Dottorato in FISICA

Titolo della tesi: Fluctuations, dissipation and conservation laws in active alignment models

This thesis gathers the research work carried out by the author (and coworkers) in the last few years on collective behavior in animal groups, using the theoretical framework of statistical physics. This kind of research has become possible and enormously benefited from the recent advancements in the collection and processing of the experimental data in biological systems. The main sources, for what concerns this thesis, are the findings of the CoBBS (Collective Behavior in Biological Systems) group in Rome, regarding natural midge swarms and starling flocks. This thesis has two primary objectives: the first one is to develop a method to write stochastic differential equations at the microscopic level, that introduces fluctuations in the dynamics and nevertheless preserves some conservation law in the system. This is done with the aim of performing microscopic numerical simulations of a flocking model that is based on a conservation law (although other applications outside the realm of biological physics are also discussed). Indeed, recent analyses, both theoretical and experimental, have highlighted the crucial role of conservation laws in determining the correct critical exponents in natural swarms. The second objective of this thesis is to analyze and characterize the linear response theory and violations of the fluctuation-dissipation theorem in flocking models across the phase diagram and across different time scales. Regarding the first problem, we successfully developed this method, we validated it on appropriate reference test systems and demonstrated its effectiveness in its application to flocking models. For the second objective, our analysis revealed that non-equilibrium effects are most pronounced at the phase transition, consistently with experimental observations in bird flocks and insect swarms. We traced the origin and impact of non-equilibrium behavior across different scales of the system, highlighting the interplay between local entropy production and large-scale correlations that propagate non-equilibrium effects to the whole system. Our approach extensively utilizes the tools of statistical physics and stochastic processes theory, particularly in non-equilibrium contexts. Also, some graph theory will come into play, particularly in the first part of the thesis. Numerical simulations are integral to our methodology and all the key results are framed within the renormalization group paradigm. The findings of this thesis hopefully could contribute to a deeper understanding of collective behavior in active matter systems and offer a powerful simulation technique for future research in this field.