Inspired by problems in biochemical kinetics, we study statistical properties of an overdamped Langevin processes with the friction coefficient depending on the state of a similar, unobserved, process. Integrating out the latter, we derive the Fokker-Planck equation for the probability distribution of the former. This has the form of diffusion equation with time-dependent diffusion coefficient, resulting in an anomalous diffusion. The diffusion exponent can not be predicted using a simple scaling argument, and anomalous scaling appears as well . The diffusion exponent of the Weiss-Havlin comb model is derived as a special case, and the same exponent holds even for weakly coupled processes . We compare our theoretical predictions with numerical simulations and find an excellent agreement. The findings caution against treating biochemical systems with unobserved dynamical degrees of freedom by means of standard, diffusive Langevin description.
Inspired by problems in biochemical kinetics, we study statistical properties of an overdamped Langevin processes with the friction coefficient depending on the state of a similar, unobserved, process. Integrating out the latter, we derive the long time behavior of the mean square displacement. Anomalous diffusion is found where the diffusion exponent can not be predicted using a simple scaling argument, and anomalous scaling appears as well . We compare our theoretical predictions with numerical simulations and find an excellent agreement. The findings caution against treating biochemical systems with unobserved dynamical degrees of freedom by means of standard, diffusive Langevin description.
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Fokker-Planck equation for the probability distribution of the former. This has the form of diffusion equation with time-dependent diffusion coefficient, resulting in an anomalous diffusion. The diffusion
long time behavior of the mean square displacement. Anomalous diffusion is found where the diffusion
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. The diffusion exponent of the Weiss-Havlin comb model is derived as a special case, and the same exponent holds even for weakly coupled processes