On the Role of Geometric and Entropic Arguments in Physics: From Classical Thermodynamics to Quantum Mechanics

Dear Colleagues,

Geometry plays a special role in the description and, to a certain extent, in the understanding of various physical phenomena. The concepts of length, area, and volume are ubiquitous in physics and their meaning can prove quite helpful in explaining physical phenomena from a more intuitive perspective. The notions of “longer” and “shorter” are extensively used in virtually all disciplines. Indeed, geometric formulations of classical and quantum evolutions along with geometric descriptions of classical and quantum mechanical aspects of thermal phenomena are becoming increasingly important in science. Concepts, such as thermodynamic length, area law, and statistical volumes are omnipresent in geometric thermodynamics, general relativity, and statistical physics, respectively.

The concept of entropy finds application in essentially any realm of science, from classical thermodynamics to quantum information science. The notions of “hotter” and “cooler” are widely used in many fields. Entropy can be used to provide measures of distinguishability of classical probability distributions, as well as pure and mixed quantum states. It can also be used to propose measures of complexity for classical motion, quantum evolution, and entropic motion on curved statistical manifolds underlying the entropic dynamics of physical systems for which only partial knowledge of relevant information can be obtained. Furthermore, entropy can also be used to express the degree of entanglement in a quantum state specifying a composite quantum system. For instance, concepts such as Shannon entropy, von Neumann entropy, and Umegaki relative entropy are ubiquitous in classical information science, quantum information theory, and information geometric formulations of mixed quantum state evolutions, respectively.

The aim of this Special Issue is to collect works exhibiting novel connections among geometry, thermodynamics, and quantum information theoretic concepts. Clearly, special attention to the role played by entropic arguments in such connections will be warmly welcomed.

Dr. Carlo Cafaro
Guest Editor

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