The fundamental equations of change in statistical ensembles and biological populations

Abstract

A recent article in Nature Physics unified key results from thermodynamics, statistics, and information theory. The unification arose from a general equation for the rate of change in the information content of a system. The general equation describes the change in the moments of an observable quantity over a probability distribution. One term in the equation describes the change in the probability distribution. The other term describes the change in the observable values for a given state. We show the equivalence of this general equation for moment dynamics with the widely known Price equation from evolutionary theory, named after George Price. We introduce the Price equation from its biological roots, review a mathematically abstract form of the equation, and discuss the potential for this equation to unify diverse mathematical theories from different disciplines. The new work in Nature Physics and many applications in biology show that this equation also provides the basis for deriving many novel theoretical results within each discipline.

References in corpus (8)

• Natural selection. IV. The Price equation
• Natural selection maximizes Fisher information
• Time-information uncertainty relations in thermodynamics
• The Price equation program: simple invariances unify population dynamics, thermodynamics, probability, information and inference
• A simple derivation and classification of common probability distributions based on information symmetry and measurement scale
• Universal expressions of population change by the Price equation: natural selection, information, and maximum entropy production
• Common probability patterns arise from simple invariances
• d'Alembert's direct and inertial forces acting on populations: the Price equation and the fundamental theorem of natural selection

Cited by in corpus (6)

• Unifying Quantum and Classical Speed Limits on Observables
• Geometric thermodynamics for the Fokker-Planck equation: Stochastic thermodynamic links between information geometry and optimal transport
• Universal constraint on nonlinear population dynamics
• Limits on the Evolutionary Rates of Biological Traits
• Thermodynamics of Evolution and the Origin of Life
• Causal attribution by the chain rule: unifying natural selection, learning, economics, and other disciplines