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Toward a universal theory of stable evolution.

¹Department of Theoretical Physics, Wigner Research Centre for Physics, H-1525, Konkoly Thege Miklós u. 29-33, Budapest, Hungary.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences

|June 19, 2023

Summary

This summary is machine-generated.

Thermodynamics provides a stability structure linking entropy to equilibrium, explaining natural selection. These universal thermodynamic concepts and mathematical tools can model dynamical theories across all sciences.

Keywords:

Lyapunov stability absolute temperature evolution equation non-equilibrium thermodynamics universality

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Area of Science:

Thermodynamics
Complex Systems Science
Theoretical Physics

Background:

Non-equilibrium thermodynamics relies on a stability structure, where entropy acts as a Lyapunov function.
System stability is fundamental to natural selection, determining survival and transience.
The universality of thermodynamic concepts allows broad applicability.

Purpose of the Study:

To explore the universal applicability of thermodynamic stability structures.
To demonstrate how thermodynamics can unify natural and social sciences.
To introduce the formalism of constrained entropy inequality.

Main Methods:

Analysis of the stability structure in non-equilibrium thermodynamics.
Application of Lyapunov function principles to entropy.
Utilizing the formalism of constrained entropy inequality.

Main Results:

Established a direct link between entropy and Lyapunov functions in thermodynamic equilibrium.
Demonstrated that stability is the basis for natural selection and system survival.
Confirmed the universal nature of thermodynamic concepts and mathematical tools.

Conclusions:

Thermodynamic stability structures offer a universal framework for understanding complex systems.
The principles of non-equilibrium thermodynamics can be applied to formulate dynamical theories in both natural and social sciences.
This work bridges natural and social sciences through the lens of thermodynamics.