Numerical Study of Continuous and Discontinuous Dynamical Phase   Transitions for Boundary Driven Systems
  The existence and search for thermodynamic phase transitions is of unfading interest. In this paper, we present numerical evidence of dynamical phase transitions occurring in boundary driven systems with a constrained integrated current. It is shown that certain models exhibit a discontinuous transition between two different density profiles and a continuous transition between a time-independent and a time-dependent profile. We also checked that the KMP model does not exhibit phase transition in a range much larger than previously explored. 
Ohad Shpielberg, Yaroslav Don and Eric Akkermans
cond-mat.stat-mech