Abstract
The Fokker-Planck-Kramers (FPK) equation for the rotational Brownian motion of a linear rigid rotator in 3D is derived from the basic principles of statistical mechanics applied to the two classical model Hamiltonians: 1. 1) The model of a rigid fixed rotor interacting with a bath of harmonic oscillators. 2. 2) The model of a linear rigid rodlike polymer diluted in a monoatomic solvent. An entropy formula is established for the rotator system allowing to formulate the second law of thermodynamics and to analyze its implication on the form of the dielectric and Kerr functions. Finally, a general scheme is proposed to solve the FPK equation in the form of series expansion. Approximative analytical expressions for the dielectric and Kerr functions, are obtained up to the third order in the electric field, considering a steady state regime of a dc field on which is superimposed an alternating field. These response functions generalize and extend all the results recently published on the topic. The particular case of the Debye-Smoluchowski diffusion model is straightforwardly recovered.
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