Stationary states of activity-driven harmonic chains.

Researchers have long sought to understand how systems driven out of equilibrium reach steady states. Prior studies have focused on equilibrium and near-equilibrium systems, where detailed balance holds and temperature is uniform. However, systems driven by active forces at boundaries often exhibit non-Gaussian fluctuations and spatially varying temperatures. This gap motivated investigations into how different types of active forces influence the stationary state of a system. Theoretical models have shown that harmonic chains can exhibit unique transport properties when driven by active reservoirs. Yet, the specific effects of different active force dynamics remain unclear. This paper addresses this uncertainty by examining three distinct active force models. The study builds on previous work by extending the analysis to include higher-order fluctuations and boundary effects. It also explores the emergence of energy equipartition in nonequilibrium systems. The paper contributes to understanding how boundary-driven active forces shape macroscopic properties of harmonic chains.

The goal of this research is to investigate the stationary state of a harmonic chain driven by active forces at its boundaries. The study aims to determine whether the type of active force affects the system’s macroscopic properties. It also explores how boundary conditions influence the distribution of energy and velocity fluctuations. The researchers focus on three distinct active force dynamics to compare their effects. The study seeks to identify universal features of the stationary state across different driving mechanisms. It also examines the behavior of energy current and velocity distributions in the bulk and at the boundaries. The authors aim to clarify whether energy equipartition holds in nonequilibrium systems driven by active forces. The study addresses the question of how different types of active driving affect the statistical properties of the system.

The researchers model a one-dimensional chain of harmonic oscillators connected to active reservoirs at both ends. They use three types of active force dynamics: active Ornstein-Uhlenbeck process, run-and-tumble process, and active Brownian process. Each model generates correlated stochastic forces with exponentially decaying temporal correlations. The study employs analytical methods to calculate stationary velocity and energy current distributions. The researchers analyze the bulk properties of the system, including kinetic and potential temperatures. They also examine the boundary regions to detect deviations from Gaussian behavior. The study compares the results across the three driving mechanisms to identify commonalities and differences. The authors use statistical mechanics to derive the stationary state properties and validate their findings through numerical simulations.

The study shows that the stationary velocity fluctuations in the bulk are Gaussian, regardless of the active force dynamics. The kinetic temperature remains uniform in the bulk for all three driving mechanisms. The researchers observe an equipartition of energy in the bulk, where kinetic and potential temperatures are equal in the thermodynamic limit. The energy current distribution in the bulk exhibits a logarithmic divergence near zero and asymmetric exponential tails. These features are consistent across all three types of active driving. The study finds that the specific dynamics of the active force influence boundary behavior. Near the boundaries, velocity distributions become non-Gaussian for run-and-tumble and active Brownian processes. The current distribution for these models has a finite cutoff, indicating strong boundary effects. The results suggest that the bulk properties are insensitive to the specific driving mechanism, while boundary effects reveal the nature of the active force.

The authors conclude that the stationary state of a harmonic chain driven by active forces is characterized by Gaussian velocity fluctuations and uniform kinetic temperature in the bulk. These findings hold true regardless of the specific active force dynamics used. The study confirms the emergence of energy equipartition in the bulk of the system in the thermodynamic limit. The energy current distribution consistently shows a logarithmic divergence and asymmetric tails. The researchers observe that boundary effects depend on the type of active force. Run-and-tumble and active Brownian processes lead to non-Gaussian boundary velocity distributions. The current distribution for these models has a finite cutoff, distinguishing them from the active Ornstein-Uhlenbeck process. The results suggest that the bulk properties are universal across different driving mechanisms. The study highlights the importance of boundary conditions in determining the statistical properties of active systems.