TL;DR
This paper extends Kramers' reaction rate theory using nonextensive formalism, analyzing its behavior in different viscosity regimes and applying it to protein reactions, showing nonextensivity's significant role.
Contribution
It introduces a nonextensive generalization of Kramers' rate, exploring its viscosity dependence and relation to experimental protein reaction data.
Findings
Nonextensive Kramers' rate proportional to friction in high viscosity limit
Inverse proportionality in low viscosity limit
Linear relation between ordinary and nonextensive rates
Abstract
The Kramers' survival probability has been generalized by using nonextensive formalism. This nonextensive survival probability is studied in detail and associated Kramers' rate has been calculated in the high and low viscosity limit. It has been showed that the proportionality of nonextensive Kramers' rate to the nonextensive friction term in the high viscosity limit changes to inverse proportionality in the low viscosity limit. It has also been observed that friction constant of nonextensive processes is of rescaled form of the ordinary frictional term. Since the relation between the ordinary rate and nonextensive rate is found out to be linear, the Arrhenius nature of the Kramers' rate is preserved. By using experimental results related to CO rebinding to myoglobin after photodissociation, we conclude that nonextensivity plays an important role in protein reactions.
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