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Different microscopic interpretations of the reaction-telegrapher equation. (English) Zbl 1162.82012
Summary: We provide some new insights into the microscopic interpretation of the telegrapher’s and the reaction-telegrapher equations. We use the framework of continuous-time random walks to derive the telegrapher’s equation from two different perspectives reported before: the kinetic derivation (KD) and the delayed random-walk derivation (DRWD). We analyze the similarities and the differences between both derivations, paying special attention to the case when a reaction process is also present in the system. As a result, we are able to show that the equivalence between the KD and the DRWD can break down when transport and reaction are coupled processes. Also, this analysis allows us to elaborate on the specific role of relaxation effects in reaction-diffusion processes.

MSC:
82B41Random walks, random surfaces, lattice animals, etc. (statistical mechanics)
82B40Kinetic theory of gases (equilibrium statistical mechanics)
82C70Transport processes (time-dependent statistical mechanics)
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