The entropy and fluctuation theorems of inertial particles in turbulence.

We study Lagrangian particles, with Stokes numbers, $\textrm{St}=0.5$, $3$, and $6$, transported by homogeneous and isotropic turbulent flows. Based on direct numerical simulations with point-like inertial particles, we identify stochastic equations describing the multi-scale cascade process. We show that the Markov property is valid for a finite step size larger than a $\textrm{St}$-dependent Einstein-Markov memory length. The formalism allows estimation of the entropy of the particles' Lagrangian trajectories. Integral, as well as detailed fluctuation theorems are fulfilled. Entropy consuming trajectories are related to specific local accelerations of the particles and may be seen as reverse cascade processes.