تابع توزيع شعاعي در نسخه سوم مكانيك آماري تساليس

Radial distribution function within the third version of the Tsallis statistical mechanics

ﺑﺎ ﺗﻮﺟﻪ ﺑﻪ اﯾﻦﮐﻪ ﭘﺪﯾﺪهﻫﺎي ﺑﺴﯿﺎر زﯾﺎدي در ﻃﺒﯿﻌﺖ وﺟﻮد دارﻧﺪ ﮐﻪ رﻓﺘﺎر ﺗﺮﻣﻮدﯾﻨﺎﻣﯿﮑﯽ آﻧﻬﺎ ﺑﻪ ﻋﻠﺖ ﻧﺎﻓﺰوﻧﻮر ﺑﻮدن ﺑﺎ ﻣﮑﺎﻧﯿﮏ آﻣﺎري راﯾﺞ ﺑﻮﻟﺘﺰﻣﻦ-ﮔﯿﺒﺲ ﻗﺎﺑﻞ ﺗﻮﺿﯿﺢ ﻧﯿﺴﺖ، ﺑﺮاي ﺗﻔﺴﯿﺮ اﯾﻦ ﭘﺪﯾﺪهﻫﺎ ﺑﺴﻂ اﻧﺘﺮوﭘﯽ ﺑﻮﻟﺘﺰﻣﻦ-ﮔﯿﺒﺲ ﺿﺮوري اﺳﺖ. در راﺳﺘﺎي اﯾﻦ ﻫﺪف از ﻣﮑﺎﻧﯿﮏ آﻣﺎري ﺟﺪﯾﺪي ﻣﺒﺘﻨﯽ ﺑﺮ ﺗﻌﺮﯾﻔﯽ ﻋﻤﻮﻣﯽ از اﻧﺘﺮوﭘﯽ ﮐﻪ ﺗﻮﺳﻂ ﺗﺴﺎﻟﯿﺲ اراﺋﻪ ﺷﺪه اﺳﺖ، اﺳﺘﻔﺎده ﻣﯽﺷﻮد. در اﯾﻦ ﻣﻘﺎﻟﻪ، در ﭼﺎرﭼﻮب ﻣﮑﺎﻧﯿﮏ آﻣﺎري ﺗﺴﺎﻟﯿﺲ، ﺗﺎﺑﻊ ﺗﻮزﯾﻊ ﺷﻌﺎﻋﯽ )RDF( در ﻧﺴﺨﮥ ﺳﻮم ﺗﺴﺎﻟﯿﺲ ﺑﻪدﺳﺖ آﻣﺪه اﺳﺖ. ﺑﺮاي اﯾﻦ ﻣﻨﻈﻮر، از ﺗﺎﺑﻊ ﺗﻮزﯾﻊ اﺣﺘﻤﺎل در ﻧﺴﺨﻪ ﺳﻮم اﺳﺘﻔﺎده ﺷﺪه و ﯾﮏ ﻓﺮم ﺑﺴﺘﻪ ﺑﺮاي RDF در ﻧﺴﺨﮥ ﺳﻮم ﭘﯿﺸﻨﻬﺎد ﺷﺪه اﺳﺖ. در ﻣﻌﺎدﻟﮥ ﺑﻪدﺳﺖ آﻣﺪه، ﺗﮑﺎﻧﻪﻫﺎ و ﻣﺨﺘﺼﺎت ﻣﮑﺎﻧﯽ ﻣﺴﺘﻘﻞ ﻫﺴﺘﻨﺪ. ﺗﺄﺛﯿﺮ ﺷﺎﺧﺺ اﻧﺘﺮوﭘﯽ q ﺑﺮ ﺗﺎﺑﻊ ﺗﻮزﯾﻊ ﺷﻌﺎﻋﯽ ﺳﯿﺎل ﻟﻨﺎرد-ﺟﻮﻧﺰ ﺑﺮرﺳﯽ ﺷﺪه اﺳﺖ. ﻧﺘﺎﯾﺞ ﻋﺪدي در ﭼﮕﺎﻟﯽﻫﺎي ﭘﺎﯾﯿﻦ، ﻧﺸﺎن ﻣﯽدﻫﺪ ﮐﻪ ﺑﺎ اﻓﺰاﯾﺶ ﻣﻘﺎدﯾﺮ q ﻫﻤﺒﺴﺘﮕﯽ اﻓﺰاﯾﺶ ﻣﯽﯾﺎﺑﺪ. اﻓﺰاﯾﺶ ﺷﺎﺧﺺ اﻧﺘﺮوﭘﯽ q و اﻓﺰاﯾﺶ اﺛﺮ ﺟﺎذﺑﻪ 𝜀، ﺗﺄﺛﯿﺮات ﻣﺸﺎﺑﻬﯽ دارﻧﺪ.

Nowadays, a variety of physical systems have been known whose thermodynamic behavior, due to non-extensive effects, is not explicable by the common Boltzmann-Gibbs (BG) statistical mechanics. Thus, the correction of the BG entropy seems to be essential. In this regard, an efficient extension has been promoted by Tsallis, which is based on a generalized entropic form. In this study, a new equation is derived for the Radial Distribution Function (RDF) by taking into account the third version of the Tsallis statistics. To this end, probability distribution function is applied within the third version of the Tsallis statistics. Moreover, a closed formula is proposed for RDF. The momenta and the coordinates are independent in this equation. The effect of the non-extensivity parameter, q, on the RDF of a Lennard-Jones fluid, was investigated. At low densities, the results of the numerical calculations performed for RDF indicated that, the correlation increases with an increase in the values of q. Increase of the non-extensivity parameter and that of has similar effects.