Thermodynamic relations and fluctuations in the Tsallis statistics

Abstract

The thermodynamic relations in the Tsallis statistics were discussed with physical temperature and physical pressure. An additive entropic variable related to the Tsallis entropy was introduced by assuming the form of the first law of the thermodynamics. The fluctuations in the Tsallis statistics were derived with physical quantities with the help of the introduced entropic variable. It was shown that these fluctuations are related to heat capacities and compressibilities, as shown in the conventional thermodynamics. The fluctuation of the Tsallis entropy was also given through the fluctuation of the entropic variable.