Related papers: Dimensional Equations of Entropy
Entropy is one of the key thermodynamic variables reflecting changes in the state of matter. Unlike other thermodynamic variables, it is well-defined also for nonequilibrium steady states through its relation to information. Applying this…
We produce a probabilistic space from logic, both classical and quantum, which is in addition partially ordered in such a way that entropy is monotone. In particular do we establish the following equation: Quantitative Probability = Logic +…
Entropic dynamics is a framework for defining dynamical systems that is aligned with the principles of information theory. In an entropic dynamics model for motion on a statistical manifold, we find that the rate of changes for expected…
Information plays an important role in our understanding of the physical world. We hence propose an entropic measure of information for any physical theory that admits systems, states and measurements. In the quantum and classical world,…
Entropic uncertainty is a well-known concept to formulate uncertainty relations for continuous variable quantum systems with finitely many degrees of freedom. Typically, the bounds of such relations scale with the number of oscillator…
Entropy is a famous and well established concept in physics and engineering that can be used for explanation of basic fundamentals as well it finds applications in several areas, from quantum physics to astronomy, from network communication…
We describe a thought experiment using an isolated system of known parameters and assuming the correctness of Clausius and Boltzmann descriptions of entropy. The experiment produced an astronomical increase in the number of possible ways…
The entropic moments of the probability density of a quantum system in position and momentum spaces describe not only some fundamental and/or experimentally accessible quantities of the system, but also the entropic uncertainty measures of…
The notion of metric entropy dimension is introduced to measure the complexity of entropy zero dynamical systems. For measure preserving systems, we define entropy dimension via the dimension of entropy generating sequences. This…
Since its origin in the thermodynamics of the 19th century, the concept of entropy has also permeated other fields of physics and mathematics, such as Classical and Quantum Statistical Mechanics, Information Theory, Probability Theory,…
In this paper, we review the concept of entropy in connection with the description of quantum unstable systems. We revise the conventional definition of entropy due to Boltzmann and extend it so as to include the presence of complex-energy…
The principal methods for the definition of thermodynamic entropy are discussed with special reference to those developed by Carath\'eodory, the Keenan School, Lieb and Yngvason, and the present authors. An improvement of the latter method…
Entropy can signify different things: For instance, heat transfer in thermodynamics or a measure of information in data analysis. Many entropies have been introduced and it can be difficult to ascertain their different importance and…
It is demonstrated that entropy and its density play a significant role in solving the problem of the vacuum energy density (cosmological constant) of the Universe and hence the dark energy problem. Taking this in mind, two most popular…
Thermodynamics is commonly presented as a theory of macroscopic systems in stable equilibrium, built upon assumptions of extensivity and scaling with system size. In this paper, we present a universal formulation of the elementary…
This is a short analysis of the changes in the concept of entropy as applied to physics of the present-day and Early Universe. Of special interest is a leading role of such a notion as deformation of a physical theory. The relation to a…
Entropy numbers and covering numbers of sets and operators are well known geometric notions, which found many applications in various fields of mathematics, statistics, and computer science. Their values for finite-dimensional embeddings…
Thermodynamic entropy, as defined by Clausius, characterizes macroscopic observations of a system based on phenomenological quantities such as temperature and heat. In contrast, information-theoretic entropy, introduced by Shannon, is a…
We present a brief history of how the famous Maximum Entropy Principle was used as closure of moments of the Boltzmann equation. In particular, we want to remark on the important role of two fundamental papers by Wolfgang Dreyer, one in the…
The physical foundations of a variety of emerging technologies --- ranging from the applications of quantum entanglement in quantum information to the applications of nonequilibrium bulk and interface phenomena in microfluidics, biology,…