Nucleation and time-reversal symmetry breaking in nonconserved scalar field theories

What the math gives to ML

The paper identifies a useful distinction for rare-event modeling: in nonequilibrium stochastic dynamics, the most probable transition path is generally not the time reversal of the deterministic relaxation path. Its reduced radius dynamics also exposes an effective state-dependent mobility, so both drift and noise geometry matter in the quasipotential barrier. This suggests training latent neural stochastic models with an explicit Freidlin–Wentzell path objective and separately learned forward and reverse drifts, rather than generating rare events by simply reversing a learned relaxation network. The most promising initial target is accelerated rare-event sampling in latent world models or diffusion-like samplers, where success can be measured by transition probability and path-action efficiency.