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This study introduces novel statistical models based on exponential families with external parameters, derived from the Maximum Entropy framework. These models offer new insights into thermodynamic systems and quantitative genetics dynamics.

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Area of Science:

  • Statistical Modeling
  • Information Geometry
  • Theoretical Physics
  • Quantitative Genetics

Background:

  • Exponential families are fundamental in statistics, often linked to the Maximum Entropy framework.
  • Thermal and mechanical parameters play distinct roles in statistical physics and information theory.

Purpose of the Study:

  • Introduce a new class of statistical models incorporating external parameters.
  • Explore the geometric properties of these models.
  • Investigate evolutionary dynamics described by Fokker-Planck equations with these models.

Main Methods:

  • Development of statistical models based on exponential families and external parameters.
  • Geometric analysis using fibration of parameter space.
  • Solution of Fokker-Planck equations for stationary distributions.
  • Application to thermodynamic and genetic models.

Main Results:

  • Characterization of the geometry of statistical models with external parameters.
  • Identification of Fokker-Planck equations with stationary distributions as exponential families.
  • Demonstration of applications in thermodynamics and quantitative genetics.

Conclusions:

  • The proposed statistical models provide a unified framework for diverse applications.
  • External parameters offer a new perspective on the structure and dynamics of statistical systems.
  • The findings have implications for understanding thermodynamic evolution and genetic trait dynamics.