A Unification between Dynamical System Theory and Thermodynamics Involving an Energy, Mass, and Entropy State Space Formalism

Abstract

In this paper, we combine the two universalisms of thermodynamics and dynamical systems theory to develop a dynamical system formalism for classical thermodynamics. Specifically, using a compartmental dynamical system energy flow model involving heat flow, work energy, and chemical reactions, we develop a state-space dynamical system model that captures the key aspects of thermodynamics, including its fundamental laws. In addition, we show that our thermodynamically consistent dynamical system model is globally semistable with system states converging to a state of temperature equipartition. Furthermore, in the presence of chemical reactions, we use the law of mass-action and the notion of chemical potential to show that the dynamic system states converge to a state of temperature equipartition and zero affinity corresponding to a state of chemical equilibrium.

Keywords

• system thermodynamics
• energy flow
• interconnected systems
• entropy
• Helmholtz free energy
• Gibbs free energy
• chemical thermodynamics
• mass action kinetics
• chemical potential
• neuroscience and thermodynamics