Now we can define the Saroglitazar (Magnesium) chemical information mutual contagion I fi ; gj = P(fi |gj ) 1 1 log P f – log P f |g = log P(fi ) , where P(f i ) is an “a ( i) ( i j) priori” estimate. Then, I (F; G) 0, I (F; G) = 0 P (F, G) = P (F) P (G) , and I is symmetric in F and G (I (F; G) = I (G; F)). Furthermore, S (F) =n i=1 P 1 n i=1 Pn -li = i = 1 pi log (K) – log n n log (K) + i = 1 pi li log () log() i = 1 pi li . Thus, S (B) Llog (), where L = n= 1 pi li . So the entropy provide a lowerifi logn i=gj log1 P(gj ), S (F | G) =n i=1 m j=1 P1 , S (G) P(fi ) m j = 1 P fi g j 1 P(fi ,gj )=log P f |g , S(F, G) = , fi , gj log ( i j) S (F, G) = S (F) + S (G | F) = S (G) + S (F | G), I (F, G) = I (F)+I (G)-I (F, G) = I (F)-I (F | G) = I (G)-I (G | F) 0, thus, we can write the mutual contagion I (F, G) as a difference between the marginal entropy and the conditional entropy. Thus, given the knowledge of G, the decreased uncertainty of F represents the mutual contagion. For this reason we call I (F, G) mutual contagion. Now we can define the “channel capacity” as CMax = MaxP(f ) I (F; G). Now we will use a standard maximum entropy principle (MEP). Let us call sr (r = 1, 2, . . . , K) some characteristics at macroscopic-level. Let us assume that these are associated (r) to characteristics at microscopic-level by = sr , i fi si onstrained by fi 0 and i fi = 1: subjected to this constraints we have to maximize Thus, a(r) si i filog1 fi, the entropy. is fi =have only one code with length l1 , l2 , . . . , ln iif K 1 where li = e(ai ) , i = 1, 2, . . . , n; and ai A. Let consider, now kn =n 1 i = 1 li ngeneralsolution,= k,Nk nl i = 1 k ,withl = Max l1 , l2 , . . . , ln . Of course Nk thus k nl k = n k = nl – n + 1 nl. Thus, K 1. Now define,-li n for 0 < Gi 1, and i = 1 Gi = 1, Gi = K . Applying the Gibbs inequality, given pi the probability to observe hi , we 1 will obtain: n= 1 pi log Gii 0 or n= 1 pi log pi n= 1 i i i pKn, where r represents the standard exp – – r r multiplayer of Lagrange. We can define H (1 , 2 , . . . , K ) = (r) . i exp – r r si Thus, e = H or = ln (H). The mathematical analytics allows researcher to study the dynamics in a formal and elegant way, but unfortunately a model calibration to real behavior is very complex, being more adapted to a theoretical approach to computational communication than to real behavioral systems. However, the above equationspi log1 Gi.Frontiers in Psychology | http://www.frontiersin.orgNovember 2015 | Volume 6 | ArticleCipressoModeling behavior dynamicsrepresent the fundamental basis for the statistical mechanics approach, which we analyze below.MODELING BEHAVIOR DYNAMICS AMONG MANY INDIVIDUALS Modeling Behavior Dynamics through "Difference Equation"There are many ways to model behavior dynamics in complex systems (Bar-Yam, 1997).