A system-theoretic foundation for thermodynamics: Energy flow, energy balance, energy equipartition, entropy, and ectropy.
hermodynamics is a physical branch of science that governs the thermal behavior of dynamical systems as simple as refrigerators io as complex as our expanding universe. The development of thermodynamics spawned out of steam tables and venous bleeding with many scientists and engineers expressing concerns about the completeness and clarity of its mathematical exposition over its tortuous history. In this paper we develop a system-theoretic foundation Cor thermodynamics using n large-scale dynamical systems perspective. Specifically, using compartmental dynamical system energy Bow models, we place the universal energy conservation, energy equipartition, temperature equipartition, and entropy nonconservation laws of thermodynamics on a system-theoretic foundation. Furthermore, we introduce a new and dual notion to entropy; namely, ecrropy, as a measure of the tendency of a dynamical system to do useful work and show that conservation of energy in an isolated thermodynamic system necessarily leads to nonconservation of ectmpy and entropy. In addition, using the system ectropy as a Lyapunov function candidate we show that our large-scale thermodynamic energy flow model has convergent trajectories to Lyapunov stable equilibria determined by the large-scale system initial subsystem energies.
|Main Author:||Haddad, Wassim.|
|Other Authors:||Chellaboina, VijaySekhar., Nersesov, Sergey.|