Magnetic Resonance and Minimum Entropy Production. Macroscopic Equations of Motion

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Abstract
A generalization and modification of a previous discussion is given. By requiring that the steady states obtained in magnetic resonance experiments correspond to the minimum rate of entropy production, a condition is obtained which must be satisfied by the equation describing the rate of change of the spin density matrix due to interactions with the surroundings. This enables one to test the adequacy of the form of equations proposed to describe relaxation phenomena in resonance by finding whether they satisfy this condition, and, conversely, one can derive directly possible forms of macroscopic terms from its solutions. As examples of this procedure, the modified Bloch equations are derived, and the equation of Codrington, Olds, and Torrey is shown to be consistent with this condition. A corrected form of the Wangsness-Bloch equation for the rate of change of the density matrix is shown to be more adequate for arbitrary values of the fields, and the justification of the modified Bloch equations is also given in this way. Other examples, as well as the general relation of this work to irreversible thermodynamics, are discussed, and a generalized reciprocal relation is derived. The steady-state solutions of the new equations of motion are given in an appendix.