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Unraveling Entropic Rate Acceleration Induced by Solvent Dynamics in Membrane Enzymes

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Entropy Maximization, Time Emergence, and Phase Transition.

Jonathan Smith¹

¹Department of Mathematics, Iowa State University, 411 Morrill Rd., Ames, IA 50011, USA.

Entropy (Basel, Switzerland)

|June 26, 2025

Summary

This summary is machine-generated.

Entropy maximization with the Gibbs Canonical Ensemble offers new insights into finite systems. This approach reinterprets temperature as ecological age, modeling biological competition and phase transitions effectively.

Keywords:

canonical ensemble carrying capacity entropy maximization negative temperature order parameter phase transition phenomenological rate equation predator–prey thermodynamic limit two-person game

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Area of Science:

Statistical Mechanics
Theoretical Physics
Mathematical Biology

Background:

The Gibbs Canonical Ensemble is a fundamental tool in statistical mechanics for describing systems in thermal equilibrium.
Applying the ensemble to finite, non-equilibrium systems, particularly in biology, presents significant theoretical challenges.
Traditional interpretations of thermodynamic variables may require re-evaluation in novel contexts.

Purpose of the Study:

To explore recent advancements in using entropy maximization to apply the Gibbs Canonical Ensemble to finite systems.
To investigate the physical and biological implications of this approach, particularly in game-theoretic and ecological models.
To re-evaluate the role and interpretation of Lagrange multipliers within this framework.

Main Methods:

Survey of developments in entropy maximization techniques for the Gibbs Canonical Ensemble.
Application of a game-theoretic approach with predator-prey roles for symmetric analysis.
Utilizing natural physical units (Planck's constant = 1) and focusing on the Lagrange multiplier method.

Main Results:

Energy is shown to have dimensions of inverse time, leading to Lagrange multipliers with time units, representing the 'Arrow of Time'.
Negative temperature singularities are eliminated in quantum optics models with bounded energy levels.
The Canonical Ensemble successfully models species competition, with the Lagrange multiplier quantifying 'ecological age' and describing phase transitions.

Conclusions:

Entropy maximization provides a robust framework for applying the Gibbs Canonical Ensemble to finite biological and physical systems.
The reinterpretation of Lagrange multipliers as measures of 'ecological age' offers novel insights into biological dynamics.
This approach successfully models complex phenomena like phase transitions in finite systems without requiring a thermodynamic limit.