Finite heat reservoir capacity, C, and temperature fluctuation, ΔT/T, lead to modifications of the well known canonical exponential weight factor. Requiring that the corrections least depend on the one-particle energy, ω, we derive a deformed entropy, K(S). The resultingformula contains the...

A mathematical procedure is suggested to obtain deformed entropy formulas of type K(SK)=∑PiK(−lnPi), by requiring zero mutual K(SK)-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...

In this paper we study the possible microscopic origin of heavy-tailed probability density distributions for the price variation of financial instruments. We extend the standard log-normal process to include another random component in the so-called stochastic volatility models. We study these...