

"When you change the way you look at things, the things you look at change." —Max Planck  
A. IntroductionPlanck's blackbody emittance equation(1) is the universally accepted model for heat radiation's equilibrium, spectral distribution. It has been found superior to any other contemporary form(2,3,4,5,6). However, this acceptance is only justified for equilibrium, and leaves two important issues unresolved. First, Planck's solution provides no insight into nonequilibrium or farfromequilibrium states, or the mechanisms of redistribution between equilibrium states(7). Only Ehrenfest (8) has explored redistribution mechanisms, and Forte(9) describes a nonequilibrium Wein Displacement Law. Secondly, Planck's energy quanta violated the continuity requirements of Maxwell's equations. Einstein first enunciated this discrepancy, and Planck spent the next 2 decades, unsuccessfully trying to resolve it. Meanwhile, the experiments of Stark(10), and Einstein's light particle theory(11) demonstrated the dual nature of light, galvanizing the discontinuity's place in physics. More recent studies of nonquantum blackbody theory(12,13,14,15,16,17) have not reconciled this conflict. This paper explores one possible avenue to a nonequilibrium blackbody equation. The goal here,
is understanding free energy partitioning between the domains of heat radiation, and molecular
motion. One of the model's solutions is then interpreted as an avenue to understanding
farfromequilibrium energy storage in living cells. B. TheoryPlanck(18) viewed the separation of all physical phenomena into reversible and irreversible
processes as the most elemental, and most important, because all irreversible processes share a
common similarity that makes them unlike any reversible process. This distinguishing
characteristic is the transformation of heat energy to motion, which can in no way be referred
back to the process from which it came. This research considers Maxwell's electromagnetic wave
traveling undiminished in time, its information content preserved, until it encounters a material
particle (Figure 1). The absorption process' second step is a dimensional restructuring that the 1D electrical quanta undergoes in evolving into its 3D equivalent, electrical charge density. This occurs in accordance with the Equipartition Theorum, along the axes of the electron's three spatial coordinates. The resulting displacement of the generalized coordinates translates to 3D motion, the evolution of Joule heat, and irreversibility. The magnetic vector has no 3D equivalent, and can only transform to 1D paramagnetic spin. Accordingly, photon decoupling distorts time's fabric, giving rise to the characteristic spectral emittance. This second absorption step is represented by a Dirac delta over the 3D transformation's time interval. Light absorption is considered a twostep process. The first is an adiabatic reversible step, wherein onedimensional light energy is absorbed in a quantum amount, , by an electron, and is wholly contained within it. The absorbed quanta is still 1dimensional(1D), remains within the domain of reversible thermodynamics, and does not emit Joule heat. There is no recourse to the Second Law during this first step. The absorption process' second step is a dimensional restructuring that the 1D electrical quanta undergoes in evolving into its 3D equivalent, electrical charge density. This occurs in accordance with the Equipartition Theorum, along the axes of the electron's three spatial coordinates. The resulting displacement of the generalized coordinates translates to 3D motion, the evolution of Joule heat, and irreversibility. The magnetic vector has no 3D equivalent, and can only transform to 1D paramagnetic spin. Accordingly, photon decoupling distorts time's fabric, giving rise to the characteristic spectral emittance. This second absorption step is represented by a Dirac delta over the 3D transformation's time interval. (1) (2) 1st Moment The probability distribution's restructuring from a 1D quanta, h, to three dimensions requires taking the next two moments of the variance function relative to the Wein frequency, _{m}. Thus: (3) The results are summarized as: (4) 2nd Moment (5) 3rd Moment The third moment represents all of the possible interconnections between any arbitrary frequency and the Wien frequency. _{m} is the most probable frequency at the prevailing temperature. _{1} is the damped frequency continuum of the blackbody spectra. Assuming the radiation absorption function to be exponentially distributed, (6) and substituting this absorption and the RalieghJeans emittance into Kirchhoff's Law: (7) Blackbody = Emittance/Absorptance Spectra (Rayleigh Law) (This study) This spectral distribution: 1) is derived entirely from classical theory; 2) contains the discontinuity indirectly, ; 3) incorporates the consequences of electromagnetic theory(RayleighJeans Law); and 4) suggests a mechanism for exchange of energy between frequencies. Sears[19] gives Wien's Displacement Law as: (8) (Wien frequency) Figure 2 displays features of the blackbody radiation spectra described in this way. The figure also displays calculations using Planck's Equation: (9) The agreement is close, but not exact, differing by less than 2% at _{m}, and in the 5%8% range to the left, where Eq.(7) better
represents RalieghJeans. The curves terminate at the point where the calculations yield partial quanta.
The number of quanta is obtained by dividing the spectral emittance by the conversion factor and then dividing by . C. DiscussionBoth the two slit experiment and the photoelectric effect are consistent with this theory. The wave properties of light are unaltered. The theory eliminates discontinuity as a property of light, placing it instead in the electron, more precisely, in the electrons absorption of light in quantum amounts. This reassignment isn't contrary to, nor does it change, existing theory. Eq.(7) offers two significant advances over Planck's which are instructive in furthering our understanding of heat processes. The first is Eq.(7)'s explicit statement for energy transference between frequencies. This was identified at the outset as the distinguishing characteristic of the required nonequilibrium blackbody form. Eq.(5) suggests that the common channel for energy redistribution is the Wien frequency, since each spectral frequency is explicitly related to it. Planck's equation can also be shown to contain the same ratio(21). Second, Eq.(7)
contains two distinct thermodynamic scales, representing the entire
range of nonequilibrium heat conditions. The concept of two
temperature scales is not new(22,23,24,25,26,27). The first of these
scales is the classical thermodynamic temperature, of the
RaylieghJeans Law, T_{m}.
It is common to both equations, and expresses the temperature of
thermal motion alone. Consider Figure 3 where T_{R}, and consequently the Wien frequency remain constant while T_{m} increases from 300°K to 10^{5}°K (Case A). This represents a sudden frictional input of heat to a material body that is initially at thermal equilibrium. Similarly, T_{R} can be increased without a corresponding increase in the thermodynamic temperature (Case B). The radiation density within the blackbody is increased without a corresponding increase in the RaylieghJeans emittance. The new region delineated by this spectral distribution consists primarily of higher energy radiation, but the process from which it arises appears to an observer to be adiabatic, and might therefore, be viewed as completely reversible. From this theory's standpoint, the energy content within this new region (Case B) consists entirely of radiation transfers that are undergoing the first stage of radiation absorption, alone. That is, radiation is fully absorbed in its one dimensional form and immediately reemitted. There is no decoupling of light's electromagnetic structure, and therefore no entropy increase. This is the initial condition when high energy radiation strikes a body initially at equilibrium. Taking this result further, one might ask: Are there states in nature that exploit the energy/entropy relationship suggested by these calculations? There might be. Living systems are constructed of high energy covalent bonds that both, represent very farfromequilibrium conditions, and store larger amounts of electromagnetic energy than would normally exist at the T_{m}. It is possible that Case B shows how farfromequilibrium energy storage might be masked from ambient thermodynamic conditions in matters living state. Each covalent electron pair shares the wave function, ^{2}, alternately absorbing and reemitting light energy, but only in a manner consistent with this theory's first absorption step. This portion of the heat radiation spectra is localized (masked) between electron pairs, and does not contribute to either the measurable heat spectra or to dielectric losses. Thus, the thermodynamic temperature of the cell (T_{m}) is unaffected, and a stable farfromequilibrium condition with lower localized entropy, is possible. The degree of entropy decrease is defined by the separation between T_{m} and T_{R}. The permanence of that change appears to depend on irreversible storage of negentropy outside mechanistic pathways back to equilibrium(28). As the energy storage requirements begin to exceed the capacity of the covalent bond system, other mechanisms for storing this biological energy in a stable farfromequilibrium state might be found in elevated electronic states, and probably even excited nuclear states as Mossbauer resonance. Eq.(5) suggests enormous capacity for farfromequilibrium entropy absorption and the information storage this implies. A second example of where this type of heat theory may prove important to scientific understanding is found in what has been called cold fusion. Energy storage in a palladium or nickel electrode might occur in the radiation domain (Case B in Figure 3), first as excited electronic states and a corresponding increase in the redox state, and later in excited nuclear states. Is it possible that such a system could exhibit radiation temperatures approaching 10^{7}°K while the ambient temperature of the electrolysis apparatus hovers around 300°K? Stranger paradigms have occurred in the history of science. A third example of farfromequilibrium spectral energy storage might be found in sonoluminesence, wherein mechanical energy is converted to electromagnetic energy. In this case, mechanical energy increases T_{m} instantaneously without a corresponding increase in T_{R} (Case A in Figure 3). Lacking any mechanism to maintain this farfromequilibrium condition, the system spontaneously moves toward equilibrium by channeling the stored mechanical energy through the Wein frequency channel, and thence, into the radiation domain. If the energy flux is high enough, visible light is observed. The 1D to 3D transform
function given by Equation 3 could possibly be a mathematical
statement of the Second Law at the boundary between electrodynamics
and mechanics. In its temporal form (19) the equation represents the
relative dominance of the forward(entropic) and backward(negentropic)
reaction directions. D. References[1] M. Planck, Verhandlunger der Deutschen Physikalischen Gesellschaft, 2, 237, (1900), or in English translation: Planck's Original Papers in Quantum Physics, Volume 1 of Classic Papers in Physics, H. Kangro ed., Wiley, New York (1972). [2] H. Rubens and F. Kurlbaum, Ann. Physik, 4, 649 (1901). [3] F. Paschen, Ann. Physik,4, 277 (1901). [4] E. Warburg, Ann. Physik, 48, 410 (1915). [5] W. Nernst and T. Wulf, Ber. deut. phys. Ges., 21, 294(1919). [6] W.W. Coblenz, Dict. Appl. Phys., Vol. IV, "Radiation". [7] T.S. Kuhn, BlackBody Theory and the Quantum Discontinuity 18941912, Oxford University Press, New York (1978). [8] Kuhn found references to nonequilibrium transitions only in Ehrenfest's notes. [9] J. Fort, J.A. Gonzalez, J. E. Llebot, Physical Letters A, 236,193200 (1997). [10] J. Stark, Phys.ZS.,8(1907), 913919, received 2 December 1907. [11] A. Einstein, Ann. d. Phys.,17(190), 132148, 1905. [12] H. Dingle, Phil Mag, XXXVII,246, 47 (1946). [13] T.H. Boyer, Phys. Rev. 182, 1374 (1969). [14] T.H. Boyer, Phys. Rev. 186, 1304 (1969). [15] T.H. Boyer, Phys. Rev. D, 11, 790 (1975). [16] T.H. Boyer, Phys. Rev. D, 29, 1089 (1984). [17] D.C. Cole, Phys. Rev. A, 45, 8471 (1992). [18] M. Planck, Eight Lectures in Theoretical Physics1909, translated by A.P. Wills, Columbia U Press, NY (1915). [19] F.W. Sears and M.W. Zemansky, >University Physics>, 3rd ed., AddisonWiley, Reading, MA (1964). [20] see T. Preston, Theory of Heat, Macmillan and Co, London (1929) for a description of their methods and results. [21] If we rearrange Equation (8) and substitute for T in Planck's Equation(9), the exponential term becomes . [22] B.C. Eu, L.S. GarciaColin, Phys. Rev. E, 54, 2501 (1996). [23] D, Jou, J. CasasVazquez, Phys. Rev. A, 45, 8371 (1992). [24] K. Henjes, Phys. Rev. A, 48, 3194 (1993). [25] W.G. Hoover, B.L. Holian, and H.A. Posch, Phys. Rev. A, 48, 3191 (1993). [26] D. Jou, J. CasasVazquez, Phys. Rev. A, 48, 3201 (1993). [27] J. Fort, D. Jou, and J.E. Lleobot, Physica A, 269, 439(1999). [28] G. Nicolis, I. Prigogine, SelfOrganization in NonEquilibrium Systems, John Wiley and Sons,
NY, 1977. Appendix A  
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