Using the mathematical results proved in [1] in the framework of large deviations theory [2], we were able to study the large fluctuations of the work injected by the random force into a force into a Brownian particle under the action of a confining harmonic potential [3]. In particular, we could compute analytically the rate function for generic uncorrelated initial conditions, showing that, depending on the initial spread, it can exhibit no, one, or two singularities associated to the onset of linear tails. A dependence on the potential strength is observed for large initial spreads (entailing two singularities), which is lost for stationary initial conditions (giving one singularity) and concentrated initial values (no singularity), confirming the results of the numerical investigation in [4]. We discuss also the mechanism responsible for the singularities of the rate function, identified in a big jump in the initial values. Finally, we also present what happens in the case of the active work in an Active Ornstein-Uhlenbeck particle [5], which can be studied by means of the same mathematical technique.
References:
[1] M. Zamparo, M. Semeraro, J. Math. Phys. 64, 023302 (2023)
[2] H. Touchette, Phys. Rep. 478, 1-69 (2009)
[3] G. B. Carollo, M. Semeraro, G. Gonnella and M. Zamparo, J. Phys. A: Math. Theor. 56 435003 (2023)
[4] J. Farago, Journal of Statistical Physics 107, 781–803 (2002)
[5] M. Semeraro, G. Gonnella, A. Suma and M. Zamparo, Phys. Rev. Lett. 131, 158302 (2023)
Marco Baiesi
