Related papers: Stefan-Boltzmann law revisited
Stefan-Boltzmann law was empirically deduced by Stefan in 1874 by fitting existing experiments and theoretically validated by Boltzmann in 1884 on the basis of a classical model involving thermodynamics principles and the Maxwell equations.…
We study thermal radiation outside equilibrium. The situation considered consists of two bodies emitting photons at two different temperatures. We show that the system evolves to a stationary state characterized by an energy current which…
Starting from the knowledge of the four fundamental quantities length L, mass M, time T, absolute temperature $\theta$ and accepting the validity of Gauss's law in all dimensions, we generalize, by the theory of physical dimensions, the…
This paper deals with quantum field theory in curved space-time using the Thermo Field Dynamics. The scalar field is coupled to the Schwarzschild space time and then thermalised. The Stefan-Boltzmann law is established at finite temperature…
The Stefan-Boltzmann constant arose from photon densities inside a cavity, but inside matter photon mode densities are material specific. Photon speeds are governed by the mode they occupy, so mode densities can be expressed in terms of…
The conventional Tolman temperature based on the assumption of the traceless condition of energy-momentum tensor for matter fields is infinite at the horizon if Hawking radiation is involved. However, we note that the temperature associated…
In this paper the Planck function is derived in the frequency domain using the method of oscillators. It is also presented in the wavelength domain and in the wave number domain. The latter is mainly used in spectroscopy for studying…
This paper generalizes the entropy maximization problem leading to the Boltzmann-Gibbs distribution through the nonadditive entropy $S_{q,s}(p)=k_{s}\sum^{W}_{i\geq1}p_{i}\ln_{q}1/p_{i}$, $q\in(0,1)$, which is a rescaled version of $S_{q}$…
Consider the linear Boltzmann equation of radiative transfer in a half-space, with constant scattering coefficient $\sigma$. Assume that, on the boundary of the half-space, the radiation intensity satisfies the Lambert (i.e. diffuse)…
Photons in blackbody radiation have non-zero interactions due to their couplings to virtual electron-positron pairs in the vacuum. For temperatures much less than the electron mass $m$ these effects can be described by an effective theory…
In 1916 Einstein introduced the first rules for a quantum theory of electromagnetic radiation, and he applied them to a model of matter in thermal equilibrium with radiation to derive Planck's black-body formula. Einstein's treatment is…
The integral law of thermal radiation by finite size emitters is studied. Two geometrical characteristics of a radiating body or a cavity, its volume and its boundary area, define two terms in its radiance. The term defined by the volume…
The general form of the Stefan-Boltzmann law for the energy density of black-body radiation is generalized to a spacetime with extra dimensions using standard kinetic and thermodynamic arguments. From statistical mechanics one obtains an…
We present a derivation of Boltzmann principle $S_{B}=k_{B}\ln \mathcal{W}$ based on classical mechanical models of thermodynamics. The argument is based on the heat theorem and can be traced back to the second half of the nineteenth…
In two respects Ludwig Boltzmann was a pioneer of quantum mechanics. First because in his statistical interpretation of the second law of thermodynamics he introduced the theory of probability into a fundamental law of physics and thus…
In 1914, Planck introduced the concept of a white body. In nature, no true white bodies are known. We assume that the universe after last-scattering is an ideal white body that contains a tremendously large number of thermal photons and is…
Beginning with Anderson (1972), spontaneous symmetry breaking (SSB) in infinite quantum systems is often put forward as an example of (asymptotic) emergence in physics, since in theory no finite system should display it. Even the…
In this paper, the existence of a massive dark photon, associated with a new gauge group is considered. The dark photon can be kinetically mixed with the photon. To study some applications, the thermo field dynamics formalism is used.…
Boltzmann's Principle S = k ln W was repeatedly criticized by Einstein since it lacked a proper dynamical foundation in view of the thermal motion of the particles, out of which a physical system consists. This suggests, in particular, that…
We give an exact information-theory treatment of the $n$-dimensional black-body radiation process in a non-extensive scenario. We develop a $q$ generalization of the laws of i) Stefan Boltzmann, ii) Planck, and iii) Wien, and show that…