Probability Theory Compatible with the New Conception of Modern Thermodynamics. Economics and Crisis of Debts

We show that G\"odel's negative results concerning arithmetic, which date back to the 1930s, and the ancient "sand pile" paradox (known also as "sorites paradox") pose the questions of the use of fuzzy sets and of the effect of a measuring device on the experiment. The consideration of these facts led, in thermodynamics, to a new one-parameter family of ideal gases. In turn, this leads to a new approach to probability theory (including the new notion of independent events). As applied to economics, this gives the correction, based on Friedman's rule, to Irving Fisher's "Main Law of Economics" and enables us to consider the theory of debt crisis.Comment: 48p., 14 figs., 82 refs.; more precise mathematical explanations are added. arXiv admin note: significant text overlap with arXiv:1111.610

Solution of the Hyperon Puzzle within a Relativistic Mean-Field Model

The equation of state of cold baryonic matter is studied within a relativistic mean-field model with hadron masses and coupling constants depending on the scalar field. All hadron masses undergo a universal scaling, whereas the coupling constants are scaled differently. The appearance of hyperons in dense neutron star interiors is accounted for, however the equation of state remains sufficiently stiff if a reduction of the $\phi$ meson mass is included. Our equation of state matches well the constraints known from analyses of the astrophysical data and the particle production in heavy-ion collisions.Comment: 7 pages, 4 figures; replaced with the published versio

q-Legendre Transformation: Partition Functions and Quantization of the Boltzmann Constant

In this paper we construct a q-analogue of the Legendre transformation, where q is a matrix of formal variables defining the phase space braidings between the coordinates and momenta (the extensive and intensive thermodynamic observables). Our approach is based on an analogy between the semiclassical wave functions in quantum mechanics and the quasithermodynamic partition functions in statistical physics. The basic idea is to go from the q-Hamilton-Jacobi equation in mechanics to the q-Legendre transformation in thermodynamics. It is shown, that this requires a non-commutative analogue of the Planck-Boltzmann constants (hbar and k_B) to be introduced back into the classical formulae. Being applied to statistical physics, this naturally leads to an idea to go further and to replace the Boltzmann constant with an infinite collection of generators of the so-called epoch\'e (bracketing) algebra. The latter is an infinite dimensional noncommutative algebra recently introduced in our previous work, which can be perceived as an infinite sequence of "deformations of deformations" of the Weyl algebra. The generators mentioned are naturally indexed by planar binary leaf-labelled trees in such a way, that the trees with a single leaf correspond to the observables of the limiting thermodynamic system

Quasithermodynamics and a Correction to the Stefan--Boltzmann Law

We provide a correction to the Stefan--Boltzmann law and discuss the problem of a phase transition from the superfluid state into the normal state.Comment: Latex, 9page

Universal Behavior of One-Dimensional Gapped Antiferromagnets in Staggered Magnetic Field

We study the properties of one-dimensional gapped Heisenberg antiferromagnets in the presence of an arbitrary strong staggered magnetic field. For these systems we predict a universal form for the staggered magnetization curve. This function, as well as the effect the staggered field has on the energy gaps in longitudinal and transversal excitation spectra, are determined from the universal form of the effective potential in O(3)-symmetric 1+1--dimensional field theory. Our theoretical findings are in excellent agreement with recent neutron scattering data on R_2 Ba Ni O_5 (R = magnetic rare earth) linear-chain mixed spin antiferromagnets.Comment: 4 pages, 2 figure