Massimiliano Semeraro — Università degli Studi di Bari and INFN Sezione di Bari #
Work Fluctuations for a Harmonically Confined Active Ornstein-Uhlenbeck Particle #
Active Particles are physical entities able to transform energy from the environment or internal reservoirs into directed self-propelled motion. From a theoretical standpoint, in recent years this class of systems gained a prominent role in statistical mechanics due to the display of intriguing properties as motility-induced phase separation [1], an inherent out of equilibrium character [2] and the occurrence of singularities in distributions of integrated observables associated to Dynamical Phase Transitions (DPTs) [3]. In this respect, Active Work, i.e. the work performed by the self-propulsion force, emerged as a key observable to monitor as at the same time it provides a measure of how efficiently energy is transformed into self propulsion [4], it is strictly related to the system entropy production [2] and its distribution has already signalled the occurrence of such singularities and DPTs [5].  In this proposed talk we would like to present our recent results on this subject from [6], in which we studied the Active Work fluctuations of a single Active Ornstein-Uhlenbeck Particle under the effect of a confining harmonic potential. The simple but not trivial framework of a single particle allowed us to tackle the problem analytically for both for stationary and generic uncorrelated initial states adopting the Large Deviations approach we developed in [7]. Our results showed that harmonic confinement can indeed induce singularities in the Active Work Rate Function, with linear tails at large positive and negative Active Work values appearing for sufficiently large self-propulsion force, harmonic confinement and/or initial values. In addition, by looking at the system trajectories we discovered these singularities to be associated to DPTs in turn originated from concentrated large values, or big jumps, in the displacement and the self-propulsion force at the initial or ending points of trajectories. Our results thus provided a connection between DPTs and a condensation-like physical mechanism and marked the relevance of boundary terms in the problem at hand.  [1] Motility-Induced Phase Separation, M. E. Cates and J. Tailleur, Annual Review of Condensed Matter Physics (6) 2015 [2] Irreversibility and Biased Ensembles in Active Matter: Insights from Stochastic Thermodynamics, E. Fodor, R. L. Jack, and M. E. Cates, Annual Review of Condensed Matter Physics (13) 2022 [3] A first-order dynamical transition in the displacement distribution of a driven run-and-tumble particle, G. Gradenigo and S. N. Majumdar, Journal of Statistical Mechanics: Theory and Experiment (5) 2019 [4] Work fluctuations in the active Ornstein–Uhlenbeck particle model, M. Semeraro, A. Suma, I. Petrelli, F. Cagnetta, and G. Gonnella, Journal of Statistical Mechanics: Theory and Experiment (12) 2021 [5] Large fluctuations and dynamic phase transition in a system of self-propelled particles, F. Cagnetta, F. Corberi, G. Gonnella, and A. Suma, Physical review letters (119) 2017 [6] Work Fluctuations for a Harmonically Confined Active Ornstein-Uhlenbeck Particle, M. Semeraro, G. Gonnella, A. Suma, and M. Zamparo, Physical Review Letters (131) 2023 [7] Large deviations for quadratic functionals of stable Gauss–Markov chains and entropy production, M. Zamparo and M. Semeraro, Journal of Mathematical Physics (64) 2023