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. 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 asHere:
- denotes a set of variables used to describe the state space. The vector can also contain variables depending on a continuous index like a temperature field. In general, is a function, where the set can contain both discrete and continuous indexes. Example: for a gas with nonuniform temperature, contained in a volume
- , are the system's total energy and entropy. For purely discrete state variables, these are simply functions from to, for continuously indexed, they are functionals
- , are the derivatives of and. In the discrete case, it is simply the gradient, for continuous variables, it is the functional derivative
- the Poisson matrix is an antisymmetric matrix describing the reversible dynamics of the system according to Hamiltonian mechanics. The related Poisson bracket fulfills the Jacobi identity.
- the friction matrix is a positive semidefinite matrix describing the system's irreversible behaviour.
which express the conservation of entropy under reversible dynamics and of energy under irreversible dynamics, respectively. The conditions on express that the energy is reversibly conserved, and the condition on express that the entropy is irreversibly non-decreasing.