Work Fluctuations for a Harmonically Confined Active Ornstein-Uhlenbeck Particle

Fluctuation Theorems for Heat Exchanges between Passive and Active Baths

“…Equation ( 9 ) also suggests that the distributions for the restart of and are and , respectively. In order to better discern the action of , here, we fix and for the sake of simplicity, we also set [ 24 , 31 , 71 ]. Moreover, as typically done [ 23 , 24 , 25 , 31 , 62 , 71 ], we control the relative magnitude activity and thermal noise by varying the adimensional Péclet number where we recall is the particle diameter.…”

“…In order to better discern the action of , here, we fix and for the sake of simplicity, we also set [ 24 , 31 , 71 ]. Moreover, as typically done [ 23 , 24 , 25 , 31 , 62 , 71 ], we control the relative magnitude activity and thermal noise by varying the adimensional Péclet number where we recall is the particle diameter. We remark that in general, the active bath configuration can be realized in actual experiments by using Janus particles [ 72 , 73 , 74 , 75 ] or optical tweezers [ 76 , 77 ], or by introducing a passive tracer particle in a suspension of active particles whose collisions with the tracer itself can be described by [ 52 , 78 ].…”

“…Following standard procedures, from Equation ( 13 ) the trajectory-wise energy balance of the system can be obtained [ 33 , 67 ]. By simply using the Langevin equation Equation ( 3 ) to replace in Equation ( 13 ) for generality in case (b) and adopting the Stratonovich prescription to calculate integrals [ 81 ], one in fact finds where and , respectively, denote the variation in kinetic and potential energy from the initial configuration at and final one at , denotes the work performed by the particle on the right passive bath defined in Equation ( 13 ), denotes the work performed by the particle on the passive component of the left bath only, i.e., the friction force plus white noise, with the number of times the particle resides in the left well, and the beginning and ending times of each of the j th residencies, and finally denotes the active work, i.e., the work performed by the additional noise in the left well providing a measure of the energy cost to sustain the particle self-propulsion [ 31 , 52 , 66 , 82 , 83 ]. In both Equations ( 15 ) and ( 16 ), ○ again underlies the Stratonovich prescription.…”

“…denotes the active work, i.e., the work performed by the additional noise in the left well providing a measure of the energy cost to sustain the particle self-propulsion [31,52,66,82,83].…”

“…The distinctive feature of all systems from this class is a continuous conversion and injection of energy from internal reservoirs or the surrounding environment into the system itself to produce self-propulsion of its minimal constituents. Interestingly, the mere introduction of a self-propulsion mechanism results in a wealth of new phenomena and features, for example, collective motion [ 13 , 18 , 19 , 20 , 21 ], motility-induced phase separation [ 22 , 23 , 24 ] a rich phase diagram [ 25 , 26 , 27 , 28 ] and dynamical phase transitions [ 29 , 30 , 31 ], most of which have no equivalent in passive counterparts. According to stochastic thermodynamics [ 32 , 33 , 34 ], the injection of energy is an irreversible process which makes active systems inherently out of equilibrium [ 35 , 36 ].…”