# Invited review: Fluctuation-induced transport. From the very small to the very large scales

## TL;DR

This review explores how fluctuation-induced transport causes directed particle motion across scales, influenced by substrate shape, fluctuation correlations, and particle properties, with implications from nanoscale to large-scale systems.

## Contribution

It synthesizes two decades of research, highlighting the universal principles governing fluctuation-induced transport across diverse physical systems and scales.

## Key findings

- Transport depends on substrate shape, fluctuation correlations, and particle properties.
- Universal principles apply from nanoscale thermal systems to large granular materials.
- The same concepts govern diverse phenomena across different scales.

## Abstract

The study of fluctuation-induced transport is concerned with the directed motion of particles on a substrate when subjected to a fluctuating external field. Work over the last two decades provides now precise clues on how the average transport depends on three fundamental aspects: the shape of the substrate, the correlations of the fluctuations and the mass, geometry, interaction and density of the particles. These three aspects, reviewed here, acquire additional relevance because the same notions apply to a bewildering variety of problems at very different scales, from the small nano or micro-scale, where thermal fluctuations effects dominate, up to very large scales including ubiquitous cooperative phenomena in granular materials.