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Condensed matter physics, hybrid energy and entropy principles, and the hybrid first and second laws of thermodynamics. (English) Zbl 07265114
Summary: In this paper, we develop an energy-based, large-scale hybrid dynamical system model to present a generic framework for hybrid thermodynamics involving hybrid energy and entropy conservation and nonconservation principles. Specifically, using a hybrid compartmental dynamical system energy flow model we develop a hybrid state-space dynamical system formalism for addressing critical phenomena and discontinuous phase transitions in thermodynamics and provide hybrid extensions to the first and second laws of thermodynamics. In addition, using Lyapunov stability theory for impulsive differential equations, we show that our hybrid large-scale thermodynamic energy flow model has convergent trajectories to Lyapunov stable equilibria determined by the system initial subsystem energies. Moreover, we show that the steady-state distribution of the hybrid large-scale system energies is uniformly distributed over all of the subsystems, leading to system energy equipartitioning corresponding to a maximum entropy equilibrium state.
MSC:
82C35 Irreversible thermodynamics, including Onsager-Machlup theory
82C26 Dynamic and nonequilibrium phase transitions (general) in statistical mechanics
82C27 Dynamic critical phenomena in statistical mechanics
80A05 Foundations of thermodynamics and heat transfer
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