Radiation Entropy Research Articles

Radiation entropy flux and entropy production of the Earth system

[1] The study of the Earth's radiation entropy flux at the top of the atmosphere is reviewed with an emphasis on its estimation methods. Existing expressions for calculating radiation entropy flux scattered in different disciplines are surveyed, and their applicabilities are examined. It is found that the Earth's net radiation entropy flux estimated from these various expressions can differ substantially, more than the typical value of the entropy production rate associated with the atmospheric latent heat process. Comparison analysis shows that the commonly used expression of radiation entropy flux as the ratio of radiation energy flux to absolute temperature underestimates the Earth's radiation entropy flux by >30%. Theoretical analysis reveals that the large difference in the Earth's reflected solar radiation entropy flux among the different expressions arises mainly from the difference of the Earth's reflection properties (i.e., Lambertian or specular) assumed in these expressions. For the Earth system with typical shortwave albedo of 0.30 and longwave emissivity between 0.50 and 1.00, the Earth's net radiation entropy flux derived from the most accurate Planck's spectral expression ranges from 1.272 to 1.284 W m−2 K−1, amounting to the overall Earth's entropy production rate from 6.481 × 1014 to 6.547 × 1014 W K−1.

A new one-dimensional radiative equilibrium model for investigating atmospheric radiation entropy flux

A new one-dimensional radiative equilibrium model is built to analytically evaluate the vertical profile of the Earth's atmospheric radiation entropy flux under the assumption that atmospheric longwave radiation emission behaves as a greybody and shortwave radiation as a diluted blackbody. Results show that both the atmospheric shortwave and net longwave radiation entropy fluxes increase with altitude, and the latter is about one order in magnitude greater than the former. The vertical profile of the atmospheric net radiation entropy flux follows approximately that of the atmospheric net longwave radiation entropy flux. Sensitivity study further reveals that a 'darker' atmosphere with a larger overall atmospheric longwave optical depth exhibits a smaller net radiation entropy flux at all altitudes, suggesting an intrinsic connection between the atmospheric net radiation entropy flux and the overall atmospheric longwave optical depth. These results indicate that the overall strength of the atmospheric irreversible processes at all altitudes as determined by the corresponding atmospheric net entropy flux is closely related to the amount of greenhouse gases in the atmosphere.

Hawking Radiation Spectrum and Entropy Correction of Apparent Horizon in a FRW Universe

Taking the reaction of the radiation to the spacetime into consideration, we discuss Hawking radiation spectrum and Bekenstein-Hawking entropy correction in Friedmann-Robertson-Walker (FRW) universe by the analytical continuation method. We derive the radiation spectrum that satisfies the unitary principle and the logarithmic correction term of entropy in FRW universe.

Thermal radiation and the second law

The purpose of this paper is to collect and interrelate the fundamental concepts about second law analysis of thermal radiation. This heat transfer mode plays a leading role in solar energy utilization and in high-temperature devices, representing a significant contribution to irreversibility that is frequently omitted in engineering analysis. Entropy and exergy of thermal radiation are reviewed first. Radiative transfer processes are reviewed next, including exchange between surfaces, the presence of a participative medium, and the analysis of combined heat transfer modes. Emphasis is put on grey body radiation when treating with non-black body radiation, due to its relevance in engineering applications. The mathematical formulation of second law analysis of thermal radiation is complex, which limits its use in conventional heat transfer analysis. For this reason, numerical approaches reported to date deal with quite simple cases, leaving an open promising field of research.

Recent progress in thermodynamics of radiation—exergy of radiation, effective temperature of photon and entropy constant of photon

The recent progress on thermodynamic properties of spectral radiant energy in the field of thermodynamics of radiation is reviewed. The effective temperature of photon Tλ representing the energy quality of photon is introduced. The relation between Tλ and the wavelength λ is given as λTλ =c3=5.33016×10−3 m·K. The entropy constant of photon is given as sλ=3.72680×10−23 J/K. The exergy, entropy and enthalpy of the spectral blackbody radiation, the equilibrium cavity radiation, the radiation flux in open system are discussed by using Tλ and sλ, as well as the entropy change in the process of the state transformation of photon gas. By analyzing the exergy of spectral radiation, the exergy efficiency of spectral radiant energy available for photosynthesis is proved to be higher than that of light energy. The method for the irreversible loss of exergy calculation in radiant energy converters is also discussed.

Entropy and efficiency in laser cooling of solids

The thermodynamics of laser cooling of solids is analyzed. Using the general theory of radiation entropy, the important roles of the optical frequency and the photon distribution function in determining the radiation entropy are identified. The usefulness of a narrowband approximation is established for a wide range of radiant sources. This approximation is then applied to compare the entropies of different light sources, including blackbody radiation, lasers, fluorescence, and the emerging class of random lasers. Based on these results, the Carnot efficiency for laser cooling of solids is determined, for emission fields with various entropy characteristics. It is shown that fluorescent emission is the most efficient form of the radiated field for laser cooling of solids, and cooling schemes based on any stimulated emission process (including random laser action) are inherently less efficient. The influence of luminescence quantum yield on cooling is also considered.Copyright © 2007 by ASME

The effect of modified dispersion relations on the thermodynamics of black-body radiation

In the study of loop quantum gravity and of models based on noncommutative geometry, there has been strong interest in some candidate modifications of the energy-momentum dispersion relation. In this paper we consider the effects of modified dispersion relation (MDR) on the thermodynamics of black-body radiation. We find a generalized Planck distribution and then apply it to find generalized Stefan–Boltzmann and generalized Wien’s law. As a consequence, we study the effects of these modifications on the entropy and specific heat of black-body radiation. We investigate also the relation between our findings and the results of E-infinity theory by considering distribution and temperature of cosmic microwave background radiation.

Entropy flow and generation in radiative transfer between surfaces

Entropy of radiation has been used to derive the laws of blackbody radiation and determine the maximum efficiency of solar energy conversion. Along with the advancement in thermophotovoltaic technologies and nanoscale heat radiation, there is an urgent need to determine the entropy flow and generation in radiative transfer between nonideal surfaces when multiple reflections are significant. This paper investigates entropy flow and generation when incoherent multiple reflections are included, without considering the effects of interference and photon tunneling. The concept of partial equilibrium is applied to interpret the monochromatic radiation temperature of thermal radiation, T λ ( λ, Ω), which is dependent on both wavelength λ and direction Ω. The entropy flux and generation can thus be evaluated for nonideal surfaces. It is shown that several approximate expressions found in the literature can result in significant errors in entropy analysis even for diffuse-gray surfaces. The present study advances the thermodynamics of nonequilibrium thermal radiation and will have a significant impact on the future development of thermophotovoltaic and other radiative energy conversion devices.

Entropy of the microwave background radiation in the observable universe

We show that the cosmological constant at late-time places a bound on the entropy of microwave background radiation deposited in the future event horizon of a given observer, $S\ensuremath{\le}{S}_{{\ensuremath{\Lambda}}_{0}}^{3/4}$. This bound is independent of the energy scale of reheating and the FRW evolution after reheating. We also discuss why the entropy of microwave background in our observable universe has its present value.

Thermodynamic consideration of the positronium decay

Electron-positron annihilation has mainly two decay channels. Firstly into two gamma-photons of equal energy forming a narrow line spectrum, and secondly into three gamma-photons forming a continuous energy spectrum. The ratio of decay events N 3 /N 2 is experimentally found with about 1:379 and depends only on the fine-structure constant a like N 3 /N 2 = 4(π 2 - 9)a/37r to the first QED expansion order. The given consideration tries to understand this ratio of decay events in a thermodynamic way and allows the computation of a theoretical ratio of 1:356 on the base of the Boltzmann distribution and the calculated temperatures of the 27-decay with k B T ≅ 1.04737·mc 2 and the 3γ-decay with k B T ≅ 1/8.0125·mc 2 . The radiation entropy produced at the 2γ-decay was calculated with 1.90975 k B and the radiation entropy of the 3γ-continuum with 5.9663 k B . The positronium system could be seen in some kind of conflict: Due to the smallness of a the construction of an additional third gamma-photon is improbable. On the other hand, much more entropy could be generated by three gamma quanta. This antagonism could be transformed into an understanding of the ratio of decay events and thus the actual value of the fine-structure constant. Due to entropy, this seems to be the optimal value for the positronium ecay-or, more general -the optimal value for the building probability of a photon. As entropy is an observable physical quantity, the calculated values should experimentally be measurable, so that the given calculations could experimentally be verified.

Radiation thermodynamics with applications to lasing and fluorescent cooling

Laser cooling of bulk matter uses thermally assisted fluorescence to convert heat into light and can be interpreted as an optically pumped laser running in reverse. Optical pumping in such devices drives the level populations out of equilibrium. Nonthermal radiative energy transfers are thereby central to the operation of both lasers and luminescent coolers. A thermodynamic treatment of their limiting efficiencies requires a careful development of the entropy and effective temperatures of radiation, valid for the entire range of light from the blackbody to the ideal laser limiting cases. In particular, the distinct meaning and utility of the brightness and flux temperatures should be borne in mind. Numerical examples help illustrate these concepts at a level suitable for undergraduate physics majors.

Exergy of solar radiation

Solar radiation reaching the ground is accompanied with radiation entropy. When the entropy production rate within any solar energy conversion device is to be calculated, the incoming radiation entropy flux has to be known. In this contribution, first it is shown how the radiation entropy flux arriving on earth is to be calculated. Secondly, the interaction between the incoming radiation and the receiver surface is identified as one entropy production source. An approach for a reversible radiation conversion device is proposed. Maximum conversion efficiencies for non-concentrating solar energy converters are found to be between 50–77% of the incoming radiation energy, depending on atmospheric conditions.

On the exergy of radiation

In the domain of heat radiation, and particularly of solar energy use, the notion of exergy (or alternatively entropy) of radiation has given rise to a fairly abundant literature; unfortunately, incoherencies and discrepancies between the various authors could lead to a complete disuse of the notion in this context. The aim of this paper is to contribute to a clarification of this issue. We propose here a derivation of the exergy of radiation, based solely on classical thermodynamics notions, making thus possible a ready check of the validity of the results. Results are given first for the blackbody case, then extended to a radiation with arbitrary spectrum. Finally, application of the notion of radiation entropy to a few simple examples shows the consistency of this notion with some well-known physical laws, and can even give some insight into the real signification of these laws.

Holography in a radiation-dominated universe with a positive cosmological constant

We discuss the holographic principle in a radiation-dominated, closed Friedmann-Robertson-Walker (FRW) universe with a positive cosmological constant. By introducing a cosmological D-bound on the entropy of matter in the universe, we can write the Friedmann equation governing the evolution of the universe in the form of the Cardy formula. When the cosmological D-bound is saturated, the Friedmann equation coincides with the Cardy-Verlinde formula describing the entropy of radiation in the universe. As a concrete model, we consider a brane universe in the background of Schwarzschild-de Sitter black holes. It is found that the cosmological D-bound is saturated when the brane crosses the black hole horizon of the background. At that moment, the Friedmann equation coincides with the Cardy-Verlinde formula describing the entropy of radiation matter on the brane.

Extensive entropy bounds

It is shown that, for systems in which the entropy is an extensive function of the energy and volume, the Bekenstein and the holographic entropy bounds predict new results. More explicitly, the Bekenstein entropy bound leads to the entropy of thermal radiation (the Unruh-Wald bound) and the spherical entropy bound implies the ``causal entropy bound.'' Surprisingly, the first bound shows a close relationship between black hole physics and the Stephan-Boltzmann law (for the energy and entropy flux densities of the radiation emitted by a hot blackbody). Furthermore, we find that the number of different species of massless fields is bounded by $\ensuremath{\sim}{10}^{4}.$

On the entropy of radiative heat transfer in engineering thermodynamics

The objective of this paper is to improve the understanding and also to simplify the calculation of the entropy transferred by thermal radiation (TR). Many thermodynamic texts incorrectly imply that the entropy flux of TR is the same as that for heat conduction, the heat flux divided by the local temperature ( q/ T). Also, fundamental equations, such as those derived from the Clausius inequality, express the entropy flux of TR in a q/ T type form. However, for blackbody radiation (BR) emission a 4/3 factor is present and in this paper it is shown that the entropy flux of non-blackbody radiation (NBR) emission is even farther removed from q/ T. The misuse of the heat conduction entropy flux equation for TR emission causes the irreversibility of a device to be underestimated whether the surface of the device is hot or cold relative to its surroundings. Further, it is shown that the reversible form of the Clausius expression applies when TR is involved yet the expression for irreversible processes does not apply. Finally, simple approximate expressions for the entropy of gray radiation (GR) are presented, as the exclusive use of numerical integration is laborious.

Measurement of emittance and degree of polarisation of surfaces for solar energy converters

The basic equations for calculating radiation entropy and the major input functions to these equations, namely the spectral and directional distribution of radiation intensity and its degree of polarisation, are presented. Thermodynamic evaluation of energy conversion processes by means of the balance equations requires all involved energy and entropy fluxes to be known. The incoming radiation energy and entropy can be obtained from atmospheric models, but the properties of the outgoing radiation strongly depend on the optical properties of the surface. As the required optical properties usually are not available over the entire spectral range and for all directions, measurements are performed in order to improve the accuracy of the energy and entropy balances. An apparatus is presented, capable of measuring the spectral directional emittance and the degree of polarisation of the emitted radiation in the range of infrared wavelengths.

Photopolarimetric characterization of the transition between two turbulent states in a nematic liquid crystal film.

This work was aimed at the photopolarimetric characterization of the transition between two dynamic scattering modes that take place in a planarly aligned nematic liquid crystal sample, under the effect of an external low-frequency electric field. The time evolution of the degree of polarization and the behavior of the radiation entropy of the transmitted light allow us to interpret the transition between two turbulent states, or dynamic scattering modes, as a decay from a two-dimensional (2D) to a (3D) turbulence.

Pre-big-bang requires the universe to be exponentially large from the very beginning

We show that in a generic case of the pre-big-bang scenario, inflation will solve cosmological problems only if the universe at the onset of inflation is extremely large and homogeneous from the very beginning. The size of a homogeneous part of the universe at the beginning of the stage of pre-big-bang (PBB) inflation must be greater than $10^{19}$ $l_s$, where $l_s$ is the stringy length. The total mass of an inflationary domain must be greater than $10^{72} M_{s}$, where $M_{s} \sim l_s^{-1}$. If the universe is initially radiation dominated, then its total entropy at that time must be greater than $10^{68}$. If the universe is closed, then at the moment of its formation it must be uniform over $10^{24}$ causally disconnected domains. The natural duration of the PBB stage in this scenario is $M_p^{-1}$. We argue that the initial state of the open PBB universe could not be homogeneous because of quantum fluctuations. Independently of the issue of homogeneity, one must introduce two large dimensionless parameters, $g_0^{-2} > 10^{53}$, and $B > 10^{91}$, in order to solve the flatness problem in the PBB cosmology. A regime of eternal inflation does not occur in the PBB scenario. This should be compared with the simplest versions of the chaotic inflation scenario, where the regime of eternal inflation may begin in a universe of size $O(M_{p}^{-1})$ with vanishing initial radiation entropy, mass $O(M_p)$, and geometric entropy O(1). We conclude that the current version of the PBB scenario cannot replace usual inflation even if one solves the graceful exit problem in this scenario.

Entropy and Polarization of a Stochastic Radiation Field

Much of the existing literature on the theory of radiation field is restricted to energy considerations. In this paper, theoretical ideas emphasizing the achievements in classical electrodynamics and numerical results concerning the entropy of a radiation field are discussed. This review also includes results using several analytical techniques, i.e. maximum entropy principle, spectral decomposition theorem. Special emphasis of these calculations is given on the effect of polarization. In particular, we find that a number of important features can be found as a direct consequence of the SU( N) Lie group expansion of the polarization density matrix. Although most of the discussion is devoted to the case of plane waves ( N=2), the evaluation of the entropy of radiation for non planar waves ( N=3) is presented in Appendix A. Through the use of the spectral decomposition theorem (Appendix B), a formula for the polarization dependence of radiation entropy is obtained, which we suggest has application in the extraction of polarization information from a range of Mueller and Jones matrices in optics. The geometrical feature (Stokes vector space formulation) that emerges is presented along with a thermodynamical analysis underlying the two-level description of a partially polarized wave. Examples are presented of applying this new formalism to problems of scattering and propagation of light. This technique is best suited to characterization of depolarizing systems, where the light undergoes a change of degree as well as polarization state. We first discuss the problems associated in extending the treatment of a plane wave to a non-plane wave radiation field. As an illustrative application of our analysis, we consider the problem of finding bounds for the degree of polarization of an incoherent mixture of partially polarized beams. We further investigate the effect of a linear optical device on the entropy of an incident partially polarized plane wave and characterize the polarization of certain common optical components, e.g. compensator, rotator, polarizer. It is argued here that depolarization is connected to a process of entropy production. We next consider elastic multiple scattering of light by a dense random collection of dielectric spheres and analyze the behavior of entropy production during the irreversible evolution of the state of polarization. Appendix C outlines the derivation of the correlation function of the field that is required to exactly solve the Bethe–Salpeter equation for point-like scattering centers whose size is small compared to the wavelength. Computational techniques, based on Monte Carlo simulations provide a useful tool for studying multiple scattering of light by a spatially random medium composed of uncorrelated and noninteracting spherical dielectric particles. In a medium containing particles which are small compared with the wavelength (Rayleigh regime), the characteristic length of depolarization for incident linearly polarized light is found to exceed that for incident circularly polarized light, while the opposite is true in a medium composed of particles large compared to the wavelength (Mie regime). These numerical results are compared against measurements on suspensions of polystyrene latex spheres in water. One of the most remarkable aspects of this problem, where no energy exchange between radiation and scatterer takes place, is that the stationary state corresponds both to the state of minimum production of radiation entropy and to the state of maximum entropy. Finally, the entropy production by propagation of light in anisotropic media is evaluated. The theory is developed in a form that is most convenient for applications to quantum electronics (such as optical fibers, fiber systems, devices, and networks) because that subject is rich in experiments that illustrate the complicated polarization phenomena in optical media [Recent progress in fibre optics, G. Cancellieri and F. Chiaraluce, Progress in Quantum Electronics, 18, 39 (1994)], as well as being of considerable practical importance.