Current fluctuations in boundary driven systems: Universality, dynamical phase transitions and quantum transport

The recently formulated macroscopic fluctuation theory is a successful  description of out of equilibrium diffusive systems. I will focus on  current fluctuations of boundary driven systems within the macroscopic  theory description, and discuss the relevance of the additivity  principle to derive the large deviation function associated with the  current fluctuations. Three results will be shown

 1) Current fluctuations in boundary driven systems are universal

 2) A criterion for the validity of the additivity principle and  application to dynamical phase transitions.

  3) Relevance of the macroscopic fluctuation theory to transport of  disordered quantum systems.