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A mathematical procedure is suggested to obtain deformed entropy formulas of type K(S_K) = sum_i P_i K(-ln P_i), by requiring zero mutual K(S_K)-information between a finite subsystem and a finite reservoir. The use of this method is first demonstrated on the ideal gas equation of state with finite constant heat capacity, C, where it delivers the Renyi and Tsallis formulas. A novel interpretation of the qstar = 2-q duality arises from the comparison of canonical subsystem and total microcanonical partition approaches. Finally a new, generalized deformed entropy formula is constructed for the linear relation C(S) = C_0 + C_1 S.
To illustrate Boltzmanns construction of an entropy function that is defined for a single microstate of a system, we present here the simple example of the free expansion of a one dimensional gas of hard point particles. The construction requires one
The underlying connection between the degrees of freedom of a system and its nonextensive thermodynamic behavior is addressed. The problem is handled by starting from a thermodynamical system with fractal structure and its analytical reduction to a f
We conduct a rigorous investigation into the thermodynamic instability of ideal Bose gas confined in a cubic box, without assuming thermodynamic limit nor continuous approximation. Based on the exact expression of canonical partition function, we per
The virial expansion of a gas is a correction to the ideal gas law that is usually discussed in advanced courses in statistical mechanics. In this note we outline this derivation in a manner suitable for advanced undergraduate and introductory gradua
We find universal structure and scaling of BEC statistics and thermodynamics for mesoscopic canonical-ensemble ideal gas in a trap for any parameters, including critical region. We identify universal constraint-cut-off mechanism that makes BEC fluctu