A minimal model of dynamical phase transition
  We calculate the large deviation functions characterizing the long-time fluctuations of the occupation of drifted Brownian motion and show that these functions have non-analytic points. This provides the first example of dynamical phase transition that appears in a simple, homogeneous Markov process without an additional low-noise, large-volume or hydrodynamic scaling limit. 
Pelerine Tsobgni Nyawo and Hugo Touchette
cond-mat.stat-mech