Geometry of Multiscale Nonequilibrium Thermodynamics

Miroslav GrmelaEcole Polytechnique de Montreal, C.P. 6079, succursale Centre-ville, Montreal H3C 3A7, QC, Canada;E-Mail: miroslav.grmela@polymtl.caAcademic Editor: George RuppeinerReceived: 2 June 2015 / Accepted: 20 August 2015 / Published: 25 August 2015Abstract: The time evolution of macroscopic systems can be experimentally observed andmathematically described on many different levels of description. It has been conjecturedthat the governing equations on all levels are particular realizations of a single abstractequation. We support this conjecture by interpreting the abstract equation as a geometricalformulation of general nonequilibrium thermodynamics.Keywords: equilibrium thermodynamics; nonequilibrium thermodynamics; contactgeometry; GENERIC1. IntroductionEuler–Navier–Stokes–Fourier fluid mechanics and Boltzmann kinetic theory are two examples ofmesoscopic dynamical theories. Their governing equations, as well as governing equations of manyother well-established (i.e., extensively tested with the results of experimental observations) mesoscopicdynamical theories, can be formally written as:x_ = LE

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