Department of BioEngineering

Nagaoka University of Technology

Nagaoka 940-2188

kmatsuno@vos.nagaokaut.ac.jp

Biology is about a specific material instance of naturalizing the interface between quantum mechanics and thermodynamics. Although physics has successfully demonstrated the proved significance of the attempt for bridging the chasm between quantum mechanics and thermodynamics with the use of the statistics of energy quanta, the statistical articulation is not the only means for accommodating the two in a mutually consistent manner. The first law of thermodynamics also has the capacity of tailoring quantum mechanics to the suit of thermodynamics exclusively on material grounds. Quantum nonlocality observed in the realm of biology makes itself amenable to energy transformation underlying the implementation of the first law of thermodynamics.

Just for the sake of focusing on the extreme exquisiteness of material coordination and configuration met in biology, let us suppose that there is a cookbook on how to make life from scratch in a planet in another remote solar system in the universe. If the cookbook is perfect enough not to require its further revision and at the same time inclusive enough to allow for the existence of the beings full of curiosity like us, it would get into trouble. If the perfect edition is in sight by any chance, there would be no room for such a curious being to appear in the first place.

On the other hand, however, if there is no likelihood of expecting the perfect edition, the best cookbook that could ever be imagined would be the one whose editors constantly come and go, while they can come up with a revised edition from time to time. The accepted cookbook would be the one coherent enough as an edited volume, but premature enough to allow for the editorial board members to think about its further revision, while the term of each board member is definitely limited. Moreover, since the editorial board of the cookbook also constitutes part of the content, the self-referential clumsiness and complication would become inevitable in the endeavor of compiling such a cookbook of life.

The overly exaggerated relationship between the occurrence of biological organization and its theoretical description as depicted in the above just points up a necessity of naturalizing whatever theoretical edifices as much as possible. Naturalization means dispensing with theoretical artifacts to the extent that can be tolerated while making access to empirical reality as closely as possible. One agenda in this regard is the occurrence of what is called the context. The context of material dynamics is constructed in a bottom-up manner, while the boundary condition addressing the context theoretically is imposed in a top-down manner. Naturalization of the context in biology is in the effort of minimizing the top-down influence of imposed character in describing biological organization (Matsuno, 1989).

Atoms and molecules constituting a biological organism are placed within the material context of an extremely specific configuration. Such a specificity of the material context makes biological organization unique compared to nonliving physical organization of atoms and molecules. Needless to say, physics has its own rich history on explicating the nature of whatever material contexts available there. One example of an extreme significance is the material context discovered by Max Planck.

Energy quantum introduced by Planck for accommodating the spectrum of black body radiation to statistical thermodynamics distinguishes the quantum from all of the rest. The stability intrinsic to each quantum requires the material context upholding the quantum stable enough against perturbations and disturbances coming from its outside. The material context preserving the integrity of a Planck quantum, that is, Planck context, is in fact characterized by the nonlocal quantum coherence as embodied in the Schrödinger equation demonstrating the occurrence of a stable standing wave between the retarded and the advanced waves. Planck context is thus ubiquitous in the material realm. Nonetheless, Planck context is not the only sort of the context of material origin available. One more type of the material context was discovered by Ludwig Boltzmann slightly before Planck did.

Boltzmann introduced the Stosszahlansatz or the hypothesis of molecular chaos stating that a gas molecule loses its past memory after a few immediately preceding collisions with other molecules, and accordingly deduced the distribution of gas molecules in thermal equilibrium. The quantitative figure characterizing the distribution in thermal equilibrium is temperature. In other words, temperature is a quantitative figure specifying the material context substantiating Boltzmann’s Stosszahlansatz, that is, Boltzmann context. Since the temperature is a figure addressing the intensity of the random kinetic movement of whatever material bodies, Boltzmann context is a material implementation of the context that guarantees the occurrence of an intensity called temperature.

We thus observe that there appear in physics two contrasting different kinds of the material context. One is Planck’s, that is almost completely coherent internally as embodied in a nonlocal quantum coherence. One more context is Boltzmann’s, that is almost completely incoherent internally as seen in the occurrence of the random kinetic movement of whatever material bodies. This observation will raise a further question of how these two different kinds of the material context could come into being integrated.

Thermodynamics specified by its intensive variable called temperature is based upon a Boltzmann context, while the occurrence of an energy quantum in quantum mechanics sets its ground upon a Planck context. These two different kinds of the material context, however, would cause a serious difficulty in the underlying material dynamics unless they are integrated in a proper manner. As a matter of fact, it was Planck himself who first recognized the need of accommodating the two different kinds of the material context as appealing to the tool of statistical thermodynamics. Planck established a shortcut to thermodynamics from quantum mechanics with the use of the statistics of energy quanta. Of course, we cannot overemphasize the proved significance of approaching thermodynamics as starting from quantum mechanics by way of statistical quantum mechanics. Despite that, one can also raise a question of whether the statistics of energy quanta would be the only way of approaching thermodynamics while starting from quantum mechanics.

If thermodynamics is thought to be obtainable from a statistics of energy quanta, it would naturally be taken for granted that a Boltzmann context will be determined after a Planck context has been fixed by some means in advance. This perspective would come to mean that the Planck context that has already been fixed controls the Boltzmann context that could come into being. This one way influencing from Planck to Boltzmann context could certainly be permissible at least theoretically. However, this theoretical stipulation does not exclude the possibility that the Boltzmann context could come to influence the Planck context to emerge in reality. A mere theoretical declaration would have no prerogative to eliminate the likelihood of Boltzmann context influencing Planck’s. Underlying the scrutiny of how a Planck context could be amenable to a Boltzmann’s is our motivation of examining the possibility of embodying the material context of a biological significance in the plastic adaptability of a Planck context to Boltzmann’s.

More than anything else, the process of implementing the first law of thermodynamics is found in the interface between biology and thermodynamics as demonstrated in the pioneering work published by Julius Robert von Mayer in 1842. In view of the fact that any biological organization is a material organization demonstrating an extremely exquisite pattern of energy transformation and transaction, the first law on energy transformation stating the occurrence of the conservation of energy in whatever transformation must assume a most significant role in the material process of biological organization.

The first law states that when the energy flow of a certain quality leaves out of a thermodynamics system, it is counterbalanced by another energy flow of an arbitrary quality entering the system from the outside heat reservoir. Likewise, the first law states that when the energy flow of a certain quality enters a thermodynamic system, it is counterbalanced by another energy flow leaving the system into the outside heat reservoir. The first law certainly applies to the thermodynamic system carrying a Boltzmann context. However, it should also be noted that the first law does not restrict its applicability only to the system carrying a Boltzmann context. We shall examine whether a Planck context can harness the first law of thermodynamics.

Suppose that there is a constant energy flow leaving out of a material system carrying a Planck context, the latter of which is immersed in a heat reservoir. The Planck context contacting the heat reservoir would then come to let in the compensating energy flow from the latter thanks to the first law of thermodynamics. In addition, if the energy outflow from the Planck context to be compensated by the counterbalancing energy inflow into it from the outside heat reservoir satisfies a homeostatic stability against perturbations and disturbances, the Planck context processing these energy flows would come to be stabilized. Rather, it is likely that a Planck context coming to terms with the Boltzmann context upholding a heat reservoir has a chance of actualizing itself compared to other alternatives. Such a Planck context is under the influence of the Boltzmann context giving the heat reservoir. The occurrence of a Planck context amenable to the Boltzmann context is just a polar opposite to what statistical quantum mechanics has provided us (Pribram, 1991; Umezawa, 1993), in the latter of which Boltzmann context is no more than a derivative of Planck’s. In order to ascertain the likelihood of a Planck context amenable to Boltzmann’s, we shall require more factual details (Rizi et al, 2000).

One example exhibiting an indirect evidence of a Planck context amenable to Boltzmann’s in the face of the first law of thermodynamics will be seen in cell motility underlying muscle contraction. An essence of cell motility giving muscle contraction is found within hydrolysis of ATP (adenosine triphosphate) molecules at an actomyosin complex. Actin-activated myosin ATPase activity underlying muscle contraction is characterized by the time interval over which one ATP molecule is hydrolyzed per myosin molecule while releasing the stored energy , with those typical values of and (or) (Harada et al, 1990; Uyeda et al, 1991). What is unique to actomyosin ATPase activity is its extreme slowness of releasing the energy stored in an ATP molecule. The energy release is punctuated by measurements internal to the actomyosin system as expressed in the energy-time uncertainty principle (Matsuno, 1989). If the energy release by the amount of happens to occur in the form of emitting a single quantum, the uncertainty principle would give an uncertainty in the timing of the emission only as much as . This value is far less than the actual time interval required for releasing energy from an ATP molecule.

The actual energy release from an ATP molecule with the aid of an actomyosin complex is to proceed through emitting a sequence of energy quanta, each of which carries energy , at every time interval of while satisfying the constraints

For the energy flow associated with measuring each quantum carrying energy over the time interval is eventually imputed to the energy release from a single ATP molecule (Matsuno, 1993, 1997). The corresponding values and would come to imply that the number of energy quanta, each of which carries energy , emitted coherently during the one cycle of energy release from an ATP molecule at an actomyosin complex would roughly be . Actomyosin ATPase activity is thus associated with emission of energy quanta, whose typical energy is or in temperature. The effective temperature of an actomyosin complex in the presence of ATP molecules comes to decrease down to as low as (Matsuno, 1999).

Actomyosin complex involved in ATP hydrolysis lowers its temperature effectively down to . That is equivalent to the occurrence of energy flow leaving the complex into the heat reservoir effectively at that low temperature. In order to facilitate such a transfer of energy flow in the form of a train of small energy quanta, the actomyosin complex would have to have the counterbalancing energy inflow from the heat reservoir at a higher temperature roughly at 310K with the aid of the operation of the first law of thermodynamics. Otherwise, the occurrence of such an extremely slow release of energy from ATP would be disturbed and then blocked. In other words, the quantum nonlocality upholding the proper functioning of ATP hydrolysis at actomyosin complexes is amenable to how the first law of thermodynamics is implemented in reality (Matsuno, 1999). The Planck context yielding the quantum nonlocality is dependent upon how the Boltzmann context specifying the heat reservoir at a high temperature comes to be substantiated and provided.

Accommodating quantum mechanics to thermodynamics with the use of the statistics of energy quanta has certainly demonstrated its proved significance in the realm of physics. However, the statistics is not the sole means to accommodate these two in a mutually consistent manner, though it is definitely rational. One more attempt for accommodating the two of quantum mechanics and thermodynamics is by means of implementing the first law of thermodynamics on material grounds, since the latter of which has the capacity of admitting contextual dynamics not only of Boltzmann’s but also of Planck’s. Although statistical manipulation is a theoretical artifact at best, energy transformation latent in implementing the first law of thermodynamics is natural. The naturalization underlying the contextual dynamics is intrinsically selective and not necessarily rational since no contextual constituents belong to two different contexts at the same time. It is this aspect of naturalization that makes biological organization unique in accommodating both quantum mechanics and thermodynamics mutually in a consistent manner.

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