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39 pages, 11 figures.-- This article is distributed under the terms of the Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made ; We analyse a continuum model for genetic circuits based on a partial integrodifferential equation initially proposed in Friedman et al. (Phys RevLett 97(16):168302, 2006) as an approximation of a chemical master equation. We use entropy methods to show exponentially fast convergence to equilibrium for this model with explicit bounds. The asymptotic equilibration for the multidimensional case of more than one gene is also obtained under suitable assumptions on the equilibrium stationary states. The asymptotic equilibration property for networks involving one and more than one gene is investigated via numerical simulations ; J. A. Cañizo and J. A. Carrillo were supported by Projects MTM2014-52056-P and MTM2017-85067-P, funded by the Spanish government and the European Regional Development Fund. J. A. Carrillo was partially supported by the EPSRC Grant Number EP/P031587/1. M. Pájaro acknowledges support from Spanish MINECO fellowships BES-2013-063112, EEBB-I-16-10540 and EEBB-I-17-12182 ; Peer reviewed

We analyse a continuum model for genetic circuits based on a partial integrodifferential equation initially proposed in Friedman et al. (Phys RevLett 97(16):168302, 2006) as an approximation of a chemical master equation. We use entropy methods to show exponentially fast convergence to equilibrium for this model with explicit bounds. The asymptotic equilibration for the multidimensional case of more than one gene is also obtained under suitable assumptions on the equilibrium stationary states. The asymptotic equilibration property for networks involving one and more than one gene is investigated via numerical simulations. ; J. A. Cañizo and J. A. Carrillo were supported by Projects MTM2014-52056-P and MTM2017-85067-P, funded by the Spanish government and the European Regional Development Fund. J. A. Carrillo was partially supported by the EPSRC Grant Number EP/P031587/1. M. Pájaro acknowledges support from Spanish MINECO fellowships BES-2013-063112, EEBB-I-16-10540 and EEBB-I-17-12182.