  The study of thermodynamic properties of microscopic systems, such as a
colloid in a fluid, has been of great interest to researchers since the
discovery of the fluctuation theorem and associated laws of stochastic
thermodynamics. However, most of these studies confine themselves to systems
where effective fluctuations acting on the colloid are in the form of
delta-correlated Gaussian white noise (GWN). In this study, instead, we look
into the work distribution function when a colloid trapped in a harmonic
potential moves from one position to another in a fluid medium with an
elongational flow field where the effective fluctuations are given by the
Ornstein-Uhlenbeck (OU) noise, a type of coloured noise. We use path integrals
to calculate this distribution function and compare and contrast its properties
to the case with GWN. We find that the work distribution function turns out to
be non-Gaussian as a result of the elongational flow field, but continues to
obey the fluctuation theorem in both types of noise. Further, we also look into
the effects of the various system parameters on the behaviour of work
fluctuations and find that although the distribution tends to broaden with
increasing noise intensity, increased correlation in fluctuations acts to
oppose this effect. Additionally, the system is found to consume heat from the
surroundings at early times and dissipate it into the media at later times.
This study, therefore, is a step towards gaining a better understanding of the
thermodynamic properties of colloidal systems under non-linear complex flows
that also display correlated fluctuations.
