Skip to main content

Advertisement

We’d like to understand how you use our websites in order to improve them. Register your interest.

Thermodynamic modeling, energy equipartition, and nonconservation of entropy for discrete-time dynamical systems

Abstract

We develop thermodynamic models for discrete-time large-scale dynamical systems. Specifically, using compartmental dynamical system theory, we develop energy flow models 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.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Wassim M Haddad.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Haddad, W.M., Hui, Q., Nersesov, S.G. et al. Thermodynamic modeling, energy equipartition, and nonconservation of entropy for discrete-time dynamical systems. Adv Differ Equ 2005, 248040 (2005). https://doi.org/10.1155/ADE.2005.275

Download citation