Fluctuation theorems from non-equilibrium Onsager-Machlup theory for a Brownian particle in a time-dependent harmonic potential

We discuss the case of a Brownian particle which is harmonically bound and multiplicatively forced-namely bound by V(x,t)=1/2 a(t)x ² where a(t)is externally controlled-as another instance that provides a generalization of Onsager-Machlup’s theory to non-equilibrium states, thus allowing establishment of several fluctuation theorems. In particular, we outline the derivation of a fluctuation theorem for work, through the calculation of the work probability distribution as a functional integral over stochastic trajectories.