Exponential peak and scaling of work fluctuations in modulated systems

We extend the stationary-state work fluctuation theorem to periodically modulated nonlinear systems. Such systems often have coexisting stable periodic states. We show that work fluctuations sharply increase near a kinetic phase transition where the state populations are close to each other. The work variance is proportional here to the reciprocal rate of interstate switching. We also show that the variance displays scaling with the distance to a bifurcation point and find the critical exponent for a saddle-node bifurcation.