Abstract
In this paper we rigorously establish the existence of the mobility coefficient for a tagged particle in a simple symmetric exclusion process with adsorption/desorption of particles, in a presence of an external force field interacting with the particle. The proof is obtained using a perturbative argument. In addition, we show that, for a constant external field, the mobility of a particle equals to the self-diffusivity coefficient, the so-called Einstein relation. The method can be applied to any system where the environment has a Markovian evolution with a fast convergence to equilibrium (spectral gap property). In this context we find a necessary relation between forward and backward velocity for the validity of the Einstein relation. This relation is always satisfied by reversible systems. We provide an example of a non-reversible system, where the Einstein relation is valid.
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Komorowski, T., Olla, S. On Mobility and Einstein Relation for Tracers in Time-Mixing Random Environments. J Stat Phys 118, 407–435 (2005). https://doi.org/10.1007/s10955-004-8815-3
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DOI: https://doi.org/10.1007/s10955-004-8815-3