[Paper Review] Nonequilibrium Thermodynamics and Lifetime of Physical Systems

V. V. Ryazanov, S. Shpyrko|arXiv (Cornell University)|Jun 16, 2004

Advanced Thermodynamics and Statistical Mechanics9 references5 citations

TL;DR

This paper introduces the lifetime of a physical system as a new thermodynamic parameter to describe nonequilibrium states, deriving expressions for nonequilibrium entropy, temperature, and entropy production using stochastic mesoscopic dynamics. It generalizes Maxwell-Cattaneo relations to mass transfer and chemical reactions, showing consistency with extended irreversible thermodynamics at small fluxes.

ABSTRACT

To describe the nonequilibrium states of a system we introduce a new thermodynamic parameter - the lifetime of a system. The statistical distributions which can be obtained out of the mesoscopic description characterizing the behaviour of a system by specifying the stochastic processes are written down. The expressions for the nonequilibrium entropy, temperature and entropy production are obtained, which at small values of fluxes coincide with those derived within the frame of extended irreversible thermodynamics. The expressions generalizing the Maxwell-Cattaneo relations of extended irreversible thermodynamics, and their analogues for mass transfer and chemical reactions are obtained.

Motivation & Objective

• To develop a thermodynamic framework for nonequilibrium systems beyond equilibrium assumptions.
• To address the lack of a systematic parameter describing the temporal evolution of nonstationary physical systems.
• To derive consistent expressions for nonequilibrium entropy, temperature, and entropy production from mesoscopic stochastic dynamics.
• To generalize extended irreversible thermodynamics relations (e.g., Maxwell-Cattaneo) to mass transfer and chemical reactions.
• To establish a theoretical basis for the lifetime of a system as a fundamental thermodynamic variable in nonequilibrium states.

Proposed method

• Introduces the lifetime of a system as a new thermodynamic parameter derived from mesoscopic stochastic processes.
• Uses a mesoscopic description based on stochastic dynamics to model the evolution of physical systems out of equilibrium.
• Derives expressions for nonequilibrium entropy and temperature by analyzing the statistical distribution of system states.
• Formulates entropy production rate using the lifetime parameter and fluxes, consistent with extended irreversible thermodynamics.
• Generalizes the Maxwell-Cattaneo relation to include mass flux and chemical reaction fluxes via the lifetime parameter.
• Applies the formalism to systems with heat, mass, and chemical fluxes, deriving generalized transport equations.

Experimental results

Research questions

• RQ1 How can the lifetime of a physical system be defined as a thermodynamic variable in nonequilibrium states?
• RQ2 What are the expressions for nonequilibrium entropy, temperature, and entropy production when lifetime is included?
• RQ3 How do the generalized Maxwell-Cattaneo relations extend to mass transfer and chemical reactions?
• RQ4 In what limit do the derived expressions reduce to those in extended irreversible thermodynamics?
• RQ5 Can the lifetime parameter unify the description of relaxation in diverse nonequilibrium processes?

Key findings

• The lifetime of a system is introduced as a fundamental thermodynamic parameter that characterizes the temporal evolution of nonequilibrium states.
• The derived expressions for nonequilibrium entropy, temperature, and entropy production reduce to those in extended irreversible thermodynamics for small fluxes.
• Generalized Maxwell-Cattaneo-type relations are obtained for heat, mass, and chemical reaction fluxes, incorporating the lifetime parameter.
• The formalism provides a consistent framework for describing relaxation dynamics in systems with multiple coupled fluxes.
• The lifetime parameter enables a unified description of relaxation in physical, chemical, and material systems under nonequilibrium conditions.
• The approach is grounded in mesoscopic stochastic dynamics, ensuring statistical consistency and physical interpretability.