Long after they are set in motion, a modeled gas of active particles can still show traces of how it began, according to an arXiv preprint. The study finds that long-time statistics of the particles' current—the net flow recorded over time—remain dependent on the initial configuration.
The finding comes from a mathematical analysis of an infinite, one-dimensional gas of non-interacting active Ornstein–Uhlenbeck particles. The analysis uses full-counting statistics and large-deviation theory to describe current fluctuations, including unusually unlikely values in the distribution.
A system built around its starting state
The particles begin in a domain-wall density profile: the average density is ρa on the left and ρb on the right. The analysis then varies how positions and velocities are treated at the start, comparing annealed and quenched position or velocity ensembles and also an ensemble with zero initial velocities.
Here, the labels distinguish starting variables that are averaged over from those treated as fixed in the calculation. That distinction matters in the long-time result: quenched averaging need not be the same as fixing a typical initial configuration.
One framework, several time scales
Across the specified ensembles, a single scaled cumulant generating function, or SCGF, describes the distinct current-fluctuation regimes and determines cumulants of all orders. In practical terms, it is one mathematical summary from which the study extracts the distribution's average, spread and higher-order features.
For the annealed-position result, all cumulants carry the same time-dependent scaling factor. The broader pattern is not governed by one simple law: the model displays diffusive, super-diffusive and sub-diffusive regimes at different time scales. The size and structure of current fluctuations therefore depend on when the system is observed.
When rare events and time gaps matter
The study also examines positive-current far tails—the extremely unlikely, high-flow outcomes—and finds that their asymptotic form depends on the initial-position ensemble. With positions annealed, the tail has a logarithmically modified exponential form; in the other ensembles, it takes a different, steeper form.
Those extreme probabilities were checked with rare-event simulations using importance sampling, a technique that gives unusual outcomes extra computational weight and then corrects for that bias. The simulations verify the analytical results and probe probabilities as small as 10 to the power of minus 1000.
The researchers then move from one-time snapshots to pairs of measurements. They derive joint large-deviation statistics for currents measured at distinct times and use those joint distributions to characterize temporal correlations—how strongly a current at one time is linked to one measured later.
The two-time analysis also exposes distinctions that a single-time calculation can hide. In the remaining velocity ensembles, two-time statistics stay distinct at equilibrium even though the corresponding single-time statistics coincide. Two setups can therefore agree on a one-time distribution while still differing in their temporal correlations.
A narrow model with broader questions
The scope is narrow: the calculation concerns an idealized infinite one-dimensional gas of non-interacting particles, and its initial-condition result is shown for the specified domain-wall and velocity ensembles.
The authors identify major open challenges: determining whether these patterns extend to interacting active-particle gases and whether experiments can realize the reported current-fluctuation and memory effects. The document is arXiv:2608.25916v1, dated 26 Aug 2026.
Paper data and sources
Original title: Current fluctuations in a gas of active Ornstein-Uhlenbeck particles
Authors: Sandeep Jangid, Aman Kumbhakar, Juliane U. Klamser, Tridib Sadhu
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-26
DOI: Not available
Original paper · Full text