Universality in equilibrium and away from it: A personal perspective

In this talk/paper I discuss the concept of universality in phase transitions and the question of whether universality classes are more robust in equilibrium than away from it. In both of these situations, the main ingredients determining universality are symmetries, conservation laws, the dimension of the space and of the order‐parameter and the presence of long‐range interactions or quenched disorder. The existence of detailed‐balance and fluctuation‐dissipation theorems imposes severe constraints on equilibrium systems, allowing to define universality classes in a very robust way; instead, non‐equilibrium allows for more variability. Still, quite robust non‐equilibrium universality classes have been identified in the last decades. Here, I discuss some examples in which (i) non‐equilibrium phase transitions are simply controlled by equilibrium critical points, i.e. non‐equilibrium ingredients turn out to be irrelevant in the renormalization group sense and (ii) non‐equilibrium situations in which equilibrium seems to come out of the blue, generating an adequate effective description of intrinsically non‐equilibrium problems. Afterwards, I shall describe different genuinely non‐equilibrium phase transitions in which introducing small, apparently innocuous changes (namely: presence or absence of an underlying lattice, parity conservation in the overall number of particles, existence of an un‐accessible vacuum state, deterministic versus stochastic microscopic rules, presence or absence of a Fermionic constraint), the critical behavior is altered, making the case for lack of robustness. However, it will be argued that in all these examples, there is an underlying good reason (in terms of general principles) for universality to be altered. The final conclusions are that: (i) robust universality classes exist both in equilibrium and non‐equilibrium; (ii) symmetry and conservation principles are crucial in both, (iii) non‐equilibrium allows for more variability (i.e. it is less constrained).