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  • 176 Reads
Using the entropy generation analysis in flow boiling conditions for enhanced heat transfer techniques : Micro-fin tube

The flow boiling heat transfer is one of the common phenomenon happens in the industries. The micro-fin tubes are one of the geometries in enhancing heat transfer rate in boiling condition. The entropy generation analysis is presented with its formulation precisely to find best operating conditions in micro-fin tubes in terms of changing in geometry and flow conditions. This analysis shows important aspects of losses in fluid systems when boiling happens. The losses include thermal loss related to the heat transfer and hydraulic one related to the pressure drop. The relevant terms are described for both of these losses. The optimum tube diameter under specified conditions is found. The effect of different flow conditions such as mass velocity, inlet vapor quality on contribution of pressure drop and heat transfer in entropy generation is discussed. It is found that, there is a desirable conditions of fluid flow and micro-fin geometrical shape to reach the minimum of entropy generation.

  • Open access
  • 90 Reads
Zeeman effects on the entanglement of non-equilibrium finite-spin systems

We study the Zeeman effect on entanglement of non-equilibrium finite-spin systems with external fields using a method based on thermofield dynamics (TFD). For this purpose, the extended density matrices and extended entanglement entropies of two systems with either non-competing or competing external fields are calculated according to the dissipative von Neumann equation, and the numerical results are compared. Consequently, through the ``twin-peaks'' oscillations of the quantum entanglement, we have illustrated the Zeeman effect on the entanglement of non-equilibrium finite-spin systems with competing external fields in the TFD algorithm.

  • Open access
  • 118 Reads
GUP Modified Phase-Space and Thermodynamics Self-Consistency

Based on the generalized uncertainty principle (GUP) with the modi cation of the phase space, the partition function has recently been modi ed . In the present work, we analyze the self-consistency of the axiomatic thermodynamic derived from the modi ed partition function. This work studies the self-consistency for the thermodynamic quantities pressure, energy density, entropy, number density and some correlated quantities. The thermal parameters at the moment of freeze-out are extracted, as well as the occupation number of the fermionic states. We found that, the deformed phase space distribution does not obey the thermodynamic consistency conditions. On the other hand, the thermodynamic quantities and freeze-out parameters are well reproduced.

  • Open access
  • 84 Reads
Information Entropy of Molecular Tunneling

Molecular tunneling process has been considered by means of radiation theory. The formula for information entropy calculation has been derived by means of interaction model of thermal equilibrium radiation with a molecule at low temperatures. The physical meaning of information entropy for low-temperature plateau of unimolecular chemical reaction has been determined. It is a measure of conversion of thermal radiation energy to mechanical energy that moves atoms in a molecule during elementary activation act. It is also a measure of uncertainty of this energy conversion. The conversion takes place at a temperature when the average energy of the elementary activation act is equal to a part of zero energy of the transforming molecule. Two unimolecular reactions have been investigated. These are Fe-CO bond recombination in β-hemoglobin and double proton transfer in benzoic acid dimer for sequential deuteration of hydrogen bond and various hydrostatic pressures. Using the information entropy formula it is possible to calculate its value in energy units of measurements for low-temperature plateau. Probabilities of occurrence of the reactions under considerations, their efficiency and mean-square fluctuations of the distribution function parameters have also been determined [1].

[1] A.V. Stepanov, International Journal of Modern Physics B, Vol. 29, No 4 (2015) 1550016 (18 pages).

  • Open access
  • 85 Reads
Interpolating Binary and Multivalued Logical Quantum Gates

A method for synthesizing quantum gates is presented based on interpolation methods applied to operators in Hilbert space. Starting from the diagonal forms of specific generating seed operators with non-degenerate eigenvalue spectrum one obtains for arity-one a complete family of logical operators corresponding to all the one-argument logical connectives. Scaling-up to n -arity gates is obtained by using the Kronecker product and unitary transformations. The quantum version of the Fourier transform of Boolean functions is presented and a Reed-Muller decomposition for quantum logical gates is derived. The common control gates can be easily obtained by considering the logical correspondence between the control logic operator and the binary logic operator. A new polynomial and exponential formulation of the Toffoli gate is presented. The method has parallels to quantum gate-T optimization methods using powers of multilinear operator polynomials. The method is then applied naturally to alphabets greater than two for multi-valued logical gates used for quantum Fourier transform, min-max decision circuits and multivalued adders.

  • Open access
  • 130 Reads
Entropy and Geometric Objects

Different notions of entropy can be identified in different communities [1]: (i) the thermodynamic sense, (ii) the information sense, (iii) the statistical sense, (iv) the disorder sense, and (v) the homogeneity sense. Especially the “disorder sense” and the “homogeneity sense” relate to and require the notion of space and time. One of the few prominent examples relating entropy to geometry and to space is the Bekenstein-Hawking entropy of a Black Hole. Although being developed for the description of a physics object – a black hole – having a mass, a momentum, a temperature, a charge etc. absolutely no information about these attributes of this object can eventually be found in the final formula. In contrast, the Bekenstein-Hawking entropy in its dimensionless form [2] is a positive quantity only comprising geometric attributes like an area A- which is the area of the event horizon of the black hole- , a length LP – which is the Planck length - and a factor ¼. A purely geometric approach towards this formula will be presented. The approach is based on a continuous 3D extension of the Heaviside function [3] drawing on the phase-field concept of diffuse interfaces [4]. Entropy enters into the local, statistical description of contrast resp. gradient distributions in the transition region of the extended Heaviside function definition. The Bekenstein- Hawking formula structure can eventually be derived based on such geometric-statistic considerations.

  1. Haglund, J.; Jeppsson, F.; Strömdahl, H.: “Different Senses of Entropy—Implications for Education.” Entropy 2010, 12, 490-515.
  2. Bekenstein, J. D. (2008): Scholarpedia, 3(10):7375.     doi:10.4249/scholarpedia.7375
  3. see e.g. : Weisstein, Eric W. "Heaviside Step Function." From MathWorld--A Wolfram Web Resource.
  4. see e.g. Provatas, N., Elder, K.: Phase-Field Methods in Materials Science and Engineering, Wiley VCH, Weinheim (2010),ISBN: 978-3-527-40747-7
  • Open access
  • 79 Reads
Boltzmann entropy, the holographic bound and Newtonian cosmology

The holographic principle sets an upper bound on the total (Boltzmann) entropy content of the Universe at around $10^{123}k_B$ ($k_B$ being Boltzmann's constant). In this work we point out the existence of a remarkable duality between nonrelativistic quantum mechanics on the one hand, and Newtonian cosmology on the other. Specifically, nonrelativistic quantum mechanics has a quantum probability fluid that exactly mimics the behaviour of the cosmological fluid, the latter considered in the Newtonian approximation. One proves that the equations governing the cosmological fluid (the Euler equation and the continuity equation) become the very equations that govern the quantum probability fluid after applying the Madelung transformation to the Schroedinger wavefunction. Under the assumption that gravitational equipotential surfaces can be identified with isoentropic surfaces, this model allows for a simple computation of the gravitational entropy of the Universe.

In a first approximation we model the cosmological fluid as the quantum probability fluid of free Schroedinger waves. We find that this model Universe saturates the holographic bound. As a second approximation we include the Hubble expansion of the galaxies. The corresponding Schroedinger waves lead to a value of the entropy lying three orders of magnitude below the holographic bound. Although a considerable improvement, this still lies above existing phenomenological estimates of the entropy of the Universe. Current work on a fully relativistic extension of our present model can be expected to yield results in even better agreement with empirical estimates of the entropy of the Universe.

  • Open access
  • 56 Reads
Exponential or power law? How to select a stable distribution of probability in a physical system

A mapping of non-extensive statistical mechanics into standard, Gibbs' statistical mechanics exists [S. Abe, Physica A 300 417-423 (2001), E. Vives, A. Planes, PRL 88 2, 020601 (2002)] which preserves the concavity of entropy and generalizes Gibbs-Duhem equation. This mapping allows generalization of the 'general evolution criterion' of [P. Glansdorff, I. Prigogine, Physica 30 351 (1964)] to non-extensive statistical mechanics with non-additivity parameter q. GEC leads to a necessary criterion for the stability of relaxed states of a wide class of physical systems [A. Di Vita, Phys. Rev. E 81 041137 (2010)]. In its generalized version, thiscriterion holds for arbitrary q and implies a suitably constrained minimization of the amount Pi-q of non-extensive entropy Sq produced per unit time in the bulk of the system. Moreover, if we assume q to be uniform throughout a non-isolated, relaxed system, then the distribution of probabilities of microstates in each small part of the system is a power law (a Boltzmann exponential) for q different from (equal to) 1. Accordingly, constrained minimization of Pi-q selects the value of q of a stable distribution of probabilities: if Pi-q = min for q equal to (different from) 1, then the probability distribution of a stable, relaxed state is a Boltzmann exponential (a power law). This value of q depends on both the detailed dynamics and on the boundary conditions of the system. As an example, we apply our result to a simple, one-dimensional system.

  • Open access
  • 131 Reads
Causal Classical Physics in Time Symmetric Quantum Mechanics

The letter (to be) submitted is an executive summary of our previous paper [3]. To solve the Einstein Podolsky Rosen "paradox" the two boundary quantum mechanics developed by Aharonov and coworkers [1] and others is taken as self consistent interpretation [2].

The difficulty with this interpretation of quantum mechanics is to reconcile it with classical physics. To avoid classical backward causation two "corresponding transition rules" are formulated which specify needed properties of macroscopic observations and manipulations. The apparent classical causal decision tree requires to understand the classically unchosen options. They are taken to occur with a "incomplete knowledge" of the boundary states typically in macroscopic considerations. The precise boundary conditions with given phases then select the actual measured path and this selection is mistaken to happen at the time of measurement. The apparent time direction of the decision tree originates in an assumed relative proximity to the initial state. Only the far away final state allows for classically distinct options to be selected from.

Cosmological the picture could correspond to a big bang initial and a hugely extended final state scenario. It is speculated that it might also under certain condition work for a big bang / big crunch world. In this case the Born probability postulate could find a natural explanation if we coexist in the expanding and the CPT conjugate contracting world.

[1] Yakir Aharonov, Peter G Bergmann, and Joel L Lebowitz. Time symmetry in the quantum process of measurement. Physical Review, 134(6B):B1410, 1964.
[2] Yakir Aharonov, Eliahu Cohen, and Tomer Landsberger. The two-time in-terpretation and macroscopic time-reversibility. Entropy, 19(3), 2017.
[3] Fritz W. Bopp. Time Symmetric Quantum Mechanics and Causal Classical Physics. Foundation of Physics, DOI:10.1007/s10701-017-0074-7, archiv:1604.04231, 2016.

  • Open access
  • 51 Reads
Maximum entropy production principle and morphological selection in hydrodynamic systems

In recent decades an idea has emerged that the maximum entropy production principle can be used to select from the different regimes of development of nonequilibrium systems. According to this principle, the process with maximum entropy production is most preferred among the possible non-equilibrium processes. As a consequence, entropy production can be used to find an actually observed pattern formation among the hypothetical ones. The entropy production is calculated for distorted and undistorted evolving phase interface and the process with the largest entropy production is assumed to be nonlinearly stable. A hypothesis is introduced that the role of entropy production for morphological transitions is similar to the role of chemical potential for equilibrium phase transitions, i.e. it can be used to find a boundary (binodal) dividing the region of absolutely stable growth from the region of growth which is unstable (metastable) with regard to arbitrary amplitude distortions. This principle has been successfully applied to analyze the interfacial morphological stability during crystallization.

The objective of this study is application of described principle in two cases. The first problem is the stability analysis of the displacement front of two immiscible fluids, where more viscous one is displaced by the less viscous one in the radial Hele–Shaw cell. Together with linear stability analysis (which describes the stability to infinitesimal distortions, i.e. gives the spinodal) entropy production approach allows to determinate the region of different interface forms coexistence. These boundaries are analyzed depending on the cell size, the injected flow rate, and the ratio of the fluid viscosities.

The second problem is the stability of a spherical surface of a vapor bubble growing under inertia control. In this case we obtain that the entropy production in the vicinity of the bubble's distorted surface is always greater than that of the undistorted surface. Such a result indicates that the morphological phase with a distorted surface is more preferable and consequently should be observable in a real system where arbitrary perturbations occur. This allows explaining the experimentally observed roughness of the bubble surface during explosive vaporization.

The reported study was funded by RFBR according to the research project
No.16-31-00255 мол_а and scientific project № 1.4539.2017/8.9

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