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Fractal entropies from the Second Inverse Maximum Entropy Principle
Marcelo R. Ubriaco
With use of the Second Inverse Maximum Entropy Principle we find entropy functions for systems with fractal distribution functions with order parameter . We compare these entrop…
Density matrix for a consistent non-extensive thermodynamics
Marcelo R. Ubriaco
Starting with the average particle distribution function for bosons and fermions for non-extensive thermodynamics , as proposed in \cite{CMP}, we obtain the corresponding density m…
The role of curvature in quantum statistical mechanics
Marcelo R. Ubriaco
In this manuscript, we calculate the scalar curvature of a two-dimensional thermodynamic space to study the properties of two thermodynamic systems. In particular, we study the sta…
Thermodynamics of bosons systems related to Dunkl differential-difference operators
Marcelo R. Ubriaco
We study the thermodynamics of systems based on a Fock space representation inspired by the differential-difference operators proposed in Ref. \cite{Dunkl}. We calculate thermodyna…
Stability and anyonic behavior of systems with M-statistics
Marcelo R. Ubriaco
Starting with the partition function for systems with -statistics, as proposed in \cite{WND}, we calculate from the metric the…
Scalar curvature of systems with fractal distribution functions
Marcelo R. Ubriaco
Starting with the relative entropy for two close statistical states we define the metric and calculate the scalar curvature for systems with classical, boson and fermion fracta…
A simple mathematical model for anomalous diffusion via Fisher's information theory
Marcelo R. Ubriaco
Starting with the relative entropy based on a previously proposed entropy function , we find the corresponding Fisher's information measure. After…
Entropies based on fractional calculus
Marcelo R. Ubriaco
We propose entropy functions based on fractional calculus. We show that this new entropy has the same properties than the Shannon entropy except additivity, therefore making this e…