Coarse graining of master equations with fast and slow states

Abstract

We propose a general method for simplifying master equations by eliminating from the description rapidly evolving states. The physical recipe we impose is the suppression of these states and a renormalization of the rates of all the surviving states. In some cases, this decimation procedure can be analytically carried out and is consistent with other analytical approaches, like in the problem of the random walk in a double-well potential. We discuss the application of our method to nontrivial examples: diffusion in a lattice with defects and a model of an enzymatic reaction outside the steady state regime.

9 pages, 9 figures, final version (new subsection and many minor improvements)

References in corpus (7)

• Community structure in social and biological networks
• Detecting fuzzy community structures in complex networks with a Potts model
• Strong disorder RG approach of random systems
• Stochastic models in population biology and their deterministic analogs
• Spectral coarse-graining of complex networks
• Oscillations and temporal signalling in cells
• Eddy diffusivities in scalar transport

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