A unified algorithm that uses the metriplectic 4-bracket of Morrison and Updike to systematically construct thermodynamically consistent dynamical systems, i.e., systems whose combined Hamiltonian and dissipative dynamics conserve total energy (first law) while never decreasing entropy (second law). Its central ingredient is the force-flux relation J_alpha = -L_{alpha beta} grad(delta H / delta xi_beta) built from phenomenological coefficients, a Hamiltonian, and the dynamical variables. Applying the algorithm to the Navier-Stokes-Fourier, Cahn-Hilliard-Navier-Stokes, and Brenner-Navier-Stokes-Fourier systems reproduces and significantly generalizes them.
A unified thermodynamic algorithm is presented for constructing thermodynamically consistent dynamical systems: systems whose Hamiltonian and dissipative parts conserve energy while producing entropy…