Sommaire:

The large scale density fluctuations of the ordered state in active matter systems are usually characterized by studying the ``giant number fluctuations'' of particles in any finite volume, as compared to the expectations from the central limit theorem. However, in ordering systems, the fluctuations in density ordering are often captured through their structure functions deviating from Porod law. We ask: (1) Do active matter systems in general violate Porod law? (2) Are the two characterizations of large fluctuations, namely Porod law violation and giant number fluctuations, related to each other? In this work, we study the relationship between giant number fluctuations and structure functions, for different models of active matter as well as other non-equilibrium systems.

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