Data Set Models and Exponential Families in Statistical Physics and Beyond

Abstract

The exponential family of models is defined in a general setting, not relying on probability theory. Some results of information geometry are shown to remain valid. Exponential families both of classical and of quantum mechanical statistical physics fit into the new formalism. Other less obvious applications are predicted. For instance, quantum states can be modeled as points in a classical phase space and the resulting model belongs to the exponential family.

References in corpus (4)

• The q-exponential family in statistical physics
• Generalised exponential families and associated entropy functions
• Geometric study for the Legendre duality of generalized entropies and its application to the porous medium equation
• Information Geometry of q-Gaussian Densities and Behaviors of Solutions to Related Diffusion Equations

Cited by in corpus (3)

• The exponential family in abstract information theory
• Extension of Information Geometry to Non-statistical Systems: Some Examples
• Score-Aware Policy-Gradient and Performance Guarantees using Local Lyapunov Stability