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Correlation Entropy and Power-Law Kinetics
1Department of Electrical and Electronics Engineering, Ariel University, Ariel 40700, Israel.
Entropy (Basel, Switzerland)
|June 26, 2026
Summary
This study introduces a thermodynamic hypothesis explaining power-law kinetics using correlation-dependent Gibbs free energy. A novel Correlation Constant (χ) links entropy and free energy to kinetic evolution in diverse systems.
Area of Science:
- Thermodynamics
- Chemical Kinetics
- Statistical Mechanics
Background:
- Power-law kinetics are prevalent in various scientific and engineering fields.
- The thermodynamic underpinnings of the power-law exponent are not fully understood.
- Existing models do not fully capture the thermodynamic origins of these kinetics.
Purpose of the Study:
- To propose a thermodynamic hypothesis for the emergence of power-law kinetics.
- To introduce a novel framework connecting entropy, free energy, and kinetic evolution.
- To provide a unified thermodynamic interpretation for diverse evolving processes.
Main Methods:
- Development of a phenomenological model incorporating correlation-dependent contributions to Gibbs free energy.
- Introduction of a Correlation Constant (χ) to quantify microstate evolution's influence on state accessibility.
- Modification of transition probabilities based on correlation entropy contributions.
Main Results:
- Power-law behavior naturally emerges from correlation-dependent free energy contributions.
- The Correlation Constant (χ) quantifies cooperative (χ > 0) or self-limiting (χ < 0) evolutionary behavior.
- The conventional Arrhenius-Eyring model is a special case (χ = 0).
Conclusions:
- The proposed framework offers a thermodynamic interpretation of the power-law exponent.
- Establishes a direct link between entropy, free energy, and kinetic evolution.
- Provides a unified thermodynamic description for processes like degradation, diffusion, and fatigue.
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