IFLP   13074
INSTITUTO DE FISICA LA PLATA
Unidad Ejecutora - UE
artículos
Título:
Notions of the ergodic hierarchy for curved statistical manifolds
Autor/es:
IGNACIO SEBASTIÁN GOMEZ
Revista:
PHYSICA A - STATISTICAL AND THEORETICAL PHYSICS
Editorial:
ELSEVIER SCIENCE BV
Referencias:
Lugar: Amsterdam; Año: 2017 vol. 484 p. 117 - 131
ISSN:
0378-4371
Resumen:
We present an extension of the ergodic, mixing, and Bernoulli levels of the ergodic hierarchy for statistical models on curved manifolds, making use of elements of the information geometry. This extension focuses on the notionof statistical independence between the microscopical variables of the system. Moreover, we establish an intimately relationship between statistical models and family of probability distributions belonging to the canonical ensemble, which for the case of the quadratic Hamiltonian systems provides a closed form for the correlations between the microvariables in terms of the temperature of the heat bath as a power law. From this we obtain an information geometric method for studying Hamiltonian dynamics in the canonical ensemble. We illustrate theresults with two examples: a pair of interacting harmonic oscillators presenting phase transitions and the 2x2 Gaussian ensembles. In both examples the scalar curvature results a global indicator of the dynamics.