Stability criteria for q-expectation values

On the robustness of q-expectation values and Rényi entropy

We study the robustness of functionals of probability distributions such as the Rényi and nonadditive Sq entropies, as well as the q-expectation values under small variations of the distributions. We focus on three important types of distribution functions, namely (i) continuous bounded (ii) discrete with finite number of states, and (iii) discrete with infinite number of states. The physical c...

CRITERIA Approaching Expectation Meeting Expectation Exceeding Expectation Speech

Generalized Expectation Criteria

This note describes generalized expectation (GE) criteria, a framework for incorporating preferences about model expectations into parameter estimation objective functions. We discuss relations to other methods, various learning paradigms it supports, and applications that can leverage its flexibility.

Computing Expectation Values for Molecular Quantum Dynamics

We compute expectation values for the solution of the nuclear Schrödinger equation. The proposed particle method consists of three steps: sampling of the initial Wigner function, classical transport of the sampling points, weighted phase space summation for the final computation of the expectation values. The Egorov theorem guarantees that the algorithm is second order accurate with respect to ...

Tsallis statistics with normalized q-expectation values is thermodynamically stable: illustrations

We present a study of both the “Iterative Procedure” and the “β → β transformation”, proposed by Tsallis et al (Physica A261, 534) to find the probabilities pi of a system to be in a state with energy ǫi, within the framework of a generalized statistical mechanics. Using stability and convexity arguments, we argue that the iterative procedure does not always provide the right temperature depend...