temporal asymmetry, entropic irreversibility, and finite-time thermodynamics from parmenides–einstein time-reversal symmetry to the heraclitan entropic arrow of time时间不对称,热力学熵的不可逆性,限定时间从逆时对称parmenides-einstein heraclitan熵的时间之箭.pdf
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Entropy 2012, 14, 407-455; doi:10.3390/
OPEN ACCESS
entropy
ISSN 1099-4300
/journal/entropy
Article
Temporal Asymmetry, Entropic Irreversibility, and Finite-Time
Thermodynamics: From Parmenides–Einstein Time-Reversal
Symmetry to the Heraclitan Entropic Arrow of Time
Wassim M. Haddad
The School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA;
E-Mail: wm.haddad@; Tel.: +1-404-894-1078; Fax: +1-404-894-2760
Received: 3 February 2012 / Accepted: 17 February 2012 / Published: 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 Poincare recurrence for our thermodynamic model and develop clear and rigorous
connections between irreversibili
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