The general equation of nonequilibrium reversible-irreversible coupling (GENERIC) is studied in light of time-reversal transformation. It is shown that Onsager-Casimir reciprocal relations are implied by GENERIC in the near-equilibrium regime. A general structure which gives the reciprocal relations but which is valid also far from equilibrium is identified, and Onsager-Casimir reciprocal relations are generalized to far-from-equilibrium regime in this sense. Moreover, reversibility and irreversibility are carefully discussed and the results are illustrated in Hamiltonian dynamics, classical hydrodynamics, classical irreversible thermodynamics, the quantum master equation, and the Boltzmann equation.

École Polytechnique de Montréal C P 6079 suc Centre ville Montréal H3C 3A7 Québec Canada

New Technologies Research Centre University of West Bohemia Univerzitní 8 306 14 Pilsen Czech Republic

New Technologies Research Centre University of West Bohemia Univerzitní 8 306 14 Pilsen Czech Republic and Department of Mathematics FNSPE Czech Technical University Prague Trojanova 13 120 00 Praha Czech Republic

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