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dc.contributor.author
Gomez, Ignacio Sebastián
dc.date.available
2018-11-02T21:37:42Z
dc.date.issued
2017-10
dc.identifier.citation
Gomez, Ignacio Sebastián; Notions of the ergodic hierarchy for curved statistical manifolds; Elsevier Science; Physica A: Statistical Mechanics and its Applications; 484; 10-2017; 117-131
dc.identifier.issn
0378-4371
dc.identifier.uri
http://hdl.handle.net/11336/63579
dc.description.abstract
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 notion of statistical independence between the microscopical variables of the system. Moreover, we establish an intimately relationship between statistical models and families 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 the results with two examples: a pair of interacting harmonic oscillators presenting phase transitions and the 2×2 Gaussian ensembles. In both examples the scalar curvature results a global indicator of the dynamics.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
Elsevier Science
dc.rights
info:eu-repo/semantics/openAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.subject
2d Correlated Model
dc.subject
Canonical Ensemble
dc.subject
Ergodic Hierarchy
dc.subject
Igeh
dc.subject
Information Geometry
dc.subject
Statistical Models
dc.subject.classification
Astronomía
dc.subject.classification
Ciencias Físicas
dc.subject.classification
CIENCIAS NATURALES Y EXACTAS
dc.title
Notions of the ergodic hierarchy for curved statistical manifolds
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2018-10-22T21:47:10Z
dc.journal.volume
484
dc.journal.pagination
117-131
dc.journal.pais
Países Bajos
dc.journal.ciudad
Amsterdam
dc.description.fil
Fil: Gomez, Ignacio Sebastián. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; Argentina
dc.journal.title
Physica A: Statistical Mechanics and its Applications
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.1016/j.physa.2017.05.012
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0378437117305149
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