https://doi.org/10.1140/epjd/e2014-50127-2
Regular Article
A generalized complexity measure based on Rényi entropy
1
Departamento de Matemática Aplicada, Universidad de
Granada, Granada,
Spain
2
Instituto “Carlos I” de Física Teórica y Computacional,
Universidad de Granada, Granada, Spain
3
Departamento de Física Atómica, Molecular y Nuclear, Universidad
de Granada, Granada,
Spain
a
e-mail: pablos@ugr.es
Received: 18 February 2014
Received in final form: 5 May 2014
Published online: 7 August 2014
The intrinsic statistical complexities of finite many-particle systems (i.e., those defined in terms of the single-particle density) quantify the degree of structure or patterns, far beyond the entropy measures. They are intuitively constructed to be minima at the opposite extremes of perfect order and maximal randomness. Starting from the pioneering LMC measure, which satisfies these requirements, some extensions of LMC-Rényi type have been published in the literature. The latter measures were shown to describe a variety of physical aspects of the internal disorder in atomic and molecular systems (e.g., quantum phase transitions, atomic shell filling) which are not grasped by their mother LMC quantity. However, they are not minimal for maximal randomness in general. In this communication, we propose a generalized LMC-Rényi complexity which overcomes this problem. Some applications which illustrate this fact are given.
Key words: Quantum Information
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2014
