We consider a broad class of strongly interacting quantum lattice gases, including the Fermi-Hubbard and Bose-Hubbard models. We focus on macroscopic particle clusters of size $\theta N$, with $\theta \in (0,1)$ and $N$ the total particle number, and we study the quantum probability that such a cluster is transported across a distance $r$ within time $t$. Conventional effective light cone arguments yield a bound of the form $\exp (vt-r)$. We report a substantially stronger bound $\exp [\theta N(vt-r)]$, which provides exponential suppression that scales with system size. Our result establishes a universal dynamical large deviation principle: macroscopic suppression of supersonic macroscopic transport (MASSMAT).

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• Ballistic transport
• Quantum transport
• Lattice models in statistical physics
• Ultracold gases
• Bose-Hubbard model