Geometrical interpretation of dynamical phase transitions in boundary-driven systems

Dynamical phase transitions are defined as nonanalytic points of the large deviation function of current fluctuations. We show that for boundary-driven systems, many dynamical phase transitions can be identified using the geometrical structure of an effective potential of a Hamiltonian, recovered from the macroscopic fluctuation theory description. Using this method we identify new dynamical phase transitions that could not be recovered using existing perturbative methods. Moreover, using the Hamiltonian picture, an experimental scheme is suggested to demonstrate an analog of dynamical phase transitions in linear, rather than exponential, time.