From an entropic measure of time to laws of motion

A hypothesis proposed in the paper Entropy (Martyushev, L.M. Entropy 2017, 19, 345) on the deductive formulation of a physical theory based on explicitly- and universally-introduced basic concepts is further developed. An entropic measure of time with a number of properties leading to an analog of the Galileo-Einstein relativity principle is considered. Using this measure and a simple model, a kinematic law which relates time to the size and number of particles of a system is obtained. Corollaries of this law are examined. In particular, accelerated growth of the system size is obtained, whereas in systems with constant size, a decrease in the number of particles is observed. An interesting corollary is the emergence of repulsive and attractive forces inversely proportional to the square of the system size for relatively dense systems and constant for systems with sufficiently low density. © 2019 by the authors

A matrix solution to pentagon equation with anticommuting variables

We construct a solution to pentagon equation with anticommuting variables living on two-dimensional faces of tetrahedra. In this solution, matrix coordinates are ascribed to tetrahedron vertices. As matrix multiplication is noncommutative, this provides a "more quantum" topological field theory than in our previous works

Temperature evaluation of a hyper-rapid plasma jet by the method of high-speed video recording

In this paper the procedure of comparative evaluation of plasma temperature using high-speed video filming of fast processes is presented. It has been established that the maximum plasma temperature reaches the value exceeding 30 000 K for the hypervelocity electric-discharge plasma, generated by a coaxial magnetoplasma accelerator with the use of the 'Image J' software

Geometric torsions and invariants of manifolds with triangulated boundary

Geometric torsions are torsions of acyclic complexes of vector spaces which consist of differentials of geometric quantities assigned to the elements of a manifold triangulation. We use geometric torsions to construct invariants for a manifold with a triangulated boundary. These invariants can be naturally united in a vector, and a change of the boundary triangulation corresponds to a linear transformation of this vector. Moreover, when two manifolds are glued by their common boundary, these vectors undergo scalar multiplication, i.e., they work according to M. Atiyah's axioms for a topological quantum field theory.Comment: 18 pages, 4 figure

Geometric torsions and an Atiyah-style topological field theory

The construction of invariants of three-dimensional manifolds with a triangulated boundary, proposed earlier by the author for the case when the boundary consists of not more than one connected component, is generalized to any number of components. These invariants are based on the torsion of acyclic complexes of geometric origin. The relevant tool for studying our invariants turns out to be F.A. Berezin's calculus of anti-commuting variables; in particular, they are used in the formulation of the main theorem of the paper, concerning the composition of invariants under a gluing of manifolds. We show that the theory obeys a natural modification of M. Atiyah's axioms for anti-commuting variables.Comment: 15 pages, English translation (with minor corrections) of the Russian version. The latter is avaible here as v