On World Religion Adherence Distribution Evolution
  Religious adherence can be considered as a degree of freedom, in a statistical physics sense, for a human agent belonging to a population. The distribution, performance and life time of religions can thus be studied having in mind heterogeneous interacting agent modeling in mind. We present a comprehensive analysis of 58 so called religion (to be better defined in the main text) evolutions, as measured through their number of adherents between 1900 and 2000, - data taken from the World Christian Encyclopedia: 40 are considered to be ''presently growing'' cases, including 11 turn overs in the XX century; 18 are ''presently decaying'', among which 12 are found to have had a recent maximum, in the XIX or the XX century. The Avrami-Kolmogorov differential equation which usually describes solid state transformations, like crystal growth, is used in each case in order to obtain the preferential attachment parameter introduced previously. It is often found close to unity, indicating a smooth evolution. However large values suggest the occurrence of extreme cases which we conjecture are controlled by so called external fields. A few cases indicate the likeliness of a detachment process. We discuss different growing and decaying religions, and illustrate various fits. Some cases seem to indicate the lack of reliability of the data. Others, departure from Avrami law. We point out two difficulties in the analysis : (i) the ''precise'' original time of apparition of a religion, (ii) the time of its maximum, both informations being necessary for integrating reliably any evolution equation. Moreover the Avrami evolution equation might be surely improved, in particular, and somewhat obviously, for the decaying religion cases. 
M. Ausloos and F. Petroni