Temporal asymmetry, entropic irreversibility, and finite-time thermodynamics: from Parmenides-Einstein time-reversal symmetry to the Heraclitan entropic arrow of time
type: Item
instance of: scholarly article
title: Temporal asymmetry, entropic irreversibility, and finite-time thermodynamics: from Parmenides-Einstein time-reversal symmetry to the Heraclitan entropic arrow of time
zbMATH Open document ID: 1310.37017
author: Wassim M. Haddad
published in: Entropy
publication date: 2014-09-08T00:00:00Z
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 we develop a state-space dynamical system model that captures the key aspects of thermodynamics, including its fundamental laws. In addition, we establish the existence of a unique, continuously differentiable global entropy function for our dynamical system model, and using Lyapunov stability theory we show that the proposed thermodynamic model has finite-time convergent trajectories to Lyapunov stable equilibria determined by the system initial energies. Finally, using the system entropy, we establish the absence of Poincaré recurrence for our thermodynamic model and develop clear and rigorous connections between irreversibility, the second law of thermodynamics, and the entropic arrow of time.
Mathematics Subject Classification ID: 37D45
Mathematics Subject Classification ID: 82C03
Mathematics Subject Classification ID: 82C21
zbMATH DE Number: 6340969
zbMATH Keywords: energy
zbMATH Keywords: entropy
zbMATH Keywords: irreversibility
zbMATH Keywords: arrow of time
zbMATH Keywords: Poincaré recurrence
zbMATH Keywords: finite-time semistability
zbMATH Keywords: interconnected systems
zbMATH Keywords: state space formalism
zbMATH Keywords: relativistic thermodynamics
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3390/e14030407
OpenAlex ID: W1988508167
cites work: Q5462974
cites work: Q5809127
cites work: Bluff your way in the second law of thermodynamics
cites work: Time-reversal symmetry in dynamical systems: a survey
cites work: Time-reversal symmetry, Poincaré recurrence, irreversibility, and the entropic arrow of time: From mechanics to system thermodynamics
cites work: Nontangency-Based Lyapunov Tests for Convergence and Stability in Systems Having a Continuum of Equilibria
cites work: Finite-Time Stability of Continuous Autonomous Systems
cites work: Q3871201
cites work: Q4274968
cites work: Q5520199
cites work: Q5848416
cites work: Geometric homogeneity with applications to finite-time stability
cites work: Homogeneous Lyapunov function for homogeneous continuous vector field
cites work: Q5440982
cites work: Q3943082
DOI: 10.3390/E14030407
description: scientific article; zbMATH DE number 6340969