Related papers: Quantropy
We show that, in spite of a rather common opinion, quantum mechanics can be represented as an approximation of classical statistical mechanics. The approximation under consideration is based on the ordinary Taylor expansion of physical…
Planck-scale quantum spacetime undergoes probabilistic local curvature fluctuations whose distributions cannot explicitly depend on position otherwise vacuum's small-scale quantum structure would fail to be statistically homogeneous. Since…
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…
We present some basic inequalities between the classical and quantum values of free energy, entropy and mean energy. We investigate the transition from the deterministic case (classical mechanics) to the probabilistic case (quantum…
A kinetic equation for a dilute gas of hard spheres confined between two parallel plates separated a distance smaller than two particle dimeters is derived. It is a Boltzmann-like equation, which incorporates the effect of the confinement…
We describe society as a nonequilibrium probabilistic system: N individuals occupy W resource states in it and produce entropy S over definite time periods. Resulting thermodynamics is however unusual because a second entropy, H, measures a…
Identical systems, or entities, are indistinguishable in quantum mechanics (QM), and the symmetrization postulate rules the possible statistical distributions of a large number of identical quantum entities. However, a thorough analysis on…
An essential quantity in quantum information theory is the von Neumann entropy which depends entirely on the quantum density operator. Once known, the density operator reveals the statistics of observables in a quantum process, and the…
In this paper I propose a new way for counting the microstates of a system out of equilibrium. As, according to quantum mechanics, things happen as if a given particle can be found in more than one state at once, I extend this concept to…
Quantum information-theoretic approach has been identified as a way to understand the foundations of quantum mechanics as early as 1950 due to Shannon. However there hasn't been enough advancement or rigorous development of the subject. In…
It is well known that a Shannon based definition of information entropy leads in the classical case to the Boltzmann entropy. It is tempting to regard the Von Neumann entropy as the corresponding quantum mechanical definition. But the…
Based on the concept of ensemble, it is proved in the manuscript that the probability amplitude function can also been used to describe the classical statistical system. The motion equations of probability amplitude functions of classical…
Although both systems analyzed are described through two theories apparently different (quantum mechanics and game theory) it is shown that both are analogous and thus exactly equivalents. The quantum analogue of the replicator dynamics is…
We propose the study of quantum games from the point of view of quantum information theory and statistical mechanics. Every game can be described by a density operator, the von Neumann entropy and the quantum replicator dynamics. There…
In classical physics there is a well-known theorem in which it is established that the energy per degree of freedom is the same. However, in quantum mechanics due to the non-commutativity of some pairs of observables and the possibility of…
We sketch and emphasize the automatic emergence of a quantum potential Q in e.g. classical WDW type equations upon inserting a (Bohmian) complex wave function. The interpretation of Q in terms of momentum fluctuations via Fisher information…
Non-relativistic quantum theory is derived from information codified into an appropriate statistical model. The basic assumption is that there is an irreducible uncertainty in the location of particles: positions constitute a configuration…
The Gibbs entropy of a macroscopic classical system is a function of a probability distribution over phase space, i.e., of an ensemble. In contrast, the Boltzmann entropy is a function on phase space, and is thus defined for an individual…
This paper is an introduction to the von Neumann entropy in a historic approach. Von Neumann's gedanken experiment is repeated, which led him to the formula of thermodynamic entropy of a statistical operator. In the analysis of his ideas we…
The aim of the paper is to derive essential elements of quantum mechanics from a parametric structure extending that of traditional mathematical statistics. The main extensions, which also can be motivated from an applied statistics point…