Non-boltzmann stationary distributions and non-equilibrium relations in active baths

Most natural and engineered processes, such as biomolecular reactions, protein folding, and population dynamics, occur far from equilibrium and, therefore, can- not be treated within the framework of classical equilibrium thermodynamics. Here, we experimentally study how some fundamental thermodynamic quantities and relations are affected by the presence of the non-equilibrium uctuations as- sociated with an active bath. We show, in particular, that, as the confinement of the particle increases, the stationary probability distribution of a Brownian particle confined within a harmonic potential becomes non-Boltzmann, featuring a transition from a Gaussian distribution to a heavy-tailed distribution. Because of this, non-equilibrium relations (e.g. Jarzynski equality, Crooks uctuation the- orem) cannot be applied. We show that these relations can be restored by using the effective potential associated with the stationary probability distribution. We corroborate our experimental findings with theoretical arguments.