Entropy production for irreversible systems with C₃ν symmetry

Lattice non reversible models characterized by the own symmetry of the imposed dynamics are dealt. The dynamics is considered Markovian and stochastic, ruling the time evolution of the system by means of the master equation, that determines in time the configuration space. The work is focused on the study of the critical behavior of the entropy production, as this physical quantity shows to be susceptible to the irreversibility of the system from its own definition, but also because its construction comes to be coherent with a treatment of the model which takes into account the contributions done by the its basic components, hence, supplying a perspective which explains the global behavior of the system as a consequence of the considerations done on its basis.

Being so, it's proposed a three state Potts model on a square lattice which is ruled by an irreversible dynamics with symmetry properties in the $C_{3\nu}$ group. For the entropy production it's chosen the Schnakenberg prescription, being harmonic with a Markovian stochastic perspective which is supposed to act in a microscopical level, as stated. Using Monte Carlo simulation its critical properties are analyzed, characterizing the expected divergent tendency of its derivative at the critical point. Other quantities as the order parameter are calculated, since these allows a complete description of the system response to the control parameter, and elucidates features as the phase transition, its nature, and also the properties of the states involved in each of the phases. Dynamics and stationary critical exponents are calculated from the numerical results, those being a signature of the universality class of the system, which, in accordance to the Grinstein conjecture, shouldn't depend on the reversible conditions, but just on the symmetries involved in the model, as most of our results confirm.