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Revisiting the ratchet principle: Lessons from active and passive stochastic dynamics
Jessica Metzger1, Sunghan Ro1,2, Julien Tailleur1
1Massachusetts Institute of Technology, Department of Physics, Cambridge, Massachusetts 02139, USA.
Physical Review. E
|July 24, 2026
Summary
Directed currents in stochastic systems require broken symmetries. However, hidden momentum conservation laws can prevent steady currents, even with asymmetric fluctuations and broken time-reversal symmetry.
Area of Science:
- Statistical physics
- Non-equilibrium systems
- Complex systems
Background:
- The ratchet principle posits that breaking parity and time-reversal symmetries is essential for directed currents.
- Generic expectation is current emergence when all such symmetries are violated.
Purpose of the Study:
- Investigate stochastic systems with asymmetric fluctuations that violate symmetries but lack steady currents.
- Identify the role of hidden conservation laws in preventing directed transport.
- Analyze various models including Brownian dynamics and active particles.
Main Methods:
- Theoretical analysis of stochastic systems.
- Numerical simulations to test for directed currents.
- Path-integral and operator methods to characterize time-reversal asymmetry.
- Perturbation theories for onset of directed currents.
Main Results:
- Hidden momentum conservation laws prevent steady directed currents in systems with asymmetric fluctuations.
- Thermal fluctuations cannot sustain directed currents in Brownian dynamics, even with broken time-reversal symmetry.
- Effective momentum conservation inhibits interaction-induced directed currents in Active Ornstein-Uhlenbeck particles.
Conclusions:
- Momentum conservation is a critical factor limiting directed transport in stochastic systems.
- Not all asymmetric fluctuations can drive steady currents; underlying conservation laws must be considered.
- Understanding these limitations is key to designing systems with controlled directed motion.
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