%A Wio,Horacio S.
%A Rodríguez,Miguel A.
%A Gallego,Rafael
%A Revelli,Jorge A.
%A Alés,Alejandro
%A Deza,Roberto R.
%D 2017
%J Frontiers in Physics
%C
%F
%G English
%K Nonequilibrium growth,scaling laws,Variational principles,stochastic methods,Interface roughening
%Q
%R 10.3389/fphy.2016.00052
%W
%L
%N 52
%M
%P
%7
%8 2017-January-18
%9 Original Research
%+ Prof Horacio S. Wio,Instituto de Física de Cantabria, Universidad de Cantabria and CSIC,Santander, Spain,wio@ifca.unican.es
%#
%! KPZ as a stochastic gradient flow in an evolving landscape
%*
%<
%T d-Dimensional KPZ Equation as a Stochastic Gradient Flow in an Evolving Landscape: Interpretation and Time Evolution of Its Generating Functional
%U https://www.frontiersin.org/article/10.3389/fphy.2016.00052
%V 4
%0 JOURNAL ARTICLE
%@ 2296-424X
%X The deterministic KPZ equation has been recently formulated as a gradient flow. Its non-equilibrium analog of a free energy—the “non-equilibrium 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 to h(x,t) from some initial configuration h_{0}(x,0). After pinpointing some implications of these facts, we study the time behavior of 〈Φ[h]〉_{t} (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. 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.