Solution to an Anomaly in Internal Energy inside Nonextensive Statistical Mechanics

TL;DR

This paper addresses an internal energy anomaly in nonextensive statistical mechanics for a two-spin system, proposing an alternative matrix approach that aligns calculations with physical expectations.

Contribution

It introduces a new matrix method using rho^q for calculating internal energy, resolving discrepancies in nonextensive statistical mechanics.

Findings

The alternative matrix approach yields consistent internal energy calculations.

Analytical results confirm the suitability of the rho^q matrix.

The method clarifies the physical interpretation of energy in nonextensive systems.

Abstract

Herein, in the context of third version of nonextensive statistical mechanics, theory generalizing the Boltzmann-Gibbs-Shannon statistics, we displayed a solution for an anomaly found by calculating the internal energy for a composite A+B, of 2 spines 1/2, with additive Hamiltonian H= H_A+ H_B; specifically, the calculation of the internal energy in the full Hilbert space is different from the calculation done in the Hilbert subspaces, in other words, U_tot is different to U_A +U_B. We carry out analytical calculations (for 2 spins 1/2). The results exactly indicate that the alternative method of matrices E_A and E_B is suitable for the calculations of the internal energy, therefore, the matrix that contains the physical information of the system is the matrix rho^q but not \rho.