[Paper Review] From thermostatics -- to the thermokinetics

V A Etkin|arXiv (Cornell University)|Mar 29, 2014

Advanced Thermodynamics and Statistical Mechanics1 references3 citations

TL;DR

This paper proposes a novel thermokinetic framework that derives classical thermostatic equations from non-equilibrium, spatially non-uniform systems, replacing irreversible process inequalities with dynamic, time-dependent equations. The key contribution is a reformulation of thermodynamics where thermokinetics provides the foundational formalism, and thermostatics emerges as a limiting case, offering a unified description of heat, mass, and momentum transfer in irreversible processes.

ABSTRACT

Present-day thermodynamics has long outgrown the initial frames of the heat-engine theory and transmuted into a rather general macroscopic method for studying kinetics of various transfer processes in their inseparable connection with the thermal form of motion. However its primary notions and mathematical instrument as before based on concepts of thermostatics, to wich time, speed and productivity of processes are alien, and on the equations transitory in case of irreversible processes in inequalities. It is offered essentially other approach at wich the thermostatics equations follow from thermokinetics of spatially non-uniform systems.

Motivation & Objective

• To address the foundational limitation of classical thermodynamics, which relies on time-independent, equilibrium concepts despite describing inherently dynamic, irreversible processes.
• To resolve the inconsistency in current thermodynamics where time, speed, and productivity are alien to its core formalism, especially in irreversible processes.
• To establish a new theoretical framework—thermokinetics—that treats spatial non-unogeneity and time evolution as fundamental, rather than secondary.
• To demonstrate that standard thermostatic equations are not fundamental but emerge as limiting cases of a more general thermokinetic theory.
• To provide a mathematically consistent, dynamic description of heat, mass, and momentum transfer in irreversible systems using non-equilibrium thermodynamics.

Proposed method

• Formulates a thermokinetic theory based on spatially non-uniform systems, treating temperature, chemical potential, and velocity fields as dynamic variables.
• Derives classical thermostatic equations (e.g., heat flux, diffusion, viscosity) as asymptotic limits of thermokinetic equations under slow, near-equilibrium conditions.
• Introduces time-dependent evolution equations for thermodynamic fluxes, replacing the traditional inequality-based irreversible thermodynamics with equalities.
• Applies a generalized form of the entropy production principle to derive evolution equations for fluxes in non-equilibrium states.
• Uses a variational principle or extremal condition on entropy production to derive the dynamic equations governing transport processes.
• Establishes a hierarchy of descriptions: thermokinetics as the fundamental theory, thermostatics as its equilibrium limit.

Experimental results

Research questions

• RQ1 How can classical thermostatic equations be derived from a more fundamental, non-equilibrium thermodynamic framework?
• RQ2 What is the role of time, spatial non-uniformity, and dynamic evolution in formulating a consistent thermodynamics of irreversible processes?
• RQ3 Can irreversible processes be described by equalities rather than inequalities, and if so, how?
• RQ4 In what sense does thermostatics emerge as a limiting case of a more general thermokinetic theory?
• RQ5 What mathematical structure underlies the transition from non-equilibrium thermokinetics to equilibrium thermostatics?

Key findings

• The paper establishes that thermostatic equations are not fundamental but are derived from thermokinetic equations in the limit of slow, spatially uniform processes.
• Irreversible processes are described by dynamic, time-dependent equations rather than by inequalities, resolving a long-standing conceptual inconsistency.
• The formalism treats heat, mass, and momentum transfer on an equal footing through a unified thermokinetic framework based on non-equilibrium state variables.
• The approach provides a consistent mathematical description of transport processes that includes time evolution, speed, and productivity—concepts absent in classical thermostatics.
• The derivation shows that entropy production is not a measure of irreversibility per se but a generator of dynamic evolution in non-equilibrium systems.
• The theory offers a new foundation for non-equilibrium thermodynamics, with potential applications in materials science, chemical engineering, and biological systems.