Acoustic dip in the effective temperature of hot Brownian motion
Abstract
A hot Brownian particle is driven by thermal fluctuations from a nonuniformly heated solvent and therefore obeys a fluctuation-dissipation relation with a frequency-dependent effective temperature. Existing theories assume an incompressible solvent. We show that finite sound speed qualitatively changes this effective temperature in the kinetic regime. Solving the compressible fluctuating-hydrodynamic problem for a heated sphere, we find that the effective noise temperature develops a pronounced acoustic dip when the sound wavelength becomes comparable to the particle radius. The dip occurs because weakly attenuated longitudinal modes carry mechanical energy away from the heated surface before it is dissipated, so that the dissipation is weighted by colder regions of the temperature field. Its position is set by aω/c=𝒪(1), while its depth is controlled by the dimensionless viscous-acoustic attenuation length ac/a. The result identifies an acoustic window in hot Brownian motion in which compressibility lowers, rather than raises, the kinetic noise temperature.
Related
- Quantum Brownian motion in a temperature gradient
- Geometric Brownian motion with intermittent entries and exits
- Broadband molecular dynamics simulation of confined Brownian motion
- Einstein's theory of Brownian motion: The non-Fickian normal diffusion
- Non-stationary Statistics and Energetics of Brownian Motion under Stochastic Harmonic Confinement
BibTeX
@misc{srivastava2026acoustic,
title = {{Acoustic dip in the effective temperature of hot Brownian motion}},
author = {Mayank Srivastava and Dipanjan Chakraborty},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.22515},
eprint = {2609.22515},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.22515},
}
RIS
TY - UNPB
TI - Acoustic dip in the effective temperature of hot Brownian motion
AU - Mayank Srivastava
AU - Dipanjan Chakraborty
PY - 2026
DA - 2026/09/18
PB - arXiv
DO - 10.48550/arxiv.2609.22515
UR - https://arxiv.org/abs/2609.22515
AB - A hot Brownian particle is driven by thermal fluctuations from a nonuniformly heated solvent and therefore obeys a fluctuation-dissipation relation with a frequency-dependent effective temperature. Existing theories assume an incompressible solvent. We show that finite sound speed qualitatively changes this effective temperature in the kinetic regime. Solving the compressible fluctuating-hydrodynamic problem for a heated sphere, we find that the effective noise temperature develops a pronounced acoustic dip when the sound wavelength becomes comparable to the particle radius. The dip occurs because weakly attenuated longitudinal modes carry mechanical energy away from the heated surface before it is dissipated, so that the dissipation is weighted by colder regions of the temperature field. Its position is set by aω/c=𝒪(1), while its depth is controlled by the dimensionless viscous-acoustic attenuation length a_c/a. The result identifies an acoustic window in hot Brownian motion in which compressibility lowers, rather than raises, the kinetic noise temperature.
ER -