Entropy and other thermodynamic properties of classical electromagnetic thermal radiation

Abstract

Building upon previous work, several new thermodynamic properties are found for classical electromagnetic random radiation in thermal equilibrium with classical electric dipole harmonic oscillators. Entropy is calculated as a function of temperature and as a function of the positions of the dipole oscillators. In the process, a new derivation is obtained for what is often called Wien s displacement law. The original derivation of this law makes a number of implicit assumptions not found in the present derivation, which prevents the original analysis from being sufficiently general to address an important class of thermal radiation spectrum candidates: namely, those that are nonzero at T=0. While leading up to the entropy calculation, a number of other thermodynamic properties are deduced. For example, a natural development is presented for reformulating the Stefan-Boltzmann law to correspond to experimental observations about changes in thermal radiation energy. Also, the Rayleigh-Jeans spectrum is shown to conflict with basic concepts of thermodynamic processes, and asymptotic limits are found for the spectrum of classical electromagnetic thermal radiation. One asymptotic restriction arises from the demand of finite specific heat for thermal radiation. This restriction is sufficient to ensure that the classical electrodynamic system of dipole oscillators and thermal radiation must obey the third law of thermodynamics. The calculations described here include full nonperturbative evaluations of retarded van der Waals thermodynarnic functions.

Simulation Results Related to Stochastic Electrodynamics

“…If one examines the thermodynamic issues surrounding this question, particularly as in Refs. [16], [44], [21], and [45], but also as supported and discussed from other perspectives in Refs. [4], [5], and [22], there is nothing contained within the three laws of classical thermodynamics that suggest that ‡uctuating motion for classical systems should not exist for systems of classical charged particles at T = 0.…”

“…References [16], [44], [21], [47], [48], and [22] proved that for the electrodynamic systems investigated, only one spectral functional form of classical electromagnetic radiation conforms with the following thermodynamic de…nition of absolute zero temperature: namely, that no heat should ‡ow during reversible thermodynamic operations. The spectral form deduced was precisely that of classical electromagnetic ZP radiation, with the energy per unit volume per unit angular frequency interval being…”

“…These derivations can be reconstructed in a very natural way without this assumption [21], thereby enabling one to deduce the functional form of the spectral energy density and its limit as T ! 0 [44], [21], [47], [48], [22].…”

Energy and thermodynamic considerations involving electromagnetic zero-point radiation

“…Reference (Cole,92a) contains more information on the changes that are necessary in the traditional arguments involving the compression of blackbody radiation (derivation of Wein's displacement law) when this physical assumption of no fluctuations is not imposed at 0 = T . References (Cole, 1990a) and (Cole, 1990b) discuss other related points that are often cited as a failure of classical physics, such as the ultraviolet catastrophe, infinite specific heat, and the third law of thermodynamics. References (Cole, 1990a), (Cole, 1992a) and (Cole, 1992b) analyze specific classical electrodynamic systems and provide derivations for the classical electromagnetic ZP spectrum, based on the thermodynamic definition of temperature.…”

“…This behavior was analyzed in some detail for several different types of systems in Refs. (Cole, 1990a), (Cole, 1990b), (Cole, 1992a), and (Cole, 1992b), resulting in the functional form of classical electromagnetic ZP radiation to be deduced in order for this property to hold.…”