In small systems, fluctuations play a crucial role. Stochastic thermodynamics is an emerging theory that deals with fluctuations in the energy changes and the entropy of a system experimenting an irreversible process. In essence, we find the so-called fluctuation theorems that relate the symmetry of the time rupture with the statistics of these fluctuations.

Two milestones of the theory are that it has strengthened the link between the information theory and thermodynamics, and it has been fundamental in the description of experimental manipulations of DNA individual molecules and trapped passive colloids. Therefore, it becomes natural to guess that applications and extensions of this theory can be beneficial for the active matter and other biological systems -where detection and restriction of non-equilibrium is essential.

Nevertheless, the attempts to generalize the stochastic thermodynamics to models that reflect these systems have failed. Therefore, on the theoretical side of this project, we will start from the solid ground of standard stochastic thermodynamics, and we will sequentially add the complexities found in the active systems.

On the theoretical side, the results derived from stochastic thermodynamics will allow us to infer hidden properties of the system.
A complementary approach consists in including, within the theoretical frame, the capacity bacteria have to detect chemical components since these systems have a mechanical and a chemical part that is highly fluctuant. The last one is the one that determines the mechanical behavior.