An arXiv preprint reports that delta-function force kicks may be optimal for minimizing work or dissipation when an inertial stochastic system, a model with inertia and randomness, is driven rapidly. The result comes from a short-time calculation and a modeled barrier-crossing comparison. The paper also states extensions to active and quantum dynamics, but its central claim depends on a defined set of dynamical assumptions.
The short-time edge
The clearest difference appears as the allowed driving time becomes very small. The paper reports linear short-duration work scaling for protocols with delta-function kicks, versus quadratic scaling for protocols without kicks. Its reported optimal-versus-naive saved-work ratio diverges as Δt approaches zero. For an overdamped quadratic trap, the comparison ratio is 3/2.
The calculation uses a first-order short-time expansion of the probability distribution. That makes the result an asymptotic statement about the rapid-driving limit, rather than a measurement from a physical trial.
For a fixed-stiffness quadratic trap, the paper gives an optimal-to-linear saved-work ratio of 6/(ξΔt). In the same comparison, δ-STEP saved work scales linearly with Δt, while linear driving scales quadratically, making the short-time contrast explicit.
A narrow set of conditions
The word “optimal” has a narrow scope in this analysis. The statement assumes initial equilibrium with zero average momentum uncorrelated with position, momentum-independent forces, inertial position dynamics, and no direct spatial noise. It therefore concerns a particular model class rather than stochastic systems in general.
Within that class, the leading-order initial impulse is A* = ΔF/(2ξ), and the final impulse is B* = A*. For affine parametric control, the leading impulse protocol is λδ = Δλ[δ(t) - δ(t - Δt)]/(2ξ). The quadratic-trap result is stated to apply to arbitrary static energy landscapes.
The simulated crossing is more mixed
The modeled test simulates underdamped barrier crossing in a quadratic trap across a double-well landscape and compares δ-STEP, δ-linear and an impulse-free linear protocol.
For short durations, both kicked protocols outperform the impulse-free linear protocol and have matching leading linear-in-Δt scaling. The comparison remains a result of the reported model and its specified setup.
The advantage is not uniform across the full time range. At longer modeled durations, δ-STEP performs worse than linear driving. In the reported intermediate-duration example, δ-linear saves over 5 kB T while traversing a 1 kB T barrier and continues to perform well at long durations.
Where the claim stops
The text extends the argument to generalized Langevin dynamics with momentum-space noise, to quantum Brownian motion when the dissipator does not directly couple to position, and to stochastic RLC circuits under inductance control. Capacitive control is excluded from that circuit analogy.
Quantum dynamics also supplies a clear caveat. Some completely positive Markovian Lindblad dynamics violate the no-position-coupling assumption. When that dissipator is included, the text reports O(Δt) dynamics for momentum-independent observables and says delta-function kicks are no longer optimal.
A model result, not a universal rule
The manuscript is an arXiv version-1 preprint dated 25 Aug 2026, identified as arXiv:2608.25070v1. Its central message is narrower than a universal prescription: the reported advantage belongs to rapid, kicked protocols under the stated assumptions, while the modeled results show that δ-STEP can perform worse than linear driving at longer durations.
Paper data and sources
Original title: Delta-Function Kicks are Optimal for Rapidly Driven Inertial Stochastic Systems
Authors: Steven Blaber
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-25
DOI: Not available
Original paper · Full text