GENERIC formalism

GENERIC equation

• 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.