Source
Das, Manikandan and Banerjee (2025), Physical Review Applied 24, 034039, LIT-947, read in full in NOTE-788 (arXiv:2504.10124v2).
What was actually shown
- The system.
- Two 1.5 µm beads in separate optical traps, coupled hydrodynamically with strength ε = 3a/(2d) − (a/d)³ (0.49 or 0.29).
- The coupling tensor is symmetric, H = [[1, ε], [ε, 1]]/γ, and the fluid also correlates the thermal noises.
- The mean position of trap 1 is moved by an Ornstein–Uhlenbeck signal λ of strength θ (0.14–0.56 in the experiment). λ is recorded.
- Direction recovered.
- At θ = 0.56 and ε = 0.49, in experiment and numerics: MI_{λ→x₁}(τ) > MI_{x₁→λ}(τ), MI_{x₁→x₂}(τ) > MI_{x₂→x₁}(τ) and MI_{λ→x₂}(τ) > MI_{x₂→λ}(τ).
- TE gives the same order, with TE_{λ→x₁} ≫ TE_{x₁→λ}.
- The measures pick out the driven particle and the order λ → x₁ → x₂. The paper calls this “a signature of hierarchical interaction”.
- But not one-way. MI_{x₂→x₁}(τ) and TE_{x₂→x₁}(τ) also peak, so the flow between the particles is two-way at moderate drive. The paper draws the pathway as λ → x₁ ⇄ x₂.
- One-way under strong drive. At θ = 5.6, in numerics only, the flow
becomes one-way: TE_{x₁→x₂} ≫ TE_{x₂→x₁}.
- The coupling is the same symmetric tensor in every case, so what changed the reading was the strength of the one-sided drive.
- No drive.
- The coupled particles are statistically independent at steady state, P(x₁, x₂) = P(x₁)P(x₂), so the steady-state MI is zero.
- The delayed measures are symmetric: MI_{x₁→x₂}(τ) ≈ MI_{x₂→x₁}(τ) and TE_{x₁→x₂}(τ) ≈ TE_{x₂→x₁}(τ).
- What could have failed.
- The measures could have pointed from x₂ to x₁, or failed to separate λ’s effect on x₂ from x₁’s. They did not.
- The two-way reading at moderate drive is an observation in the experiment.
- The one-way reading under strong drive is a simulation of the fitted linear model.
What this does not say
- It does not say information measures can tell a shared drive from coupling. The drive here acts on one unit and is recorded. The measures locate where it enters. An unrecorded cue acting on both units was not studied. That is QUESTION-063’s main case, and it remains open.
- It does not say that directional flow reveals the coupling. It says the opposite. A symmetric coupling read as two-way at moderate drive and one-way at strong drive.
- It does not say information moves from one particle to the other. “Flow” here is the direction of predictive improvement. Transfer entropy is unique plus synergistic information, not information attributable to the source alone (CLAIM-335), and the paper’s transfer entropy uses a single target value (TERM-057).
- It does not establish the strong-drive result experimentally. θ ≫ 1 is “beyond our experimental regime”.
- It does not say “two-way” against a symmetric null. The significance threshold is computed on shuffled trajectories. It tests against independence, so “two-way” means both directions clear it.
- It is one linear, Gaussian, two-body system with an analytically known covariance. Nothing is shown for nonlinear units or for more than two.
- Its account of the irreversibility trend is a parallel of trends, TE asymmetry against partial entropy production. That is not filed here.
Connections
- QUESTION-063: answers in part. Since 2026-10-23 the part answered is
the child QUESTION-263, which this entry answers in full; the
points below say what it leaves the parent.
- The question asks what measurement tells which architecture produced a collective outcome. This account says what one family of measurements can and cannot see.
- Transfer entropy and delayed MI, with the drive recorded, locate where a drive enters.
- They do not read the symmetry of the coupling, since that reading changes with the drive’s strength.
- So separating a symmetric coupling with one-sided input from an asymmetric coupling needs an intervention on a member, as the question’s “perturb one member and measure the others” proposes.
- CLAIM-172 and CLAIM-167.
- These read peer or hierarchical architecture from whether coupling runs both ways or one.
- Here a mutually coupled pair shows a one-way “hierarchical” information flow once one member is driven hard.
- So an observational direction test would class this pair as hierarchical. CLAIM-172’s “each side’s timing shifts with the other’s” needs an intervention to be applied, not observational flow.
- THEORY-129. Coral colonies synchronized by a shared light cue are the case this account does not reach: a common, unrecorded drive on every member.
Note of 2026-10-19: scope at promotion
Promoted on one study read in full (ADR-047 v3). Each ordering in the title is stated in LIT-947’s text: the moderate-drive orderings beside Figs. 3–4 and in App. F, strong drive in App. D, no drive in App. H. NOTE-788 read the figures from their captions, so the title gives orderings and no values. The general claim, that directional information measures between reciprocally coupled units follow a one-sided drive, is QUESTION-186. In the linear Gaussian pair it could be settled exactly, because delayed-MI asymmetry there is c_xy(τ)² − c_yx(τ)², computable from the stationary covariance.
Note of 2026-10-20: the wider claim, filed apart
Under ADR-047 v4, what this entry’s narrowing dropped is filed as its own Proposed entry, so that evidence can later confirm or reject it as a thesis. CLAIM-396 carries the generalization beyond this system, that directional information measures between reciprocally coupled units follow a one-sided drive and not the coupling. The source makes no general claim, so it is filed as the record’s own interpretive claim. It names this entry in its grounds, as its evidence. Nothing here changes.