When a group of spins is placed in a magnetic field, each spin aligns in one of the two possible orientations. The relative numbers of spins with different alignments will be given by the Boltzmann distribution.
Definition: if a system of particles, which are able to exchange energy in collisions is in thermal equilibrium, then the relative number (population) of particles, N1 and N2, in two particular energy levels with corresponding energies, E1 and E2, is given by N1/N2 = exp [-(E1 - E2)/kT] where k is the Boltzmann constant and T is the absolute temperature.
For example, in NMR of protons at room temperature in a magnetic field of 0.25 tesla, the difference in relative numbers of spins aligned with the magnetic field and against the field is about one part in a million; the small excess of nuclei in the lower energy state is the basis of the net magnetization and the resonance phenomenon.

The numbers of nuclei or electrons in different energy levels. At thermal equilibrium, the relative populations of the energy levels will be given by the Boltzmann distribution.

See also Boltzmann Distribution.

The initial energy level of a spinning proton is depended of thermodynamics conditions (see Boltzmann distribution). In a magnetic field, each spin can exist in one of a number of distinct states having different energy levels. Each level is given a magnetic quantum number, m.

A state in which all parts of a system are at the same effective temperature, in particular where the relative alignment of the spins with the magnetic field is determined solely by the thermal energy of the system (in which case the relative numbers of spins with different alignments will be given by the Boltzmann distribution).

The process by which molecules or other particles intermingle and migrate due to their random thermal motion. Microscopic particles are jittering around with translational and rotational motions as a result of their thermal energy, which is half the Boltzmann constant multiplied by the absolute temperature of the system (0.5kT) per degree of freedom (3 directions of translation and 3 directions of rotation for ordinary particles).
MRI provides a sensitive technique for measuring diffusion of some substances. These diffusive processes mean that particles reach areas of low from areas of high concentration, thus leading to equilibration. In body fluids, the distribution of capillaries within tissues is such that transport over macroscopic distances is accomplished by the blood circulation, while over intercapillary distances substances are carried by diffusion. The fluid diffusion constant is itself inversely proportional to the viscosity and the radius of the diffusing particles.

See also Diffusion Tensor Imaging and Diffusion Weighted Imaging.