Information analysis in free and confined harmonic oscillator

TL;DR

This paper reviews recent advances in applying information theoretic measures like Shannon and Fisher entropy to analyze free and confined harmonic oscillators, highlighting their physical and chemical implications.

Contribution

It provides a comprehensive overview of information measures in quantum systems, emphasizing their role in understanding confined harmonic oscillators and related physical phenomena.

Findings

Information measures effectively characterize quantum uncertainties.

Confined systems exhibit notable changes in information-theoretic quantities.

These measures help explain physico-chemical properties of quantum systems.

Abstract

In this chapter we shall discuss the recent progresses of information theoretic tools in the context of free and confined harmonic oscillator. Confined quantum systems have provided appreciable interest in areas of physics, chemistry, biology,etc., since its inception. A particle under extreme pressure environment unfolds many fascinating, notable physical and chemical changes. The desired effect is achieved by reducing the spatial boundary from infinity to a finite region. Similarly, in the last decade, information measures were investigated extensively in diverse quantum problems, in both free and constrained situations. The most prominent amongst these are: Fisher information, Shannon entropy, Renyi entropy , Tsallis entropy, Onicescu energy and several complexities. Arguably, these are the most effective measures of uncertainty, as they do not make any reference to some specific points of a respective Hilbert space. These have been invoked to explain several physico-chemical properties of a system under investigation. Kullback-Leibler divergence or relative entropy describes how a given probability distribution shifts from a reference distribution function. This characterizes a measure of discrimination between two states. In other words, it extracts the change of information in going from one state to another.