vix.ing · top · new · best · stats · spec

Multiple phases in stochastic dynamics: Geometry and probabilities

2006/03/24 by Bernard Gaveau, B. Gaveau, L. S. Schulman · 2 citations
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.other #cond-mat.stat-mech

paper · pdf · doi:10.1103/physreve.73.036124

published as Phys. Rev. E 73, 036124 (2006)

openalex publication_date 2006/03/24 · arxiv created 2006/04/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Stochastic dynamics is generated by a matrix of transition probabilities. Certain eigenvectors of this matrix provide observables, and when these are plotted in the appropriate multidimensional space the phases (in the sense of phase transitions) of the underlying system become manifest as extremal points. This geometrical construction, which we call an observable representation of state space, can allow hierarchical structure to be observed. It also provides a method for the calculation of the probability that an initial points ends in one or another asymptotic state.

Cited by