The collision theory reaction rate coefficient for power-law distributions

• The collision theory reaction rate coefficient for power-law distributions is derived.
• The power-law rate coefficient strongly depends on the power-law parameter.
• The new collision theory can overcome the difficulties in the Lindemann–Christiansen mechanism.
• The new pre-exponential factor calculated is exactly in agreement with the measurements of experimental studies.

The collision theory for power-law distributions and the generalized reaction rate coefficient are studied when reactions take place in nonequilibrium systems with power-law distributions. We obtain the power-law reaction rate coefficient, and by numerical analyses we show a very strong dependence of the rate coefficient on the power-law parameter. We find that the power-law collision theory can successfully overcome the two difficulties of the Lindemann–Christiansen mechanism. We take three reactions as examples to calculate the new pre-exponential factor and yield the values that can be exactly in agreement with those measured in the experimental studies.