The heat distribution of harmonically trapped single particles in active viscoelastic media

The present paper is a continuation of efforts spanning several years to better understand the stochastic thermodynamics of small systems. It presents exact calculations of the heat distribution function of two different harmonically confined systems driven by thermal and athermal noise in a viscoelastic medium under overdamped conditions: one, a single particle in one dimension, and the other an elastic dumbbell in three dimensions. The calculations build on work carried out recently by Darabi <i>et al.</i> [<i>New J. Phys</i>. 2023, <b>25</b>, 103021] and Gomez-Solano [<i>Phys. A</i>, 2024, <b>646</b>, 129889] on the heat distribution of a Brownian oscillator evolving under the action of non-Markovian memory effects, which in one case originate in viscoelasticity, and in the other in hydrodynamic backflow. The heat distributions calculated in this paper both involve modified Bessel functions, as in earlier studies, but also contain multiplicative exponential factors. These factors reflect the irreversibility induced in the systems by the athermal noise, and lead to their obeying a fluctuation theorem for the heat.