Trajectory Statistics Govern Mechanical Power Transfer in Active Baths

@misc{woo2026trajectory,
  title = {{Trajectory Statistics Govern Mechanical Power Transfer in Active Baths}},
  author = {Chul-Ung Woo and Jiwon Choi and Heiko Rieger},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.17047},
  eprint = {2609.17047},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.17047},
  note = {CC BY 4.0},
}

TY  - UNPB
TI  - Trajectory Statistics Govern Mechanical Power Transfer in Active Baths
AU  - Chul-Ung Woo
AU  - Jiwon Choi
AU  - Heiko Rieger
PY  - 2026
DA  - 2026/09/15
PB  - arXiv
DO  - 10.48550/arxiv.2609.17047
UR  - https://arxiv.org/abs/2609.17047
AB  - The mechanical response of a moving probe in an active bath reflects both the dynamics of the bath and how the probe couples to it. For a probe moving at velocity V and interacting weakly with an ideal active bath, we show that the trajectory statistics of a free bath particle determine a density response from which the bath force on the probe follows. The probe-particle interaction determines how this response is weighted over wave vector q, while the probe motion selects frequencies ω_q=q· V. This trajectory-response relation separates the bath dynamics from the wave-vector weighting, so neither the stationary state nor force correlations need to be recalculated for each probe interaction and velocity. Applying this relation to active-particle models, we prove that positive power transfer is excluded for active Ornstein--Uhlenbeck particles in all dimensions and for complete-reset run-and-tumble particles in d≥2, while one-dimensional run-and-tumble particles and two-dimensional active Brownian particles possess modes that can transfer positive mechanical power. For a given probe, this response predicts drag reversal, spontaneous probe motion, and motion-induced density distortions, all in quantitative agreement with simulations. Varying the probe geometry changes how the same bath response is weighted, thereby selecting different moving states. Beyond the leading weak-probe, ideal-bath limit, higher orders in probe strength involve multi-interval trajectory statistics, while finite-density corrections involve interacting-particle dynamics. Our results connect the trajectory statistics of active bath particles to the mechanical response of a passive probe, providing a route to predict probe response from single-particle trajectory statistics measured in the absence of the probe.
ER  -