Related papers: Empirical relationship as a stepping-stone to theo…
We present a general framework in which we can accurately describe the non-equilibrium dynamics of trapped atomic gases. This is achieved by deriving a single Fokker-Planck equation for the gas. In this way we are able to discuss not only…
Ultra-relativistic electromagnetic plasmas can be used for improving our understanding of the quark-gluon plasma. In the weakly coupled regime both plasmas can be described by transport theoretical and quantum field theoretical methods…
A new family of inflationary models is introduced and analysed. The behaviour of the parameters characterising the models suggest preferred values, which generate the most interesting testable predictions. Results are further improved if…
Historically, the thermodynamic behavior of gasses was described first and the derived equations were adapted to solids. It is suggested that the current thermodynamic description of solid phase is still incomplete because the isothermal…
This article is a sequel to our previous paper (arXiv:2511.12311), where we considered the conceptual problem on the empirical laws for the Klein\textendash Gordon quantum field theory in curved spacetime (QFTCS), and we will consider the…
A version of quantum theory is derived from a set of plausible assumptions related to the following general setting: For a given system there is a set of experiments that can be performed, and for each such experiment an ordinary…
We study the Poisson-Boltzmann equation in the context of dense charged fluids where steric effects become important. We generalise the lattice gas theory by introducing a Flory-Huggins entropy for ions of differing volumes and then compare…
It is shown that: in the case when two parameters of the Van der Waals equation of state are defined from the critical temperature and pressure the exact parametrical solution of the equations of the liquid-vapor phase equilibrium of the…
In this work a field theoretical model is constructed to describe the statistical mechanics of an arbitrary number of topologically linked polymers in the context of the analytical approach of Edwards. As an application, the effects of the…
Realistic equations of state valid in the whole state space of a multi-component mixture should satisfy at least three important constraints: (i) The Gibbs phase rule holds. (ii) At low densities, one can deduce a virial equation of state…
The centuries-long practice of the teaching turned mechanics into an academic construct detached from its underlying science, the physics of macroscopic bodies. In particular, the regularities that delineate the scope of validity of…
We derive a stochastic wave equation for an inflaton in an environment of an infinite number of fields. We study solutions of the linearized stochastic evolution equation in an expanding universe. The Fokker-Planck equation for the inflaton…
Previous approaches of emergent thermalization for condensed matter based on typical wavefunctions are extended to generate an intrinsically quantum theory of gases. Gases are fundamentally quantum objects at all temperatures, by virtue of…
We report a numerical study of thermo-osmotic slip, i.e. the particle flux induced by a thermal gradient along a solid-fluid interface. To facilitate comparison with theory, we consider a model of an ideal but viscous gas. We compare three…
Symmetry properties of PDE's are considered within a systematic and unifying scheme: particular attention is devoted to the notion of conditional symmetry, leading to the distinction and a precise characterization of the notions of ``true''…
In this paper, using of the rigorous statement and rigorous proof the Maxwell distribution as an example, we establish estimates of the distribution depending on the parameter $N$, the number of particles. Further, we consider the problem…
We have improved the procedure for calculating distribution functions and the thermal equation of state for real gases by introducing modified functions of probability distributions into the gas phase state sum. Calculation of real gas…
We consider the group of permutations of the vertices of a lattice. A random walk is generated by unit steps that each interchange two nearest neighbor vertices of the lattice. We study the heat equation on the permutation group, using the…
As an example of empirical metamathematics, we present a detailed study of the dependency structure of the 465 theorems in Euclid's Elements, finding empirical signatures of concepts such as the power of a theorem. We apply similar methods…
Conditioning is crucial in applied science when inference involving time series is involved. Belief calculus is an effective way of handling such inference in the presence of epistemic uncertainty -- unfortunately, different approaches to…