New thought-provoking points of view on KPZ dynamics

A variational approach has been recently introduced allowing to define a
non-equilibrium thermodynamic-like potential (NEP) for the paradigmatic
Kardar--Parisi--Zhang (KPZ) equation as well as for other related kinetic
equations. For the KPZ case, the knowledge of such a potential together
with its numerical evaluation (in 1, 2 and 3 dimensions) allowed us to
obtain information about the system's time dynamical behavior. Such an
analysis opens new perspectives over possible relations between the NEP
asymptotic behavior and the critical exponents. In addition, a functional
Taylor expansion admitted by the KPZ nonequilibrium potential, that results to be naturally truncated at third order, gives rise to a related nonlinear stochastic partial differential equation offering some insight on the origin of a diffusive instability as well as on the asymptotic time behavior. This variational scheme is exploited to inquire on the dynamical behavior of the KPZ equation through a path-integral approach. All these aspects offers novel points of view, shedding light on particular aspects of the KPZ equation dynamics.