Mapping the master equation of 3-state systems on the 2-sphere

Authors

  • Joaquin Nicholas C. Mercado ⋅ PH National Institute of Physics, University of the Philippines Diliman
  • Michael Francis Ian G. Vega II ⋅ PH National Institute of Physics, University of the Philippines Diliman

Abstract

Motivated by information geometry, we map 3-state stochastic systems to the 2-sphere in order to write the master equations as a dynamical system on a 2-sphere in terms of angular coordinates. We provide a framework for finding the angular coordinates for the equilibrium points of the dynamical system, which involves obtaining the physical solutions of a cubic equation. When performing linearization on the dynamical system, the eigenvalues of the dynamical system are shown to always have a negative real-part. Hence, mapping the master equation to the 2-sphere can provide a way to interpret spiral trajectories on a sphere in terms of stochastic thermodynamics.

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Issue

Article ID

SPP-2024-PC-23

Section

Poster Session C (Theoretical and Mathematical Physics)

Published

2024-06-28

How to Cite

[1]
JNC Mercado and MFIG Vega, Mapping the master equation of 3-state systems on the 2-sphere, Proceedings of the Samahang Pisika ng Pilipinas 42, SPP-2024-PC-23 (2024). URL: https://proceedings.spp-online.org/article/view/SPP-2024-PC-23.