Related papers: Dimensionless Groups by Entropic Similarity
This paper analyses the turbulent energy cascade from the perspective of statistical mechanics, and relates inter-scale energy fluxes to statistical irreversibility and information-entropy production. The microscopical reversibility of the…
(2+1) dimensional diffusion equation is considered within the framework of equivalence transformations. Generators for the group are obtained and admissible transformations between linear and nonlinear equations are examined. It is shown…
The ``Gibbs Paradox'' refers to several related questions concerning entropy in thermodynamics and statistical mechanics: whether it is an extensive quantity or not, how it changes when identical particles are mixed, and the proper way to…
Hierarchical structures, which include multiple levels, are prevalent in statistical and machine-learning models as well as physical systems. Extending the foundational result that the maximum entropy distribution under mean constraints is…
The principle of entropy increase is not only the basis of statistical mechanics, but also closely related to the irreversibility of time, the origin of life, chaos and turbulence. In this paper, we first discuss the dynamic system…
Entanglement is central both to the foundations of quantum theory and, as a novel resource, to quantum information science. The theory of entanglement establishes basic laws, such as the non-increase of entanglement under local operations,…
We introduce a class of information measures based on group entropies, allowing us to describe the information-theoretical properties of complex systems. These entropic measures are nonadditive, and are mathematically deduced from a series…
To better understand the collisionless dark matter flow on different scales, statistical theory involving kinematic and dynamic relations must be developed for different types of flow, e.g. incompressible, constant divergence, and…
*First-principles derivation of the entropy production in erectric static conduction. *The second-order (symmetric) density matrix contributes to the entropy production. *New schemes of steady states formulated using a relaxation-type von…
The stochastic entropy generated during the evolution of a system interacting with an environment may be separated into three components, but only two of these have a non-negative mean. The third component of entropy production is…
We develop an axiomatic reconstruction of thermodynamics based entirely on two primitive components: a description of what aspects of a system are observed and a reference measure that encodes the underlying descriptive convention. These…
The infinite reduction of couplings is a tool to consistently renormalize a wide class of non-renormalizable theories with a reduced, eventually finite, set of independent couplings, and classify the non-renormalizable interactions. Several…
We study the nonextensive thermodynamics for open systems. On the basis of the maximum entropy principle, the dual power-law q-distribution functions are re-deduced by using the dual particle number definitions and assuming that the…
The paper presents a versatile framework for solids which undergo nonisothermal processes with irreversibly changing microstructure at large strains. It outlines rate-type and incremental variational principles for the full thermomechanical…
The microscopic explanation of entropy has been challenged from both experimental and theoretical point of view. The expression of entropy is derived from the first law of thermodynamics indicating that entropy or the second law of…
Identifying dissipation is essential for understanding the physical mechanisms underlying nonequilibrium processes. {In living systems, for example, the dissipation is directly related to the hydrolysis of fuel molecules such as adenosine…
Using the recently developed ``Maximum Entropy'' (or ``least biased'') distribution function to truncate the moment hierarchy arising from kinetic theory, we formulate a far-from-equilibrium macroscopic theory that provides the possibility…
Entropy is a central concept in physics, but can be challenging to calculate even for systems that are easily simulated. This is exacerbated out of equilibrium, where generally little is known about the distribution characterizing simulated…
The notions of generating sets of conservation laws of systems of differential equations with respect to symmetry groups and equivalence groups are introduced and applied. This allows us to generalize essentially the procedure of finding…
Stimulated by the need of describing useful notions related to information measures, we introduce the `pdf-related distributions'. These are defined in terms of transformation of absolutely continuous random variables through their own…