From Wandering Thoughts to Mental Stillness: A Minimal Computational Statistical-Mechanical Model of Driven Relaxation

Reduced spontaneous thought during meditation is often described phenomenologically, but a mechanistic account should specify how a dynamical system can enter and persist in such a regime. Here we formulate a minimal statistical-mechanical model in which a dimensionless coordinate q represents a coarse-grained propensity for spontaneous-thought activity and a slowly relaxing variable r ( t ) represents the history-dependent effect of an attentional manipulation. The model combines a tilted double-well landscape with Langevin noise, allowing a high- q and a low- q dynamical regime to coexist. We numerically integrate the model under a controlled focusing protocol followed by removal of the drive and quantify low-state occupancy, first-passage times, dwell times, occupancy entropy, and transition entropy. For the chosen dimensionless parameterization, increasing the drive amplitude produces a sharp crossover in low-state occupancy near the deterministic spinodal threshold A _sp ≃0.0148. At noise intensity D = 0.01, the probability of occupying the low- q regime at drive removal increases from 0.094 at A = 0 to 0.994 at A = 0.02, while the mean first-passage time decreases from 48.0 to 13.5 model time units. Noise produces a non-monotonic effect: for A = 0.01, low-state occupancy at drive removal is only 0.033 at D = 0.0025, rises to 0.842 at D = 0.02, and falls to 0.718 at D = 0.04. Strong driving also reduces the effective number of occupied states while changing transition entropy much less, illustrating why a single entropy measure cannot identify thoughtlessness. These results do not establish that human neural dynamics obey this model. Instead, they show that a driven stochastic bistable system can generate the qualitative sequence of focusing, switching, relaxation, and metastable low-activity residence, and they provide quantitative predictions that can be tested against time-resolved neural recordings and independent reports of subjective experience.