@article {3453,
	title = {Nonequilibrium phase transitions and pattern formation as consequences of second-order thermodynamic induction},
	journal = {Physical Review E},
	volume = {100},
	year = {2019},
	pages = {1-22},
	abstract = {Development of thermodynamic induction up to second order gives a dynamical bifurcation for thermodynamic variables and allows for the prediction and detailed explanation of nonequilibrium phase transitions with associated spontaneous symmetry breaking.\&nbsp; By taking into account nonequilibrium fluctuations, long range order is analyzed for possible pattern formation.\&nbsp; Consolidation of results up to second order produces thermodynamic potentials that are maximized by stationary states of the system of interest.\&nbsp; These new potentials differ from the traditional thermodynamic potentials.In particular a generalized entropy is formulated for the system of interest which becomes the traditional entropy when thermodynamic equilibrium is restored.\&nbsp; This generalized entropy is maximized by stationary states under nonequilibrium conditions where the standard entropy for the system of interest is not maximized.\&nbsp; These new nonequilibrium concepts are incorporated into traditional thermodynamics, such as a revised thermodynamic identity, and a revised canonical distribution.\&nbsp;\&nbsp; Detailed analysis shows that the second law of thermodynamics is never violated even during any pattern formation, thus solving the entropic coupling problem.\&nbsp; Examples discussed include pattern formation during phase front propagation under nonequilibrium conditions and the formation of Turing patterns.\&nbsp; The predictions of second order thermodynamic induction are consistent with both observational data in the literature as well as the modeling of this data.},
	url = {https://journals.aps.org/pre/abstract/10.1103/PhysRevE.100.022116},
	author = {S.N. Patitsas}
}
