  Active matter describes systems whose constituents convert energy from their
surroundings into directed motion, such as bacteria or catalytic colloids. We
unravel a remarkable direct link between the dynamics and thermodynamics for
suspensions of such active particles: The thermodynamic equivalent of
irreversibility is the swim pressure. Like in the famous fluctuation theorems
of stochastic thermodynamics, irreversibility is defined as the log-ratio of
the probabilities to observe a given set of particle trajectories and their
time reverses. Our discovery is thus similar in spirit to what is known for
passive systems, for which those fluctuation theorems relate the
irreversibility to the thermodynamic entropy. It is based on numerical
simulations and on analytical arguments for the limits of low particle density
and/or high activity in the paradigmatic model of active Ornstein-Uhlenbeck
particles.
