Scaling functions for nonequilibrium fluctuations: A picture gallery

TL;DR

This paper explores the universal behavior of non-Gaussian fluctuations in nonequilibrium steady states, focusing on interface dynamics, signal roughness, and boundary condition effects, highlighting their criticality and underlying universality.

Contribution

It provides a comprehensive overview of scaling functions for nonequilibrium fluctuations, emphasizing their universality and critical behavior across different physical phenomena.

Findings

Identification of the upper critical dimension for KPZ interface fluctuations

Connection between 1/f noise and extreme-value statistics

Impact of boundary conditions on fluctuation distributions

Abstract

The emergence of non-gaussian distributions for macroscopic quantities in nonequilibrium steady states is discussed with emphasis on the effective criticality and on the ensuing universality of distribution functions. The following problems are treated in more detail: nonequilibrium interface fluctuations (the problem of upper critical dimension of the Kardar-Parisi-Zhang equation), roughness of signals displaying Gaussian 1/f power spectra (the relationship to extreme-value statistics), effects of boundary conditions (randomness of the digits of pi).