Boltzmann sampling technique, equilibrium

Transitions among the various spin states are governed by rate equations fliat represent two counteraeting probability funetions. The first of fliese fimctions pertains to the radiation-indueed transition and the probabihty that the time-dependent eleetric field of the ineident radiation eouples to the sample medium and induces transitions among the allowed spin states. The counterpart, spin relaxation, denotes the multifaceted dynamics of the spin population as it returns to thermal i.e., Boltzmann) equilibrium. The relative rates of these two processes determine the EMR signal intensity, and the associated spin dynamic processes serve as the basis for advanced EMR techniques and their specialized niches for determining super-hyperfine parameters. 

The MC technique is a stochastic simulation method designed to generate a long sequence, or Markov chain of configurations that asymptotically sample the probability density of an equilibrium ensemble of statistical mechanics [105, 116]. For example, a MC simulation in the canonical (NVT) ensemble, carried out under the macroscopic constraints of a prescribed number of molecules N, total volume V and temperature T, samples configurations rp with probability proportional to, with, k being the Boltzmann constant and T the... 

---