Tsallis’ deformation parameter quantifies the classical–quantum transition

Abstract

a b s t r a c tWe investigate the classical limit of a type of semiclassical evolution, the pertinent system representing the interaction between matter and a given field. On using Tsallis q-entropy as a quantifier of the ensuing dynamics, we find that it not only appropriately describes the quantum-classical transition, but that the associated deformation-parameter q itself characterizes the different regimes involved in the process, detecting the most salient fine details of the changeover.

Generalized Complexity and Classical-Quantum Transition

“…Finally, we find r , i.e., it distinguishes between the two subsections into which the transitional region divides itself. These last results reconfirm a previous one obtained for H S q in [36], namely, that the parameter q by itself can be regarded as the "looking glass" through which one can observe the quantum-classical transition.…”

“…5g)-5h) allude to the classical region. Although H Sq possesses only one minimum as a function of q [36], C q,J instead may exhibit either a minimum and/or a maximum, plus one or more saddle-points. Consequently, C q,J intersects Shannon's curve C J at least at one point, i.e., i) at q = 1 and at one or more points, depending on E r .…”

Generalized Complexity and Classical-Quantum Transition

“…In [36], we found that the normalized Tsallis wavelet entropy H S q , in the range 0 < q < 5, correctly describes the "E r −evolution", identifying the stages of the transition. As a second result we ascertained that within the subrange 0.1 < q ≤ 0.4, H S q , portrays the quantum sector, something that Shannon's measure is unable to do, concluding that it is the most appropriate entropy, and not the orthodox, q = 1 of Shannon's.…”

“…In [36] we showed that a wavelet-evaluated q-entropy not only describes correctly the quantumclassical border but also that the associated deformation-parameter q itself characterizes the different regimes involved in the concomitant process, detecting the most salient fine details of the transition. The purpose of the present effort is to gather new insights into the q-statistics' contribution to this problem by recourse to a new tool: the q−statistical complexity.…”

Relative Entropies and Jensen Divergences in the Classical Limit

“…The pertinent dynamics displays regular zones, chaotic ones, and other regions that, although not chaotic, possess complex features. The system has been investigated in detail from a purely dynamic viewpoint [20] and also from a statistical one [21][22][23]. For this a prerequisite emerges: how to extract information from a time-series (TS) [24]?…”