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Complete Integrability of the Problem of Full Statistics of Nonstationary Mass Transfer in the Simple Inclusion Process

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arXiv:2403.19536v1 Announce Type: new
Abstract: The Simple Inclusion Process (SIP) interpolates between two well-known lattice gas models: the independent random walkers and the Kipnis-Marchiro-Presutti model. Here we study large deviations of nonstationary mass transfer in the SIP at long times in one dimension. We suppose that $N\gg 1$ particles start from a single lattice site, and we are interested in the full probability density $\mathcal{P}(M,N,T)$ of observing $M$ particles, $0\leq M\leq N$, at $x>0$ at a specified time $T\gg 1$. At large times, the probability distribution has a large-deviation behavior, $-\ln \mathcal{P}(M,N,T) \simeq \sqrt{T} s(M/N,N/\sqrt{T})$. We determine the rate function $s$ exactly by uncovering and utilizing complete integrability, by the inverse scattering method, of the underlying equations of the macroscopic fluctuation theory. We also analyze different asymptotic limits of the rate function $s$.

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