Bistable potential and Kramers escape

Purpose

Test whether persistent distinctions correspond to suppressed transition rates.

Links to claims

• Persistent distinction equals suppressed transition rate

System

Particle in a double-well potential with thermal noise.

Setup

• Control parameters: barrier height, noise strength
• Noise model: Gaussian white noise
• Initial conditions: ensemble localized in one well

Distinction definition

• Effective variable: position
• Partition: left well vs right well

Measurement / metric

• Mean first-passage time
• Escape rate distribution
• Lifetime scaling with barrier height

Expected outcomes

• If claim holds: exponential dependence of lifetime on barrier height.
• If claim fails: weak or no correlation.