Numerical Study of the Thermodynamic Uncertainty Relation for the KPZ-Equation
arXiv:2009.12126 · doi:10.1007/s10955-020-02692-z
Abstract
A general framework for the field-theoretic thermodynamic uncertainty relation was recently proposed and illustrated with the dimensional Kardar-Parisi-Zhang equation. In the present paper, the analytical results obtained there in the weak coupling limit are tested via a direct numerical simulation of the KPZ equation with good agreement. The accuracy of the numerical results varies with the respective choice of discretization of the KPZ non-linearity. Whereas the numerical simulations strongly support the analytical predictions, an inherent limitation to the accuracy of the approximation to the total entropy production is found. In an analytical treatment of a generalized discretization of the KPZ non-linearity, the origin of this limitation is explained and shown to be an intrinsic property of the employed discretization scheme.
References in corpus (35)
- Thermodynamic uncertainty relation for biomolecular processes
- Dissipation bounds all steady-state current fluctuations
- Probability Distribution of the Free Energy of the Continuum Directed Random Polymer in 1+1 dimensions
- Exact scaling functions for one-dimensional stationary KPZ growth
- A KPZ Cocktail- Shaken, not stirred: Toasting 30 years of kinetically roughened surfaces
- Exact height distributions for the KPZ equation with narrow wedge initial condition
- An appetizer to modern developments on the Kardar-Parisi-Zhang universality class
- Evidence for geometry-dependent universal fluctuations of the Kardar-Parisi-Zhang interfaces in liquid-crystal turbulence
- Inferring dissipation from current fluctuations
- Exact solution for the stationary Kardar-Parisi-Zhang equation
- Critical Exponents of the KPZ Equation via Multi-Surface Coding Numerical Simulations
- Stochastic thermodynamics: From principles to the cost of precision
- Approximations to the Stochastic Burgers Equation
- Numerical study of the Kardar-Parisi-Zhang equation
- A pseudo-spectral method for the Kardar-Parisi-Zhang equation
- High-precision simulation of the height distribution for the KPZ equation
- Superdiffusivity of the 1D lattice Kardar-Parisi-Zhang equation
- The height distribution of the KPZ equation with sharp wedge initial condition: numerical evaluations
- Pseudospectral versus finite-differences schemes in the numerical integration of stochastic models of surface growth
- Kardar-Parisi-Zhang Interfaces with Inward Growth
- Field-Theoretic Thermodynamic Uncertainty Relation -- General formulation exemplified with the Kardar-Parisi-Zhang equation
- KPZ equation with short-range correlated noise: emergent symmetries and non-universal observables
- Kardar-Parisi-Zhang Equation with temporally correlated noise: a non-perturbative renormalization group approach
- The 1+1 dimensional Kardar-Parisi-Zhang equation: more surprises
- Nonequilibrium Steady State of a Weakly-Driven Kardar-Parisi-Zhang Equation
- Generalized discretization of the Kardar-Parisi-Zhang equation
- Direct Evidence for Universal Statistics of Stationary Kardar-Parisi-Zhang Interfaces
- Kardar-Parisi-Zhang Interfaces with Curved Initial Shapes and Variational Formula
- Competing Universalities in Kardar-Parisi-Zhang (KPZ) Growth Models
- The derivative of the Kardar-Parisi-Zhang equation is not in the KPZ universality class
- Some recent progress in singular stochastic PDEs
- Feedback control of surface roughness in a one-dimensional KPZ growth process
- "Sinc"-Noise for the KPZ Equation
- Transient Growth in Stochastic Burgers Flows
- Numerical Simulation and the Universality Class of the KPZ Equation for Curved Substrates