AUTHOR=Wio Horacio S. , Rodríguez Miguel A. , Gallego Rafael , Revelli Jorge A. , Alés Alejandro , Deza Roberto R. 

TITLE=d-Dimensional KPZ Equation as a Stochastic Gradient Flow in an Evolving Landscape: Interpretation and Time Evolution of Its Generating Functional

JOURNAL=Frontiers in Physics

VOLUME=Volume 4 - 2016

YEAR=2017

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2016.00052

DOI=10.3389/fphy.2016.00052

ISSN=2296-424X

ABSTRACT=The deterministic KPZ equation has been recently formulated as a gradient flow. Its nonequilibrium analog of a free energy---the "nonequilibrium potential''  Φ[h], providing at each time the landscape where the stochastic dynamics of h(x ⃗,t)   takes place---is however unbounded, and its exact evaluation involves all the detailed histories leading from some initial configuration h(x ⃗,0) to a final one  h(x ⃗,t). After pinpointing some implications of these facts, we study the time behavior of  〈Φ[h]  〉  (the average of  Φ[h] over noise realizations at time t)  and show the interesting consequences of its structure when an external driving force F is included (i.e. the KPZ behavior as an activation-like process). The asymptotic form of the time derivative Φ ̇[h]    is shown to be valid for any substrate dimensionality d, thus providing a valuable tool for studies in d>1.