One of the most fundamental quantities in Science is Entropy. It finds applications in a wide range of fields like Thermodynamics, Statistical Mechanics, Information Theory, Chemistry, Biology and Finance. The most widely studied entropy is the one of the form:
S = −k pi ln pi
But it is not adequate to study systems with Memory effects, Long-range interactions and Complex systems. To overcome this generalized entropies were introduced in which the ln function is replaced by a generalized function which recovers the logarithm in a particular limit. In this work we examine the basic properties which are to be satisfied by the generalized entropies. Based on these properties we introduced the generalized forms of the Shannon-Kinchinn axioms. Finally I would like to discuss about the extension of statistical mechanics based on generalized entropy and explore some applications.
Chandrashekar Radhakrishnan is a Postdoctoral Research Associate at NYU-ECNU Institute of Physics at NYU Shanghai. He previously worked at National Chung Hsing University in Taiwan and Institute of Mathematical Science in India. He has published 8 articles on International Journals. His interests include Quantum Information and Quantum Computation, Statistical Mechanics and Condensed Matter Physics.
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