GENERIC formalism

In non-equilibrium thermodynamics, GENERIC is an acronym for General Equation for Non-Equilibrium Reversible-Irreversible Coupling. It is the general form of dynamic equation for a system with both reversible and irreversible dynamics (generated by energy and entropy, respectively). GENERIC formalism is the theory built around the GENERIC equation, which has been proposed in its final form in 1997 by Miroslav Grmela and Hans Christian Öttinger.
GENERIC equation.
The GENERIC equation is usually written as
Here:
In addition to the above equation and the properties of its constituents, systems that ought to be properly described by the GENERIC formalism are required to fulfill the degeneracy conditions
which express the conservation of entropy under reversible dynamics and of energy under irreversible dynamics, respectively. The conditions on formula_24 (antisymmetry and some others) express that the energy is reversibly conserved, and the condition on formula_25 (positive semidefiniteness) express that the entropy is irreversibly non-decreasing.