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Entropy 2012, 14(3), 407-455; doi:10.3390/e14030407
Article

Temporal Asymmetry, Entropic Irreversibility, and Finite-Time Thermodynamics: From Parmenides–Einstein Time-Reversal Symmetry to the Heraclitan Entropic Arrow of Time

Received: 3 February 2012; Accepted: 17 February 2012 / Published: 28 February 2012
(This article belongs to the Special Issue Arrow of Time)
Download PDF [356 KB, uploaded 28 February 2012]
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 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.
Keywords: energy; entropy; irreversibility; arrow of time; poincaré recurrence; finite-time semistability; interconnected systems; state space formalism; relativistic thermodynamics energy; entropy; irreversibility; arrow of time; poincaré recurrence; finite-time semistability; interconnected systems; state space formalism; relativistic thermodynamics
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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MDPI and ACS Style

Haddad, W.M. Temporal Asymmetry, Entropic Irreversibility, and Finite-Time Thermodynamics: From Parmenides–Einstein Time-Reversal Symmetry to the Heraclitan Entropic Arrow of Time. Entropy 2012, 14, 407-455.

AMA Style

Haddad WM. Temporal Asymmetry, Entropic Irreversibility, and Finite-Time Thermodynamics: From Parmenides–Einstein Time-Reversal Symmetry to the Heraclitan Entropic Arrow of Time. Entropy. 2012; 14(3):407-455.

Chicago/Turabian Style

Haddad, Wassim M. 2012. "Temporal Asymmetry, Entropic Irreversibility, and Finite-Time Thermodynamics: From Parmenides–Einstein Time-Reversal Symmetry to the Heraclitan Entropic Arrow of Time." Entropy 14, no. 3: 407-455.


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