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Cold Tracer in a Hot Bath: In and out of Equilibrium
Amer Al-Hiyasat1, Sunghan Ro2, Julien Tailleur1
1Massachusetts Institute of Technology, Department of Physics, Cambridge, Massachusetts 02139, USA.
Physical Review Letters
|April 3, 2026
Summary
A cold tracer in Brownian particles transitions from active to equilibrium dynamics as density increases. In a lattice, the tracer drives the bath out of equilibrium, suppressing fluctuations.
Area of Science:
- Statistical Mechanics
- Soft Matter Physics
- Non-equilibrium Systems
Background:
- Studying tracer dynamics in complex fluids is crucial for understanding transport phenomena.
- The behavior of tracers can reveal underlying bath properties and interactions.
- Non-equilibrium systems present unique challenges to traditional statistical mechanics.
Purpose of the Study:
- To investigate the dynamics of a zero-temperature overdamped tracer in a bath of Brownian particles.
- To analytically and numerically characterize the tracer's transition from active to equilibrium dynamics.
- To explore the impact of bath structure (lattice vs. continuous) on tracer and bath behavior.
Main Methods:
- Numerical simulations of tracer-bath systems.
- Analytical derivation by eliminating bath degrees of freedom.
- Perturbation theory for finite bath densities.
- Analysis of systems with bath particles arranged in a lattice.
Main Results:
- Tracer dynamics transition from active (boundary accumulation, ratchet currents) to equilibrium with increasing bath density.
- Analytical results confirm convergence to equilibrium dynamics at high densities.
- Perturbation theory reveals intermediate time-reversible, non-Boltzmann, and fully irreversible regimes.
- A cold tracer in a lattice bath drives the entire system out of equilibrium, suppressing bath fluctuations.
Conclusions:
- The tracer's dynamics are highly sensitive to bath density and structure.
- A lattice structure fundamentally alters the system's equilibrium properties.
- The study provides a theoretical framework for understanding non-equilibrium tracer behavior in soft matter systems.
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