A unification between dynamical system theory and thermodynamics involving an energy, mass, and entropy state space formalism
type: Item
instance of: scholarly article
title: A unification between dynamical system theory and thermodynamics involving an energy, mass, and entropy state space formalism
zbMATH Open document ID: 1310.37016
author: Wassim M. Haddad
published in: Entropy
publication date: 2014-09-19T00:00:00Z
review text: Summary: 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.
Mathematics Subject Classification ID: 37D35
Mathematics Subject Classification ID: 80A10
zbMATH DE Number: 6346140
zbMATH Keywords: system thermodynamics
zbMATH Keywords: energy flow
zbMATH Keywords: interconnected systems
zbMATH Keywords: entropy
zbMATH Keywords: Helmholtz free energy
zbMATH Keywords: Gibbs free energy
zbMATH Keywords: chemical thermodynamics
zbMATH Keywords: mass action kinetics
zbMATH Keywords: chemical potential
zbMATH Keywords: neuroscience and thermodynamics
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3390/e15051821
OpenAlex ID: W2147565203
cites work: Q3880798
cites work: Q5462974
cites work: Time-reversal symmetry, Poincaré recurrence, irreversibility, and the entropic arrow of time: From mechanics to system thermodynamics
cites work: Temporal asymmetry, entropic irreversibility, and finite-time thermodynamics: from Parmenides-Einstein time-reversal symmetry to the Heraclitan entropic arrow of time
cites work: Q5440982
cites work: Q3933274
cites work: Stability and dissipativity theory for nonnegative dynamical systems: a unified analysis framework for biological and physiological systems
cites work: Modeling and analysis of mass-action kinetics
cites work: Q4883939
cites work: Multistability, bifurcations, and biological neural networks: A synaptic drive firing model for cerebral cortex transition in the induction of general anesthesia
DOI: 10.3390/E15051821
description: scientific article; zbMATH DE number 6346140