Multiple phases in stochastic dynamics: geometry and probabilities

Details Multiple phases in stochastic dynamics: geometry and probabilities Multiple phases in stochastic dynamics: geometry and probabilities

2006-04-06

arxiv.org/abs/cond-mat/0604159v1

Phys. Rev. E 73, 036124 (2006)

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

10.1103/PhysRevE.73.036124

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 multi-dimensional 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 \textit{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.

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