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Exact Solution of the Macroscopic Fluctuation Theory for the Symmetric Exclusion Process

Kirone Mallick1,*, Hiroki Moriya2,†, and Tomohiro Sasamoto2,‡

  • 1Institut de Physique Théorique, CEA, CNRS, Université Paris–Saclay, F–91191 Gif-sur-Yvette cedex, France
  • 2Department of physics, Tokyo Institute of Technology, Tokyo 152-8551, Japan

  • *kirone.mallick@ipht.fr
  • †hmoriya@stat.phys.titech.ac.jp
  • ‡sasamoto@phys.titech.ac.jp
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Phys. Rev. Lett. 129, 040601 – Published 19 July, 2022

DOI: https://doi.org/10.1103/PhysRevLett.129.040601

Abstract

We present the first exact solution for the time-dependent equations of the macroscopic fluctuation theory (MFT) for the symmetric simple exclusion process by combining a generalization of the canonical Cole-Hopf transformation with the inverse scattering method. For the step initial condition with two densities, we obtain exact and compact formulas for the optimal density profile and the response field that produce a required fluctuation, both at initial and final times. The large deviation function of the current is derived and coincides with the formula obtained previously by microscopic calculations. This provides the first analytic confirmation of the validity of the MFT for an interacting model in the time-dependent regime.

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Phys. Rev. Lett. 129, 040601– Published 19 July, 2022
  • Received 20 February 2022
  • Accepted 24 June 2022
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