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Entropic Dynamics on Gibbs Statistical Manifolds
Pedro Pessoa1, Felipe Xavier Costa1, Ariel Caticha1
1Department of Physics, University at Albany (SUNY), Albany, NY 12222, USA.
Entropy (Basel, Switzerland)
|April 30, 2021
Summary
Entropic dynamics derives physical laws from probabilistic inference. This study applies entropic methods to statistical manifolds, introducing an intrinsic, directional "entropic time" for systems.
Area of Science:
- Theoretical Physics
- Statistical Mechanics
- Information Geometry
Background:
- Entropic dynamics offers a framework for deriving physical laws from probabilistic principles.
- Previous successes include deriving quantum mechanics and quantum field theory.
- The dynamics of a system can be viewed on a statistical manifold.
Purpose of the Study:
- To develop entropic dynamics for systems described by probability distributions.
- To investigate the role of statistical manifold geometry, specifically curvature, in entropic dynamics.
- To explore an intrinsic, system-tailored notion of 'entropic time'.
Main Methods:
- Utilizing information geometry to define a metric structure on the statistical manifold.
- Focusing the dynamics on the statistical manifold of Gibbs (exponential family) distributions.
- Developing a system-specific 'entropic time' as an intrinsic measure of temporal progression.
Main Results:
- The dynamics unfold on a statistically manifold endowed with a natural metric structure.
- The curvature of the statistical manifold significantly influences the dynamics.
- An intrinsic, directional 'entropic time' emerges, driven by entropic considerations.
Conclusions:
- Entropic dynamics can be effectively applied to systems described by probability distributions on statistical manifolds.
- The geometric properties of these manifolds are crucial for understanding the resulting dynamics.
- The concept of entropic time provides a natural arrow of time rooted in entropic principles.
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