Verallgemeinerte physikalische Entropien auf informationstheoretischer Grundlage

1965 ◽  
Vol 20 (12) ◽  
pp. 1543-1553 ◽  
Author(s):  
H. Schwegler
Keyword(s):  
Density Operator ◽  
Gibbs Equation ◽  
Macroscopic Equation ◽  
Von Neumann ◽  
Special Cases ◽  
Self Consistent ◽  
Von Neumann Equation ◽  
The Times ◽  
Experimental Values ◽  
Special Case

Physical entropies SB are defined with respect to a certain set of variables, the observationlevel B. For all times in which B exists, SB is the uncertainty H of a density operator RB making H a maximum with respect to the experimental values of B. This definition is not restricted to the thermodynamic equilibrium. The entropies SB measure the vagueness of the description in Hilbert-space caused by the choice of B. The time dependence of the density operator RB is not governed by the von Neumann equation, but in the special case of a “self-consistent“ B it may be calculated with the help of this equation. An increasing SB is obtained.If the times for which B exists are sufficiently close, a macroscopic equation for the time deriva· tive of SB is given. Three special cases of B are considered, leading to the Gibbs equation, a generalized entropy equation for heat conduction and an entropy equation for the multipole relaxation.

DISSIPATIVE BLACKBODY RADIATION: RADIATION IN A LOSSY CAVITY

2004 ◽  
Vol 18 (03) ◽  
pp. 317-324 ◽  
Author(s):  
J. R. CHOI
Keyword(s):  
Energy Density ◽  
Density Operator ◽  
Invariant Operator ◽  
Blackbody Radiation ◽  
Von Neumann ◽  
The Media ◽  
Von Neumann Equation

We defined normalized density operator that satisfies Liouville–von Neumann equation in terms of the invariant operator. The energy density inside the cavity decreased exponentially with time due to the conductivity of the media. We also evaluated the total number of photons in the cavity.

scholarly journals Phenomenological quantum thermodynamics resource theory for closed bipartite Schottky systems

2020 ◽  
Vol 378 (2170) ◽  
pp. 20190173 ◽  
Author(s):  
Wolfgang Muschik
Keyword(s):  
Quantum Mechanics ◽  
Density Operator ◽  
Nonequilibrium Thermodynamics ◽  
Discrete Systems ◽  
Resource Theory ◽  
Quantum Thermodynamics ◽  
Theme Issue ◽  
Von Neumann ◽  
Starting Point ◽  
Von Neumann Equation

How to introduce thermodynamics to quantum mechanics? From numerous possibilities of solving this task, the simple choice is here: the conventional von Neumann equation deals with a density operator whose probability weights are time-independent. Because there is no reason apart from the reversible quantum mechanics that these weights have to be time-independent, this constraint is waived, which allows one to introduce thermodynamical concepts to quantum mechanics. This procedure is similar to that of Lindblad’s equation, but different in principle. But beyond this simple starting point, the applied thermodynamical concepts of discrete systems may perform a ‘source theory’ for other versions of phenomenological quantum thermodynamics. This article is part of the theme issue ‘Fundamental aspects of nonequilibrium thermodynamics’.

Unbounded Linear Operators

2018 ◽  
Author(s):  
D. E. Edmunds ◽  
W. D. Evans
Keyword(s):  
Hilbert Spaces ◽  
Linear Operators ◽  
Von Neumann ◽  
Limit Circle ◽  
Sectorial Operators ◽  
Closed Operators ◽  
The Stability ◽  
Symmetric Operators ◽  
Unbounded Linear Operators ◽  
Special Case

This chapter is concerned with closable and closed operators in Hilbert spaces, especially with the special classes of symmetric, J-symmetric, accretive and sectorial operators. The Stone–von Neumann theory of extensions of symmetric operators is treated as a special case of results for compatible adjoint pairs of closed operators. Also discussed in detail is the stability of closedness and self-adjointness under perturbations. The abstract results are applied to operators defined by second-order differential expressions, and Sims’ generalization of the Weyl limit-point, limit-circle characterization for symmetric expressions to J-symmetric expressions is proved.

RATIONALLY ℵα-COMPLETE COMMUTATIVE RINGS OF QUOTIENTS

2009 ◽  
Vol 08 (05) ◽  
pp. 601-615
Author(s):  
JOHN D. LAGRANGE
Keyword(s):  
Commutative Rings ◽  
Von Neumann ◽  
Von Neumann Regular Rings ◽  
Von Neumann Regular ◽  
Ring Of Quotients ◽  
Rings Of Quotients ◽  
Special Case ◽  
Regular Rings

If {Ri}i ∈ I is a family of rings, then it is well-known that Q(Ri) = Q(Q(Ri)) and Q(∏i∈I Ri) = ∏i∈I Q(Ri), where Q(R) denotes the maximal ring of quotients of R. This paper contains an investigation of how these results generalize to the rings of quotients Qα(R) defined by ideals generated by dense subsets of cardinality less than ℵα. The special case of von Neumann regular rings is studied. Furthermore, a generalization of a theorem regarding orthogonal completions is established. Illustrative example are presented.

Filtering of Markov renewal queues, IV: Flow processes in feedback queues

1985 ◽  
Vol 17 (2) ◽  
pp. 386-407 ◽  
Author(s):  
Jeffrey J. Hunter
Keyword(s):  
Queue Length ◽  
Queueing Systems ◽  
Arrival Process ◽  
Markov Renewal Process ◽  
Renewal Processes ◽  
Flow Process ◽  
Special Cases ◽  
Flow Processes ◽  
Transition Points ◽  
The Times

This paper is a continuation of the study of a class of queueing systems where the queue-length process embedded at basic transition points, which consist of ‘arrivals’, ‘departures’ and ‘feedbacks’, is a Markov renewal process (MRP). The filtering procedure of Çinlar (1969) was used in [12] to show that the queue length process embedded separately at ‘arrivals’, ‘departures’, ‘feedbacks’, ‘inputs’ (arrivals and feedbacks), ‘outputs’ (departures and feedbacks) and ‘external’ transitions (arrivals and departures) are also MRP. In this paper expressions for the elements of each Markov renewal kernel are derived, and thence expressions for the distribution of the times between transitions, under stationary conditions, are found for each of the above flow processes. In particular, it is shown that the inter-event distributions for the arrival process and the departure process are the same, with an equivalent result holding for inputs and outputs. Further, expressions for the stationary joint distributions of successive intervals between events in each flow process are derived and interconnections, using the concept of reversed Markov renewal processes, are explored. Conditions under which any of the flow processes are renewal processes or, more particularly, Poisson processes are also investigated. Special cases including, in particular, the M/M/1/N and M/M/1 model with instantaneous Bernoulli feedback, are examined.

Analytical Techniques for the Optimisation of Rocket Trajectories

1963 ◽  
Vol 14 (2) ◽  
pp. 105-124 ◽  
Author(s):  
Derek F. Lawden
Keyword(s):  
Gravitational Field ◽  
Artificial Satellite ◽  
Analytical Techniques ◽  
Present Position ◽  
Mayer Problem ◽  
Special Cases ◽  
Minimum Expenditure ◽  
Law Of Attraction ◽  
Special Case

SummaryThe development during the last two decades of analytical techniques for the solution of problems relating to the optimisation of rocket trajectories is outlined and the present position in this field of research is summarised. It is shown that the determination of optimal trajectories in a general gravitational field can be expressed as a Mayer problem from the calculus of variations. The known solution to such a problem is stated and applied, first to the special case of the launching of an artificial satellite into a circular orbit with minimum expenditure of propellant and, secondly, to the general astronautical problem of the economical transfer of a rocket between two terminals in a gravitational field. The special cases when the field is uniform and when it obeys an inverse square law of attraction to a point are then considered, and the paper concludes with some remarks concerning areas in which further investigations are necessary.

scholarly journals Water entry of an expanding wedge/plate with flow detachment

2016 ◽  
Vol 797 ◽  
pp. 322-344 ◽  
Author(s):  
Yuriy A. Semenov ◽  
Guo Xiong Wu
Keyword(s):  
Free Surface ◽  
General Solution ◽  
Water Entry ◽  
Hodograph Method ◽  
Fixed Length ◽  
Pressure Distributions ◽  
Initial Stage ◽  
Special Cases ◽  
Wedge Plate ◽  
Special Case

A general similarity solution for water-entry problems of a wedge with its inner angle fixed and its sides in expansion is obtained with flow detachment, in which the speed of expansion is a free parameter. The known solutions for a wedge of a fixed length at the initial stage of water entry without flow detachment and at the final stage corresponding to Helmholtz flow are obtained as two special cases, at some finite and zero expansion speeds, respectively. An expanding horizontal plate impacting a flat free surface is considered as the special case of the general solution for a wedge inner angle equal to ${\rm\pi}$. An initial impulse solution for a plate of a fixed length is obtained as the special case of the present formulation. The general solution is obtained in the form of integral equations using the integral hodograph method. The results are presented in terms of free-surface shapes, streamlines and pressure distributions.

scholarly journals On Reay's Relaxed Tverberg Conjecture and Generalizations of Conway's Thrackle Conjecture

10.37236/6516 ◽  
2018 ◽  
Vol 25 (3) ◽  
Author(s):  
Megumi Asada ◽  
Ryan Chen ◽  
Florian Frick ◽  
Frederick Huang ◽  
Maxwell Polevy ◽  
...  
Keyword(s):  
Geometric Property ◽  
Convex Sets ◽  
Convex Hulls ◽  
Open Problems ◽  
Higher Dimensional ◽  
Special Cases ◽  
Minimum Number ◽  
Point Set ◽  
Colored Version ◽  
Special Case

Reay's relaxed Tverberg conjecture and Conway's thrackle conjecture are open problems about the geometry of pairwise intersections. Reay asked for the minimum number of points in Euclidean $d$-space that guarantees any such point set admits a partition into $r$ parts, any $k$ of whose convex hulls intersect. Here we give new and improved lower bounds for this number, which Reay conjectured to be independent of $k$. We prove a colored version of Reay's conjecture for $k$ sufficiently large, but nevertheless $k$ independent of dimension $d$. Pairwise intersecting convex hulls have severely restricted combinatorics. This is a higher-dimensional analogue of Conway's thrackle conjecture or its linear special case. We thus study convex-geometric and higher-dimensional analogues of the thrackle conjecture alongside Reay's problem and conjecture (and prove in two special cases) that the number of convex sets in the plane is bounded by the total number of vertices they involve whenever there exists a transversal set for their pairwise intersections. We thus isolate a geometric property that leads to bounds as in the thrackle conjecture. We also establish tight bounds for the number of facets of higher-dimensional analogues of linear thrackles and conjecture their continuous generalizations.

A Theoretical Study on the Pressure Dependence of the Band Gap in ${\rm A^{I}B^{III}C^{VI}_2}$ Compounds

1997 ◽  
Vol 11 (16) ◽  
pp. 1959-1967 ◽  
Author(s):  
R. Asokamani ◽  
R. Mercy Amirthakumari ◽  
G. Pari
Keyword(s):  
Theoretical Study ◽  
Energy Gap ◽  
Ambient Pressure ◽  
Chalcopyrite Structure ◽  
Deformation Potential ◽  
Equilibrium Lattice Constant ◽  
Self Consistent ◽  
Direct Energy ◽  
Experimental Values ◽  
Direct Energy Gap

The self-consistent scalar relativistic band structure for AgGaX 2 (X = S, Se, Te) performed in chalcopyrite structure using the TBLMTO method at various pressures are reported here. Empty spheres were introduced in the calculations as the chalcopyrite structure is loosely packed. From the total energy calculations, the equilibrium lattice constant and the bulk modulus at zero pressure were calculated and these values agree well with the reported experimental values. All these compounds are found to have direct energy gap at ambient pressure with the gap widening with increased pressures which are in agreement with the experimental results. The deformation potential, dE g /dP for the compounds are also reported here. The metallisation volumes are calculated and the possibility of observing superconductivity in these compounds is discussed.

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