Statut  Confirmé 
Série  FORUMENS 
Domaines  condmat.statmech 
Date  Mercredi 22 Novembre 2023 
Heure  12:45 
Institut  LPENS 
Salle  3 rue d Ulm, College de France 
Nom de l'orateur  O'byrne 
Prenom de l'orateur  Jeremy 
Addresse email de l'orateur  
Institution de l'orateur  Cambridge 
Titre  Irreversibility and active matter: a geometric insight 
Résumé  Active systems are made up of elementary agents that are able to selfpropel, ``microscopically'' driving the system outofequilibrium by doing so. The collective behaviors of such systemsof which collective motion or motility induced phase separation (MIPS) are emblematic instancesare best described by field theories. At this largescale longtime level, the irreversibility of these systems can be subtle to capture. To fill this gap, we introduce a functional generalization of the exterior derivative, which is itself a generalization of the curl operator to (finite) dimensions higher than 3. This functional exterior derivative allows to associate to a field dynamics a functional ``vorticity'', or ``cycle affinity''. As soon as this vorticity vanishes timereversal symmetry (TRS) is effectively restored at the macroscopic scale, which implies that all the machinery of equilibrium statistical field theory can be applied to determine e.g. the phase diagram. Whenever the dynamics of the system is macroscopically irreversible, the functional vorticity is not identically zero and provides a valuable insight on the way TRS is broken, from the shape of the stationary probability current to the counterparts of this current in the physical space. For instance, in the case of the active model B  that is a minimal field theoretic description of MIPS  the latter correspond to the permanent excitation of anisotropic, propagating modes that are localized at the liquidgas interface. Furthermore, for stochastic vector fields over a onedimensional space, we exhibit a basis of functional vorticities, the elements of which can be seen as independent sources of irreversibility on which the entropy production rate can be decomposed. In addition, these basis elements allow classifying the potential outofequilibrium behaviours the field theory can display. 
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