Fractional Calculus, Wavelet Analysis, and Entropy

Dear Colleagues,

Entropy can be used as a measure of disorder, from total order and total disorder. Entropy as a concept emerged in classical thermodynamics as a way to measure the amount of energy in a system that cannot produce work. In 1872, Ludwig Boltzmann presented his H-theorem and a statement about fundamentally irreversible processes. Later, this was translated to other physics and mathematics fields, taking on diverse meanings. In 1927, John von Neumann defined von Neumann entropy from a statistical mechanics perspective, extending the concept of Gibbs entropy to quantum mechanics as a measure of disorder. Moreover, in 1948, Claude E. Shannon published A Mathematical Theory of Communication, defining entropy as a measure of uncertainty or information; as randomness or chaos in dynamic metric systems; and as a measure of complexity in continuous dynamic systems, such as Lempel–Ziv complexity, proposed by Dr. Sam Kwong and Yu Fan Ho in 2001. Entropy is a fascinating and challenging concept with applications in many scientific disciplines, including equilibrium and non-equilibrium thermodynamics, statistical mechanics, cosmology, life sciences, chemistry and biochemistry, geosciences, linguistics, social sciences, and information theory.

For this Special Issue, we invite reviews and expository and original research articles highlighting recent advances in the application of fractional calculus and wavelet analysis in the concept of entropy and its applications.

The main topics of this Special Issue include (but are not limited to):

•  Entropy theory;
•  Fractional entropy;
•  Wavelet entropy;
•  Shannon and Renyi entropy of entropy;
•  MRA and entropy;
•  Astronomical data analysis;
•  Multiresolution signal processing and entropy coding.

Dr. Emanuel Guariglia
Guest Editor

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• entropy
• wavelet basis
• MRA
• Shannon entropy
• Renyi entropy
• entropy coding