Readout-induced decay of records

Purpose

Test whether a persistent distinction qualifies as a record only when it can be accessed repeatedly without significantly accelerating decay.

Links to claims

• Records require readable persistence
• Persistent distinction equals suppressed transition rate (optional)

System

A bistable memory element (two metastable basins) subject to noise, with an adjustable readout coupling that extracts state information.

Setup

• Memory variable: x(t) (effective state coordinate)
• Basins: A and B (partition defined by x < 0 vs x > 0, or by attractor membership)
• Noise model: thermal or stochastic forcing with known intensity D
• Readout channel: a probe that couples to x(t) with strength g and is applied at rate f (reads per unit time)

Distinction definition

• Effective state variables: x(t)
• Partition rule: A if x(t) < 0, B if x(t) > 0 (or basin membership)
• Persistence baseline: measure lifetime τ0 with g = 0

Readout implementation (conceptual)

During readout events, the probe interacts with the memory element. That interaction should have two effects:

1. It reveals state (increases measurement signal-to-noise).
2. It perturbs the dynamics (adds back-action noise or reduces barrier height).

Measurement / metric

Primary:

• τ(g, f): mean dwell time in a basin (or mean first-passage time across the boundary)
• k(g, f) = 1 / τ(g, f): transition rate

Secondary:

• Readout fidelity: P(correct state | probe output)
• Back-action proxy: additional effective diffusion ΔD(g) or effective barrier reduction ΔU(g)

Experimental protocol

1. Calibrate baseline: measure τ0 at g = 0 across noise levels D.
2. Turn on readout with fixed f; sweep g; measure τ(g, f) and fidelity.
3. Fix g; sweep f; measure τ(g, f).
4. Repeat across at least two barrier heights (or constraint strengths).

Expected outcomes

If claim holds:

• τ(g, f) decreases as g increases and as f increases (readout accelerates decay).
• There exists a regime where fidelity is high yet τ is not strongly reduced (a “usable record regime”).

If claim fails:

• τ is insensitive to g and f, or decay is dominated entirely by baseline noise regardless of probing.

Notes

This tests an operational distinction between:

• a persistent distinction (stable state),
• and a record (stable state that remains stable under repeated access).