Author(s): Wassim M. Haddad
Journal: Entropy
ISSN 1099-4300
Volume: 14;
Issue: 3;
Start page: 407;
Date: 2012;
Original page
Keywords: energy | entropy | irreversibility | arrow of time | poincaré recurrence | finite-time semistability | interconnected systems | state space formalism | relativistic thermodynamics
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.
Journal: Entropy
ISSN 1099-4300
Volume: 14;
Issue: 3;
Start page: 407;
Date: 2012;
Original page
Keywords: energy | entropy | irreversibility | arrow of time | poincaré recurrence | finite-time semistability | interconnected systems | state space formalism | relativistic thermodynamics
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.
