Polarization entropy transfer and relative polarization entropy

The concept of polarization entropy is extended to include its transfer by an optical system (or scattering medium) characterized by a Jones matrix (or equivalently, a Mueller-Jones matrix) and also by a general Mueller matrix. It is shown that physical realizability for a deterministic, passive medium governed by a Jones matrix implies enpolarization (i.e., output degree of polarization is greater than input degree of polarization) and that the output entropy is less than the input entropy. Thus enpolarization leads to a decrease in the uncertainty of the output relative to the input as characterized by the respective degree of polarization. General Mueller matrices can depolarize (i.e., output degree of polarization is less than input degree of polarization), leading to an output entropy that is greater than the input entropy. Thus depolarization leads to an increase in the uncertainty of the output relative to the input. An entropic measure of the ''distance'' between input and output degrees of polarization, the relative entropy, is introduced and studied.