The Two Scaling Regimes of the Thermodynamic Uncertainty Relation for the KPZ-Equation

Abstract

We investigate the thermodynamic uncertainty relation for the $(1+1)$ dimensional Kardar-Parisi-Zhang equation on a finite spatial interval. In particular, we extend the results for small coupling strengths obtained previously to large values of the coupling parameter. It will be shown that, due to the scaling behavior of the KPZ equation, the TUR product displays two distinct regimes which are separated by a critical value of an effective coupling parameter. The asymptotic behavior below and above the critical threshold is explored analytically. For small coupling, we determine this product perturbatively including the fourth order; for strong coupling we employ a dynamical renormalization group approach. Whereas the TUR product approaches a value of $5$ in the weak coupling limit, it asymptotically displays a linear increase with the coupling parameter for strong couplings. The analytical results are then compared to direct numerical simulations of the KPZ equation showing convincing agreement.

References in corpus (18)

• Thermodynamic uncertainty relation for biomolecular processes
• 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
• Evidence for geometry-dependent universal fluctuations of the Kardar-Parisi-Zhang interfaces in liquid-crystal turbulence
• Thermodynamic uncertainty relation for time-dependent driving
• Operationally accessible bounds on fluctuations and entropy production in periodically driven systems
• Thermodynamic Uncertainty Relation for Arbitrary Initial States
• Thermodynamic uncertainty relation for systems with unidirectional transitions
• Field-Theoretic Thermodynamic Uncertainty Relation -- General formulation exemplified with the Kardar-Parisi-Zhang equation
• The 1+1 dimensional Kardar-Parisi-Zhang equation: more surprises
• Accessing Kardar-Parisi-Zhang universality sub-classes with exciton polaritons
• Steady state entropy production rate for scalar Langevin field theories
• A thermodynamic uncertainty relation for a system with memory
• 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
• Skewness in (1+1)-dimensional Kardar-Parisi-Zhang-type growth
• Numerical Study of the Thermodynamic Uncertainty Relation for the KPZ-Equation