The Einstein relation for the KPZ equation

Abstract

We compute the non-universal constants in the KPZ equation in one dimension, in terms of the thermodynamical quantities associated to the underlying microscopic dynamics. In particular, we derive the second-order Einstein relation $\lambda =\frac{1}{2}\frac{d^2}{d{\rho }^2}\chi (\rho )D(\rho )$ for the transport coefficient $\lambda$ of the KPZ equation, in terms of the conserved quantity $\rho$, the diffusion coefficient $D$ and the static compressibility of the system $\chi$.

9 pages

References in corpus (8)

• Shape Fluctuations and Random Matrices
• Probability Distribution of the Free Energy of the Continuum Directed Random Polymer in 1+1 dimensions
• The one-dimensional KPZ equation: an exact solution and its universality
• Asymptotics in ASEP with Step Initial Condition
• Exact scaling functions for one-dimensional stationary KPZ growth
• Nonlinear fluctuations of weakly asymmetric interacting particle systems
• Crossover to the KPZ equation
• Large deviation principles for nongradient weakly asymmetric stochastic lattice gases

Cited by in corpus (2)

• Stochastic Dynamics, Large Deviations Principle, and Non-equilibrium Thermodynamics
• Characterization of Gradient Condition for Asymmetric Partial Exclusion Processes and Their Scaling Limits