REVIEW
Ultrafast directed transport via energy recuperation in non-Markovian systems
Statistical Mechanics · Submitted 26 Jun 2026 · 37 references
Pith's verdict: The paper extends the 2025 experiment to free particles and inertia-only recuperation but the memory kernel transfer is unverified and likely the main weakness.
Why Pith says this
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Referee report
The paper
The paper claims
Energy recuperation is a generic feature of non-Markovian systems, including free Brownian particles, and drives ultrafast directed transport in periodic potentials.
The reading
What carries the argument
The memory kernel in the generalized Langevin equation, which encodes non-Markovian bath interactions and enables the particle to recover dissipated energy.
Extended reading notes
Core claim
Energy recuperation is a generic feature of non-Markovian systems both in and out of equilibrium, even as simple as a free Brownian particle. Moreover, inertia alone, even in the strong damping regime, can lead to this effect despite the absence of any external forcing. This novel mechanism of energy recovery is the source of memory-induced ultrafast directed transport of a particle in a periodic potential in which it almost attains its top speed corresponding to the system with no energy barriers.
Load-bearing premise
The viscoelastic fluid model and its memory kernel accurately represent the non-Markovian dynamics that produce energy recuperation in the extended cases.
Editorial extensions
If this is right
- Energy recuperation occurs without external driving in inertial non-Markovian systems.
- Inertia suffices to produce recuperation even in the overdamped limit.
- Memory effects allow particles to traverse periodic barriers at speeds approaching the free-particle limit.
- Viscoelasticity of the cytosol may facilitate efficient intracellular particle transport.
Reading between the lines
- The same recuperation mechanism may operate in other memory-bearing media such as polymer solutions or crowded cellular environments.
- Microscale devices could exploit non-Markovian baths to achieve directed motion without continuous external input.
- Extensions to active matter or multi-particle systems would test whether recuperation scales to collective transport.
Original abstract
A recent pioneering experiment [Nat. Commun. 16, 10114 (2025)] demonstrated that a driven overdamped colloidal particle in a harmonic trap immersed in a viscoelastic fluid can recuperate energy dissipated into the surrounding bath and convert it into useful work. In this article we considerably extend the original predictions. In particular, we show that energy recuperation is a generic feature of non-Markovian systems both in and out of equilibrium, even as simple as a free Brownian particle. Moreover, we demonstrate that inertia alone, even in the strong damping regime, can lead to this effect despite the absence of any external forcing. These results suggest that energy recuperation can be ubiquitous in nature and it may be the modus operandi of various phenomena in setups with memory. We show that this novel mechanism of energy recovery is the source of memory-induced ultrafast directed transport of a particle in a periodic potential in which it almost attains its top speed corresponding to the system with no energy barriers. Our results may answer from the fundamental point of view the question why the cytosol, the intracellular fluid in biological cells, is viscoelastic.
Figures
Figures reproduced from arXiv:2606.28567 by the authors.
References
Discussion
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