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The Price Equation Program: Simple Invariances Unify Population Dynamics, Thermodynamics, Probability, Information
1Department of Ecology and Evolutionary Biology, University of California, Irvine, CA 92697-2525, USA.
Entropy (Basel, Switzerland)
|December 3, 2020
Summary
The Price equation reveals a universal mathematical structure underlying diverse scientific disciplines. It unifies concepts like natural selection, thermodynamics, and mechanics by separating frequency and value in dynamic systems.
Area of Science:
- Cross-disciplinary mathematics
- Theoretical physics
- Evolutionary biology
Background:
- Fundamental equations across disciplines (e.g., natural selection, Bayesian updating, thermodynamics, mechanics) exhibit similar mathematical structures.
- Analogies exist between information theory, entropy, and physical mechanics (e.g., Newtonian force-acceleration balance).
- These similarities suggest a deeper, unifying mathematical framework.
Purpose of the Study:
- To identify and articulate a universal mathematical structure underlying diverse scientific equations.
- To propose the Price equation as the expression of this underlying universal structure.
- To demonstrate how this structure explains common forms in equations across different fields.
Main Methods:
- Utilizing an abstract formulation of the Price equation to describe dynamics.
- Analyzing the Price equation's separation of frequency and value, analogous to Shannon's information theory.
- Identifying universal invariances and geometric aspects of change derived from this separation.
Main Results:
- The Price equation provides a generalized framework separating the change in frequency of entities from the change in their values.
- This separation reveals simple invariances, such as the conservation of total frequency.
- These invariances impose constraints that explain the common structural forms observed in equations across various scientific disciplines.
Conclusions:
- The Price equation offers a unifying mathematical perspective for diverse scientific phenomena.
- Concepts like natural selection, information, entropy, force, and physical work can be understood as arising from this shared geometric structure.
- This framework provides a deeper understanding of the interconnectedness of scientific laws.
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