Applications of Kramers Escape Rate Theory With Power-Law Distributions

Yanjun Zhou

doi:10.19142/rpq.v9i18.339

Yanjun Zhou Unidade Universitária de Ciências Exatas e Tecnológicas, Universidade Estadual de Goiás (UEG), Anápolis

DOI: https://doi.org/10.19142/rpq.v9i18.339

Palavras-chave: Kramers escape rate theory. Power-law distribution.

Resumo

Kramers escape rate theory is the most important one of modern reaction rate theories. However, one key assumption of the theory that thermodynamic equilibrium must prevail throughout the entire system studied is farfetched for open complex systems. Thereby, Kramers escape rates are generalized to describe rates of reactions in nonequilibrium systems with power-law distributions. Kramers escape rates in the very low damping systems, in overdamped systems and in the low-to-intermediate damping (LID) systems are investigated and the corresponding escape rates are obtained respectively on the basis of nonextensive statistics. When apply to biological, physical and chemical systems in each damping systems, these generalized escape rates with power-law distribution show a better agreement with experimental rates as compared with the traditional Kramers escape rates. It is expected that the generalized result can lead to an insight into the research on reaction rate theory for nonequilibrium complex systems with power-law distributions.

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