How the Nonextensivity Parameter Affects Energy Fluctuations

In this article, the effect of the nonextensivity parameter on the energy fluctuations of nonextensive systems is studied in two different versions of the Tsallis statistical mechanics. Once a general expression has been reported for the energy fluctuations in the second version (Tsallis work in 1988), the energy fluctuations of an ideal gas and a harmonic oscillator are studied in the second and fourth(OLM choice for the mean energy constrain) versions of the Tsallis statistical mechanics. The results for the fourth version indicate that relative energy fluctuations are strongly affected by the nonextensivity parameter via the number of accessible states. In fact, in the case of subextensive systems, the nonextensivity parameter leads to fewer accessible states as compared to extensive systems and, therefore, smaller relative energy fluctuations are expected. For super-extensive systems, however, relative energy fluctuations are found to be larger than those in extensive systems because of the greater accessible states available. Our studies show that very large relative energy fluctuations are caused as a result of the un-normalized nature of the second version which, in some cases, limits its application.