The classical derivation of entropy: A reexamination

2002 ◽  
Vol 2 (3) ◽  
pp. 135-139
Author(s):  
Lindon C. Thomas
Keyword(s):  
Classical Derivation

A HAMILTONIAN TREATMENT OF FIVE-DIMENSIONAL KALUZA–KLEIN GRAVITY

2000 ◽  
Vol 09 (04) ◽  
pp. 445-458 ◽  
Author(s):  
W. N. SAJKO
Keyword(s):  
Total Mass ◽  
Soliton Solutions ◽  
Schwarzschild Solution ◽  
Coordinate Dependence ◽  
Klein Theory ◽  
The One ◽  
Induced Matter ◽  
Classical Derivation ◽  
Area Law ◽  
Kaluza Klein

We give a Hamiltonian treatment of 5D vacuum Kaluza–Klein theory that is unrestricted in the extra coordinate dependence. When the extra coordinate dependence is removed from the 5D metric we recover the Hamiltonian for gravity and electromagetism nonminimally coupled to a scalar field. The energies of 5D uncharged and charged soliton solutions are calculated via the Hamiltonian and are identified with the total mass. The expressions for the total mass are shown to agree with the sum of scalar and gravitational masses calculated from the scalar-tensor induced matter in 4D. A semi-classical derivation of the temperature for the uncharged solitons is calculated and it is shown that the only nontrivial member of the 5D class is the 4D Schwarzschild solution trivially embedded in 5D, and therefore the entropy obeys the one-quarter area law.

scholarly journals LÉVY–VASICEK MODELS AND THE LONG-BOND RETURN PROCESS

2018 ◽  
Vol 21 (03) ◽  
pp. 1850026
Author(s):  
DORJE C. BRODY ◽  
LANE P. HUGHSTON ◽  
DAVID M. MEIER
Keyword(s):  
Interest Rates ◽  
Kernel Method ◽  
Pricing Kernel ◽  
Vasicek Model ◽  
One Dimensional ◽  
Market Incompleteness ◽  
Exponential Moments ◽  
Bond Return ◽  
Classical Derivation ◽  
Return Process

The classical derivation of the well-known Vasicek model for interest rates is reformulated in terms of the associated pricing kernel. An advantage of the pricing kernel method is that it allows one to generalize the construction to the Lévy–Vasicek case, avoiding issues of market incompleteness. In the Lévy–Vasicek model the short rate is taken in the real-world measure to be a mean-reverting process with a general one-dimensional Lévy driver admitting exponential moments. Expressions are obtained for the Lévy–Vasicek bond prices and interest rates, along with a formula for the return on a unit investment in the long bond, defined by [Formula: see text], where [Formula: see text] is the price at time [Formula: see text] of a [Formula: see text]-maturity discount bond. We show that the pricing kernel of a Lévy–Vasicek model is uniformly integrable if and only if the long rate of interest is strictly positive.

A classical derivation of the Meissner effect?

Nature ◽  
1982 ◽  
Vol 299 (5885) ◽  
pp. 681-682 ◽  
Author(s):  
J. B. Taylor
Keyword(s):  
Meissner Effect ◽  
Classical Derivation

scholarly journals Classical derivation of black-hole entropy

1987 ◽  
Vol 35 (2) ◽  
pp. 449-454 ◽  
Author(s):  
Andrew Gould
Keyword(s):  
Black Hole ◽  
Black Hole Entropy ◽  
Classical Derivation

EXPERIMENTAL TEST OF A QUANTUM-LIKE THEORY: MOTION OF ELECTRONS IN A UNIFORM MAGNETIC FIELD, IN A VARIABLE POTENTIAL WELL

1999 ◽  
Vol 14 (07) ◽  
pp. 479-490 ◽  
Author(s):  
C. S. UNNIKRISHNAN ◽  
C. P. SAFVAN
Keyword(s):  
Electric Fields ◽  
Uniform Magnetic Field ◽  
Anomalous Behavior ◽  
Supporting Evidence ◽  
Potential Well ◽  
Electron Current ◽  
Secondary Electrons ◽  
Electron Transmission ◽  
Variable Potential ◽  
Classical Derivation

We describe an experiment to test a quantum-like theory which predicts quantum-like behavior for an ensemble of electrons in a classical configuration with static magnetic and electric fields. Some of the earlier experiments had supporting evidence for anomalous, quantum-like effects in such a situation showing systematic modulations of electron current when a retarding potential is varied, even though the quantum wavelength of the electrons in such a configuration was less than a billionth of the spatial width of the potential well. Our experiment conclusively rules out any nonclassical, quantum-like behavior in electron transmission through simple electric barriers, when magnetic fields are present. We identify secondary electrons generated at various electrodes as the main source of apparent anomalous behavior. We also present a classical derivation of the quantum-like equation describing the modulations.

A Generalized Expression for the Energy Density of Electromagnetic Waves in Media with Strong Temporal Dispersion

1972 ◽  
Vol 27 (7) ◽  
pp. 1094-1097 ◽  
Author(s):  
Dan Anderson
Keyword(s):  
Energy Density ◽  
Electromagnetic Waves ◽  
Standard Form ◽  
Higher Order ◽  
Chirp Pulse ◽  
Higher Order Terms ◽  
Simple Medium ◽  
Derivatives Of ◽  
Classical Derivation ◽  
Temporal Dispersion

Abstract An expression is derived for the energy density of an electromagnetic wave of rather general form in a lossless, homogeneous and isotropic medium exhibiting temporal dispersion. The result is a generalization of the standard form and takes into account higher order derivatives of the di-electric and permeability functions as well as of the electric and magnetic field amplitudes of the wave. The classical derivation of the expression for the energy density given by BRILLOUIN1, is dis-cussed in some detail and, finally, a qualitative example of a chirp pulse in a simple medium is given, which illustrates the importance of higher order terms

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