Entropy production as tool for characterizing nonequilibrium phase transitions

Nonequilibrium phase transitions can be typified in a similar way to equilibrium systems, for instance, by the use of the order parameter. However, this characterization hides the irreversible character of the dynamics as well as its influence on the phase transition properties. Entropy production has revealed to be an important concept for filling this gap since it vanishes identically for equilibrium systems and is positive for the nonequilibrium case. Based on distinct and general arguments, the characterization of phase transitions in terms of the entropy production is presented. Analysis for discontinuous and continuous phase transitions has been undertaken by taking regular and complex topologies within the framework of mean field theory (MFT) and beyond the MFT. A general description of entropy production portraits for $Z_2$ (``up-down'') symmetry systems under the MFT is presented. Our main result is that a given phase transition, whether continuous or discontinuous has a specific entropy production hallmark. Our predictions are exemplified by an icon system, perhaps the simplest nonequilibrium model presenting an order-disorder phase transition and spontaneous symmetry breaking: the majority vote model. Our work paves the way to a systematic description and classification of nonequilibrium phase transitions through a key indicator of system irreversibility.