Constant Specific Heat Approximation in Multifractal Thermodynamics in Multiparticle Production in Relativistic Heavy-Ion Collisions

Abstract

The study of specific heat is motivated by the fact that a sudden change in the value of specific heat might be interpreted as a signal of a phase transition. It is also an established fact that multifractal analysis has been proved to be highly effective in characterizing fluctuations which is considered to be important tool for understanding the mechanism of quark-gluon plasma (QGP) in high energy nucleus-nucleus collisions. The Present research work provides some fascinating investigations on multifractal specific heat, c using the concept of entropy, f_q which is found as a potential procedure in the study of multifractal specific heat along with the earlier known approaches. The investigations are done for the produced shower particles in nuclear emulsion detector for ²⁸Si-nucleus interactions at 14.5 A GeV/c in the framework of generalized dimension. An attempt is also made to discuss certain universal properties of multifractal specific heat and entropy. We have computed c, by applying the methodology of modified and Takagi moments (T_q). Experimental results are compared with the predictions of LUND model FRITIOF. Moreover, the constant-specific heat method, which is based on the concept of entropy and is commonly accepted in conventional thermodynamics, is demonstrated to be suitable in multifractal thermodynamics also. The values of ‘c’ calculated from these methods are compared with constant specific heat approximations (CSHs) obtained using multifractal entropy (f_q). It is found that the values of ‘c’, estimated using Takagi approach are consistent with those of Bershadskii's work as compared to those calculated using (G_a^m) moments and multifractal entropy, f_q. This is obtained for both experimental and for the FRITIOF generated data for the three types of interactions namely, CNO, emulsion and AgBr. The findings of this paper reveal useful information regarding the choice of method used and our results are consistent with CSH approximation for both experimental and simulated data and also in conjunction with recent studies on multifractal specific heat.