  In chemical reaction networks, bistability can only occur far from
equilibrium. It is associated with a first-order phase transition where the
control parameter is the thermodynamic force. At the bistable point, the
entropy production is known to be discontinuous with respect to the
thermodynamic force.We show that the fluctuations of the entropy production
have an exponential volume-dependence when the system is bistable. At the phase
transition, the exponential prefactor is the height of the effective potential
barrier between the two fixed-points. Our results obtained for Schl\"ogl's
model can be extended to any chemical network.
