Power-law Fokker–Planck equation of unimolecular reaction based on the approximation to master equation

• We obtain a generalized expression of the Fokker–Planck equation of the unimolecular reaction.
• The steady-state solution of FPE and microscopic dynamics Ito–Langevin equation of concentration variables are given.
• Two unimolecular reactions are taken as examples.

The Fokker–Planck equation (FPE) of the unimolecular reaction with Tsallis distribution is established by means of approximation to the master equation. The memory effect, taken into transition probability, is relevant and important for lots of anomalous phenomena. The Taylor expansion for large volume is applied to derive the power-law FPE. The steady-state solution of FPE and microscopic dynamics Ito–Langevin equation of concentration variables are therefore obtained and discussed. Two unimolecular reactions are taken as examples and the concentration distributions with different power-law parameters are analyzed, which may imply strong memory effect of hopping process.