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Related Experiment Video

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Setting Limits on Supersymmetry Using Simplified Models

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Published on: November 15, 2013

Symmetry Classes of Classical Stochastic Processes.

Lucas Sá¹, Pedro Ribeiro^2,3, Tomaž Prosen^4,5

¹TCM Group, Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, Cambridge, CB3 0HE UK.

Journal of Statistical Physics

|March 17, 2025

Summary

This summary is machine-generated.

This study systematically classifies symmetries in classical stochastic processes, revealing new dynamics like Kramers degeneracy and dihedral spectral symmetry. The research extends existing schemes and identifies solvable models, opening avenues for further exploration.

Keywords:

Markov generator Non-Hermitian physics Stochastic processes Symmetry classes

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Area of Science:

Mathematical Physics
Statistical Mechanics
Probability Theory

Background:

Classical stochastic processes are fundamental to modeling complex systems.
Understanding the symmetries of Markov generators is crucial for analyzing process dynamics.
Existing classification schemes require extension to encompass classical stochastic processes.

Purpose of the Study:

To systematically classify the symmetries of Markov generators for classical stochastic processes.
To extend the Bernard-LeClair scheme to this domain.
To identify new dynamical properties and solvable models.

Main Methods:

Systematic symmetry classification using involutive transformations.
Construction of solution families for specific symmetry classes.
Application of stochastic optimization algorithms to find generators in challenging classes.

Main Results:

A classification scheme yielding up to fifteen allowed symmetry classes for Markov generators.
Construction of solutions for five classes, interpretable as particle hopping on multipartite graphs.
Identification of generators in six additional classes using optimization, with four classes remaining open.

Conclusions:

Symmetry classification reveals new possibilities in classical stochastic processes dynamics.
Observed phenomena include Kramers degeneracy, dihedral spectral symmetry, and novel time reversal properties.
The study provides a framework for exploring complex stochastic systems and their underlying symmetries.