Classical and Quantum H-Theorem Revisited: Variational Entropy and Relaxation Processes

We propose a novel framework to describe the time-evolution of dilute classical and quantum gases, initially out of equilibrium and with spatial inhomogeneities, towards equilibrium. Briefly, we divide the system into small cells and consider the local equilibrium hypothesis. We subsequently define a global functional that is the sum of cell H-functionals. Each cell functional recovers the corresponding Maxwell–Boltzmann, Fermi–Dirac, or Bose–Einstein distribution function, depending on the classical or quantum nature of the gas. The time-evolution of the system is described by the relationship dH/dt≤0, and the equality condition occurs if the system is in the equilibrium state. Via the variational method, proof of the previous relationship, which might be an extension of the H-theorem for inhomogeneous systems, is presented for both classical and quantum gases. Furthermore, the H-functionals are in agreement with the correspondence principle. We discuss how the H-functionals can be identified with the system’s entropy and analyze the relaxation processes of out-of-equilibrium systems.

Visual Variations between Pairs of SARS-CoV-2 Genomes on Integrated Density Matrix

This paper is the B2 module of the MAS. The quantification matrix is formed according to the four-base arrangement in the genome sequence. The differences in new coronavirus genome sequencing sequences in different samples were demonstrated by using the most concise methods. Using 4 primitive variable value measures, changes in the virus genome sequence base order conditions were deter-mined. When two relatively large genomic sequences are slightly different, the integrated distribution of the difference calculation is subtly similar to the Bose-einstein distribution, while the sum calculation shows a powerful distribution complexity. It can be formed under the macroscopic angle and can distinguish 16 combinations of supersymmetric structures. In view of the abundant transformation structure in this kind of transformation system, the detailed exploration remains to be followed by the systematic expansion of theory and medical application.

Visual Variations between Pairs of SARS-CoV-2 Genomes on Integrated Density Matrix

This paper is the B2 module of the MAS. The quantification matrix is formed according to the four-base arrangement in the genome sequence. The differences in new coronavirus genome sequencing sequences in different samples were demonstrated by using the most concise methods. Using 4 primitive variable value measures, changes in the virus genome sequence base order conditions were determined. When two relatively large genomic sequences are slightly different, the integrated distribution of the difference calculation is subtly similar to the Bose-Einstein distribution, while the sum calculation shows a powerful distribution complexity. It can be formed under the macroscopic angle and can distinguish 16 combinations of supersymmetric structures. In view of the abundant transformation structure in this kind of transformation system, the detailed exploration remains to be followed by the systematic expansion of theory and medical application.

On the Chemical Potential of Ideal Fermi and Bose Gases

Knowledge of the chemical potential is essential in application of the Fermi–Dirac and the Bose–Einstein distribution functions for the calculation of properties of quantum gases. We give expressions for the chemical potential of ideal Fermi and Bose gases in 1, 2 and 3 dimensions in terms of inverse polylogarithm functions. We provide Mathematica functions for these chemical potentials together with low- and high-temperature series expansions. In the 3d Bose case we give also expansions about $$T_{{{{\mathrm {B}}}}}$$ T B . The Mathematica routines for the series allow calculation to arbitrary order.

Stimulated emission of relic gravitons and their super-Poissonian statistics

The degree of second-order coherence of the relic gravitons produced from the vacuum is super-Poissonian and larger than in the case of a chaotic source characterized by a Bose–Einstein distribution. If the initial state does not minimize the tensor Hamiltonian and has a dispersion smaller than its averaged multiplicity, the overall statistics is by definition sub-Poissonian. Depending on the nature of the sub-Poissonian initial state, the final degree of second-order coherence of the quanta produced by stimulated emission may diminish (possibly even below the characteristic value of a chaotic source) but it always remains larger than one (i.e. super-Poissonian). When the initial statistics is Poissonian (like in the case of a coherent state or for a mixed state weighted by a Poisson distribution) the degree of second-order coherence of the produced gravitons is still super-Poissonian. Even though the quantum origin of the relic gravitons inside the Hubble radius can be effectively disambiguated by looking at the corresponding Hanbury Brown–Twiss correlations, the final distributions caused by different initial states maintain their super-Poissonian character which cannot be altered.