We find novel phase transitions and critical phenomena that occur only
outside the linear-response regime of current-driven nonequilibrium states. We
consider the strongly-interacting (3+1)-dimensional N=4 large-Nc SU(Nc)
supersymmetric Yang-Mills theory with a single flavor of fundamental N=2
hypermultiplet as a microscopic theory. We compute its nonlinear non-ballistic
quark-charge conductivity by using the AdS/CFT correspondence. We find that the
system exhibits a novel nonequilibrium first-order phase transition where the
conductivity jumps and the sign of the differential conductivity flips at
finite current density. A nonequilibrium critical point is discovered at the
end point of the first-order regime. We propose a nonequilibrium steady-state
analogue of thermodynamic potential in terms of the gravity-dual theory in
order to define the transition point. Nonequilibrium analogues of critical
exponents are proposed as well. The critical behavior of the conductivity is
numerically confirmed on the basis of these proposals. The present work
provides a new example of nonequilibrium phase transitions and nonequilibrium
critical points.Comment: 5 pages, 2 figures; v2: slightly short version is published in PRL.
The title is changed in the PRL forma
