Irreversibility in active matter systems: Fluctuation theorem and mutual information

We consider a Brownian particle which, in addition to being in contact with a thermal bath, is driven by active fluctuations.
The goal is to derive a thermodynamic (-like) description for this kind of active matter.

In an introductory part, we will recapitulate what is known for passive Brownian motion about its stochastic thermodynamics, starting from the underlying Langevin-equation.
We will then extend these concepts to the Brownian particle which is subject to both, thermal and active fluctuations.
We will derive a generalized “entropy production”, which fulfills an integral fluctuation theorem.
We show that those parts of this “entropy production’’, which are different from the usual dissipation of heat
in the thermal environment, can be associated with the mutual information between the particle trajectory and the
history of the active fluctuations.