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.
Highlights
Thermodynamics is a physical branch of science that governs the thermal behavior of dynamical systems from those as simple as refrigerators to those as complex as our expanding universe
We show that entropy production during chemical reactions is nonnegative and the dynamical system states of our chemical thermodynamic state space model converge to a state of temperature equipartition and zero affinity
We developed a system-theoretic perspective for classical thermodynamics and chemical reaction processes
Summary
Thermodynamics is a physical branch of science that governs the thermal behavior of dynamical systems from those as simple as refrigerators to those as complex as our expanding universe. The concept of entropy for a nonequilibrium state of a dynamical process is defined, and its global existence and uniqueness is established This state space formalism of thermodynamics shows that the behavior of heat, as described by the conservation equations of thermal transport and as described by classical thermodynamics, can be derived from the same basic principles and is part of the same scientific discipline. The central thesis of this paper is to present a state space formulation for equilibrium and nonequilibrium thermodynamics based on a dynamical system theory combined with interconnected nonlinear compartmental systems that ensures a consistent thermodynamic model for heat, energy, and mass flow. If the positive limit set of Equation (1) contains a Lyapunov n stable (with respect to R+ ) equilibrium point y, y = limt→∞ s(t, x)
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