux.

Entropy and Entropy Production: Old Misconceptions and New Breakthroughs

“…We have advanced a hypothesis [35][36][37][38]: the increase of the entropy production is a necessary condition [57] for a nonequilibrium (kinetic) transition between two nonequilibrium regimes (phases) of a process [58] and the equality of the entropy production of two phases determines the kinetic binodal of the transition [59]. The development of this hypothesis has yielded the following results: (1) a complete morphological diagram (with stable, unstable and metastable regions) was calculated for different regimes of nonequilibrium growth of the initially spherical and cylindrical nucleus [35,36].…”

“…It is important that all statements were introduced: (1) independently; (2) for different systems and different scales (and levels) of description; (3) are reduced to the maximum entropy production principle; (4) demonstrate effectiveness in the solution of problems. All of the above made it possible for us to propose a generalized formulation of the maximum entropy production principle (MEPP) applicable to different scales of description [37,38]: at each level of description, with preset external constraints, the relationship between the cause and the response of a nonequilibrium system is established in order to maximize the entropy production density.…”

A matrix solution of the pentagon equation with anticommuting variables

“…We plan to write another paper containing interesting calculations, especially for twisted complexes (like those in [9], [10] but for manifolds with a boundary), and other material such as the generalization of our complex (5) to the case of a boundary with any number of components. Moreover, it turns out that complex (5) admits a rather straightforward generalization to four-dimensional manifolds; this will be the theme of separate research.…”

“…There are some arguments [8] showing that this "more quantum" character is properly manifested only in a context involving a nontrivial, even non-Abelian, representation of the fundamental group of the manifold, as described in [9], [10]. But our aim here is merely to construct the solution of the pentagon equation and show that it also works for the moves 1 ↔ 4, and we therefore leave those "quantum" calculations for future work.…”

Entropy Production from the Master Equation for Driven Lattice Gases

“…Dissipation of work to heat makes entropy production a property of the DLG, as it is of other driven systems. The hypothetical principle of maximum entropy production [4][5][6][7][8][9][10] or the converse principle of minimum entropy production would suggest that entropy production may be not just a property but an organizing principle of driven systems such as the DLG. Recent discussions of the role of entropy production in non-equilibrium systems include those by Ross, Vellela and Qian and Attard [11][12][13] A critical review of entropy-production ideas, giving a thorough historical perspective from Carnot's work through the present, was written by Velasco, García-Colín and Uribe [14] The present work is a largely numerical study of the meaning and possible extrema of entropy production in the simple, well-defined DLG model.…”