Condensed matter physics, hybrid energy and entropy principles, and the hybrid first and second laws of thermodynamics

Abstract

Abstract 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.