THERMODYNAMIC MODELING, ENERGY EQUIPARTITION, AND NONCONSERVATION OF ENTROPY FOR DISCRETE-TIME DYNAMICAL SYSTEMS

Authors

Wassim H. Haddad, Georgia Institute of TechnologyFollow
Qing Hui, Georgia Institute of TechnologyFollow
Sergey G. Nersesov, Georgia Institute of TechnologyFollow
Vijaysekhar Chellaboina, The University of TennesseeFollow

Document Type

Article

Date of this Version

11-19-2004

Citation

2005 Hindawi Publishing Corporation

Comments

Advances in Difference Equations 2005:3 (2005) 275–318 DOI: 10.1155/ADE.2005.275

Abstract

We develop thermodynamic models for discrete-time large-scale dynamical systems. Specifically, using compartmental dynamical system theory, we develop energy flowmodels possessing energy conservation, energy equipartition, temperature equipartition, and entropy nonconservation principles for discrete-time, large-scale dynamical systems. Furthermore, we introduce a new and dual notion to entropy; namely, ectropy, as a measure of the tendency of a dynamical system to do useful work and grow more organized, and show that conservation of energy in an isolated thermodynamic system necessarily leads to nonconservation of ectropy and entropy. In addition, using the system ectropy as a Lyapunov function candidate, we show that our discrete-time, large-scale thermodynamic energy flow model has convergent trajectories to Lyapunov stable equilibria determined by the system initial subsystem energies.