The KPZ equation as a (noise-driven) gradient flow

A. ALÉS; G.G. IZÚS; R.R. DEZA; J.A.REVELLI; HORACIO WIO

TANDIL

Congreso; MACI; 2015

Two variational formulations are introduced of the Kardar?Parisi?Zhang (KPZ) equation for interfacegrowth, resulting in thermodynamic-like potentials. The first one is a genuine Lyapunov function for the deterministicdynamics, and allows to prove global invariance properties previously conjectured by other authors. The second oneallows to formally write the deterministic KPZ equation as a gradient flow, so providing a potential landscape forthe noise-driven dynamics. It also exhibits the Lyapunov property, but it is unbounded. A formal functional Taylorexpansion of this so-called ?nonequilibrium potential? truncates naturally at the third order, so providing a clearlyinterpretable background for the dynamics to take place. Some conjectures drawn from its form are described.