From Wandering Thoughts to Mental Stillness: A Minimal Computational Statistical-Mechanical Model of Driven Relaxation
- 1IIT Kharagpur
Abstract
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 of 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-sub-sp, approximately equal to 0.0148. At a noise intensity of D equal to 0.01, the probability of occupying the low-q regime at drive removal increases from 0.094 at A equal to zero to 0.994 at A equal to 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 equal to 0.01, low-state occupancy at drive removal is only 0.033 at D equal to 0.0025, rises to 0.842 at D equal to 0.02, and falls to 0.718 at D equal to 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.
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BibTeX
@misc{karmakar2026from,
title = {{From Wandering Thoughts to Mental Stillness: A Minimal Computational Statistical-Mechanical Model of Driven Relaxation}},
author = {S. Karmakar},
howpublished = {bioRxiv},
year = {2026},
month = oct,
doi = {10.64898/2026.10.11.758288},
url = {https://www.biorxiv.org/content/10.64898/2026.10.11.758288v1},
note = {CC BY},
}
RIS
TY - UNPB
TI - From Wandering Thoughts to Mental Stillness: A Minimal Computational Statistical-Mechanical Model of Driven Relaxation
AU - S. Karmakar
PY - 2026
DA - 2026/10/11
PB - bioRxiv
DO - 10.64898/2026.10.11.758288
UR - https://www.biorxiv.org/content/10.64898/2026.10.11.758288v1
AB - 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 of 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-sub-sp, approximately equal to 0.0148. At a noise intensity of D equal to 0.01, the probability of occupying the low-q regime at drive removal increases from 0.094 at A equal to zero to 0.994 at A equal to 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 equal to 0.01, low-state occupancy at drive removal is only 0.033 at D equal to 0.0025, rises to 0.842 at D equal to 0.02, and falls to 0.718 at D equal to 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.
ER -