Radiation Entropy Research Articles

Neutrino viscosity and isotropization of Bianchi type-VIII and type-IX cosmological models

We investigate the isotropization of Bianchi type-VIII and type-IX spaces due to neutrino viscosity. We find that, owing to a peculiar coupling between curvature and anisotropy, neutrino viscosity does not guarantee the present-day isotropy of the cosmological expansion in such spaces. The observed isotropy of the background radiation imposes stringent limits either on the initial anisotropy or on the curvature of space, in contrast with the principle of chaotic cosmology. On the other hand, the amplification of the radiation entropy depends weakly on curvature and may be as large as 1012.

Entropy of radiation in biology

The concept of the entropy of electromagnetic radiation and the relationship between entropy and probability for radiation fields are explained. Equations for the variations of entropy and temperature in the reversible and irreversible volume changes of black radiation fields are given. Following Boltzmann and Schrödinger, it is pointed out that living matter, e.g., in a stationary state, struggles for the chance of acquiring the needed free energy by converting low-entropy solar energy radiation into high-entropy terrestrial energy radiation. The amount of energy available from a Carnot process with utilization of high-temperature (low-entropy) radiation and the influence of radiation scattering are computed. The considerations are applied to photosynthesis. Technically useful amounts of hydrogen could in principle be obtained through water photolysis by means of artificial, simulated, photosynthesis. For the purpose, the membrane principle has central importance, i.e., by means of asymmetric, vectorial, membranes separation of the primary products of photolysis is sought.

Production of entropy and viscous damping of anisotropy in homogeneous cosmological models: Bianchi type-I spaces

We investigate world models in which strong initial anisotropies are damped out by viscous dissipation at temperatures lower than 1012K. The corresponding entropy production is calculated and is proved to be simply related to the initial anisotropy. The radiation entropy increases up to a factor 1010 in those models in which the big bang starts atT∼-1010 K. In all cases here investigated the volume expansion is dominated by viscosity in a «superviscous stage» preceding a Kasner epoch. In these models, despite of very different initial conditions, the anisotropy of the cosmic background radiation is approximately the same, namely ΔT/T∼-4·10−7 at the present epoch.

Thermodynamic processes induced by coherent radiation

It is shown by quantum statistics that under certain stated conditions the entropy of coherent radiation is zero and it is still negligible for multimode laser operation. This makes possible gas kinetic processes which, to a small extent, have already been observed or even utilized, but which can be greatly enhanced by an optimized choice of molecular structures and radiation conditions. Radiative cooling of gases is discussed in detail. The conditions for maximum heat withdrawal are derived, and it is proposed that the processes of cooling and relaxation heating can be sufficiently separated in time to achieve certain effects and thermodynamic cycles. One of these is the complete conversion, possible in principle, of coherent radiation into work. This concept is based on a heat pump process followed by heat-to-work conversion, the heat rejected being just equal to that withdrawn by radiation. The conditions for complete conversion turn out to be the same as for maximum heat withdrawal. The feasibility of these processes depends on the degree to which practical conditions can be met, and on the validity of certain assumptions which have to await experimental verification.

Entropy per particle in the early Bianchi type-I Universe

We consider the behaviour of the radiation entropy per particle in the early stage of the Universe according to the Bianchi type I in which there are nonvanishing terms for the shear viscosity in the energy-momentum tensorTμν. The viscosity coefficient η is a function of the temperature η=ωTm, where ω andm are constants. We rewrite Einstein equations in such a manner that we can analyse the influence of dissipation on the isotropization. Results of the above analysis reveal that, in the framework of the considered model, the effects of the shear viscosity appear to be significant only under very special initial conditions for the dissipation parameter and form<1; in such a case the radiation entropy increases in the course of the evolution by a substantial factor. The expansion is practically isoentropic in all the remaining cases. The dissipation parameters are found for the lepton and radiation epochs.

Estimate of the entropy of radiation by means of weight functions

Estimate of the entropy of radiation by means of weight functions

On the relation between the coherence and entropy of radiation

On the relation between the coherence and entropy of radiation

Relativistic Statistical Mechanics and Blackbody Radiation

A manifestly Lorentz-invariant generalization of the Gibbs's canonical density operator is derived for the free fields of quantum electrodynamics from the maximum-entropy principle. Known results for the energy density, entropy, and other thermodynamic functions of blackbody radiation are very simply rederived. Use of the invariant density operator makes it clear that, contrary to recent assertions of Ott and others, it is not necessarily most natural to assume that temperature transforms like an energy. What is more to the point, it is shown that the concept of temperature in a moving system can be eliminated altogether if desired. Temperature may be conveniently considered as a purely rest-frame concept. The invariant density operator is then used to investigate the second-order two-point space-time correlation functions of the blackbody radiation field. The recent results of Mehta and Wolf and others are generalized to an arbitrary uniformly moving corodinate system, and the most interesting cases of pure temporal and spatial coherence are presented graphically. Two examples are given in which a moving observer measures a higher degree of coherence than he would in the rest system. Some remarks are made concerning the Gaussian nature of the phase-space distribution function, and the consequences for higher-order correlation functions in a moving frame are discussed briefly.

Thermodynamic Limitations on the Conversion of Radiant Energy into Work

The fraction of radiant energy incident on an absorber which may appear as work is limited by the radiation entropy and entropy gained in irreversible transfer from the radiation field to an absorber. Irreversibility may result from directionality of the radiation field, and some irreversibility is necessary to cause a net flow of energy from a radiation absorber into work or free-energy storage. Impedance in the conversion apparatus may further limit the efficiency. Maximization of power storage under these constraints is discussed, and the general arguments are then applied to photoelectrical and photochemical systems; in these systems nonresonant decay of the excited state represents a major source of inefficiency, which may be minimized by appropriate choices for the Boltzmann temperature and optical density of the absorber. The relationships are developed for narrow-band absorption, and application to broad-band systems is discussed only briefly.

Thermodynamic Entropy of Partially Coherent Light Beams

The thermodynamic entropy of partially coherent light beams, as shown by M. von Laue, is given by the sum of the entropy of the principal waves, which represent the given light beams and are statistically independent of each other. The principal waves and their intensities are respectively the eigenfunctions and eigenvalues of the mutual intensity, cross-correlation function of waveamplitudes, which is positive semidefinite Hermitian operator. The well-known entropy of thermal radiation is applied to principal waves obtained after appropriate reversible optical transmission.

Entropy of Radiation

In view of the recent publication of a derivation of the expression for the entropy flux of radiation, in terms of its spectral specific intensity, a brief comparative study of various known methods for obtaining the entropy formula is presented.

Entropy of Radiation

An expression for the entropy flux of linearly polarized electromagnetic radiation of any specific intensity, ${K}_{\ensuremath{\nu}}$, is obtained. The latter expression is then generalized to include radiation of any type of polarization.

Radiation Laws Describing the Emission of Photons by Black Bodies

Photon Laws for Black Body Radiation: Starting with a relation showing the temperature volume changes for black body radiation which is undergoing an adiabatic change, it is shown how photon laws which correspond one by one with known radiant energy laws may be derived. In all instances, excepting two, namely λm′T=const and νm′T=const, the photon relations differ from the corresponding radiant energy relations chiefly by having a power of T decreased by one, a power of λ increased by one, or a power of ν decreased by one. The entropy of black body radiation is strictly proportional to the number of photons involved. Table of Black Body Radiation Constants: A table includes values in common units for the collective groups of constants entering the various photon and radiant energy equations mentioned in the paper.

The Entropy of Radiation

The Entropy of Radiation

The Entropy of Radiation

A QUANTITY of heat Q is transferred by radiation from a body the surface of which is at temperature T1 to a body the surface of which is at a lower temperature T2. From this cause alone the former body loses a quantity of entropy Q/T1, while the latter gains a quantity of entropy Q/T2. The net gain of entropy of the bodies arising from the transaction is Q(i/T2_ i/T1). Where and how does this gain take place? Vorlesungen über die Theorie der Wärrnestrahlung. By Dr. Max Planck. Pp. viii + 222. (Leipzig: Johann Ambrosius Barth, 1906.) Price 7 marks.