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 .
Inspired by problems in biochemical kinetics, we study statistical properties of an overdamped Langevin process whose friction coefficient depends on the state of a similar, unobserved process. Integrating out the latter, we derive the long time behaviour of the mean square displacement. Anomalous diffusion is found . Since the diffusion exponent can not be predicted using a simple scaling argument, anomalous scaling appears as well. We also find that the coupling can lead to ergodic or non-ergodic behaviour of the studied process. We compare our theoretical predictions with numerical simulations and find an excellent agreement. The findings caution against treating biochemical systems coupled with unobserved dynamical degrees of freedom by means of standard, diffusive Langevin descriptions .
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processes with the friction coefficient depending
process whose friction coefficient depends
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,
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behavior
behaviour
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where
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and
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also find that the coupling can lead to ergodic or non-ergodic behaviour of the studied process. We
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coupled
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description
descriptions