Inverse Scattering Method Solves the Problem of Full Statistics of Nonstationary Heat Transfer in the Kipnis-Marchioro-Presutti Model

Eldad Bettelheim (1) , Naftali Smith (2, 3) , Baruch Meerson (1)

1 HUJ - The Hebrew University of Jerusalem
2 LPENS - Laboratoire de physique de l'ENS - ENS Paris
3 BGU - Ben-Gurion University of the Negev

We determine the full statistics of nonstationary heat transfer in the Kipnis-Marchioro-Presutti lattice gas model at long times by uncovering and exploiting complete integrability of the underlying equations of the macroscopic fluctuation theory. These equations are closely related to the derivative nonlinear Schrödinger equation (DNLS), and we solve them by the Zakharov-Shabat inverse scattering method (ISM) adapted by D. J. Kaup and A. C. Newell, J. Math. Phys. 19, 798 (1978) for the DNLS. We obtain explicit results for the exact large deviation function of the transferred heat for an initially localized heat pulse, where we uncover a nontrivial symmetry relation.

Keywords: Fluctuations & noise; Heat transfer; Stochastic process; Statistical physics; Nonlinear dynamics

Domains: Chemical Sciences; Mathematics [math]; Statistics [math.ST]

Eldad Bettelheim, Naftali Smith, Baruch Meerson. Inverse Scattering Method Solves the Problem of Full Statistics of Nonstationary Heat Transfer in the Kipnis-Marchioro-Presutti Model. Physical Review Letters, 2022, 128 (13), pp.130602. ⟨10.1103/PhysRevLett.128.130602⟩. ⟨hal-03666013⟩