The Sciences: Physics:


Negentropy of Computation

and the Activity of Living Systems based on Superluminal Particles

by Dr. Takaaki Musha

Advanced Science-Technology Research Organization

Yokohama, Japan

Foundation of Physics Research Center (FoPRC)

Cosenza, Italy



Link for Citation Purposes:




The concept and phrase "negative entropy" was introduced by Erwin Schrödinger in 1944. But the physical meaning of negative entropy is not clear until now. In this paper, the author shows that negative entropy will appear in the computational steps by using superluminal particles and also in the activity of living systems.


Key Words: negative entropy, negentropy, superluminal particle, computation, brain

           microtuble, evanescent photon



The concept and phrase "negative entropy" was introduced by Erwin Schrödinger in his 1944 popular-science book gWhat is Life?h [1] Later, Léon Brillouin shortened the phrase to negentropy [2]. In 1974, Albert Szent-Györgyi proposed replacing the term negentropy with syntropy. That term may have originated in the 1940s with the Italian mathematician Luigi Fantappiè, who tried to construct a unified theory of biology and physics. Buckminster Fuller tried to popularize this usage, but negentropy remains common. Ideas about the relationship between entropy and living organisms have inspired hypotheses and speculations in many contexts, including psychology, information theory, the origin of life, and the possibility of extraterrestrial life.


This, Schrödinger argues, is what differentiates life from other forms of the organization of matter. In this direction, although life's dynamics may be argued to go against the tendency of the second law, life does not in any way conflict with or invalidate this law, because the principle that entropy can only increase or remain constant applies only to a closed system which is adiabatically isolated, meaning no heat can enter or leave, and the physical and chemical processes which make life possible do not occur in adiabatic isolation. Contrary to this principle, it can be shown that the computation by superluminal particles, negentropy will appear during the computation.


In this paper, the negentropy by superluminal computation is considered and it is also shown that the negentropy will appear in the activity of the brain organism which is associated with the superluminal computation.


Entropy of Computation

  We assume the computation to be sitting in one of two states, with energy  or  according the definition given by R.Feynman [3].



         Figure.1 The general transition during computation


As shown in Fig.1, the ratio of the forward to backward rate of computation becomes


               ,                           (1)

where  is the Boltzman constant and  is an absolute temperature.

According to Feynman, entropy of the computation can be given by [3]


                ,                           (2)


Then we have , where .

From which, the energy loss per step is equal to the entropy generated in that step.


According to the paper by S. Lloyd [4], it is required for the quantum system with average energy  to take time at least  to evolve to an orthogonal state given by

                     ,                                   (3)

where  is the Plank constant divided by .


According to the paper by Musha [5], computation by using superluminal particles can be considered instead of subluminal particles including photons.


E.Recami claimed in his paper [6] that tunneling photons which travel in evanescent mode (i.e.evanescent photon) can move with superluminal group speed inside the barrier. Chu and S.Wong at AT&T Bell Labs measured superluminal velocities for light traveling through the absorbing material [7]. Furthermore Steinberg, Kwait and Chiao measured the tunneling time for visible light through the optical filter consisting of the multilayer coating about m thick [8]. Experimental results obtained by Steinberg and co-workers have shown that the photons seemed to have traveled at 1.7 times the speed of light. Recent optical experiments at Princeton NEC have verified that superluminal pulse propagation can occur in transparent media [9]. These results indicate that the process of tunneling in quantum physics is superluminal, as claimed by E.Recami [6].


From the relativistic equation of energy and momentum of the moving particle, given by

                   ,                           (4)


                   ,                           (5)


the relation between energy and momentum can be shown as .

From which, we have [10]

 .                    (6)

Supposing that the approximationholds, Eq.(6) can be simplified as

.                           (7)

This relation is also valid for the superluminal particle (which has an imaginary mass ), the energy and the momentum of which are given by following equations, respectively.

 ,                      (8)

 .                      (9)


According to the paper by M.Park and Y.Park [11], the uncertainty relation for the superluminal particle can be given by

 ,                    (10)

where  and  are the velocities of a superluminal particle after and before the measurement. By substituting Eq.(7) into (10), we obtain the uncertainty relation for superluminal particles given by

,                     (11)

when we let  and .


Entropy of Computation by Subluminal and Superluminal Particles


 If we suppose  is

                     ,                     (12)

where  is the relative speed of the observer to the observed system and  is the light speed.

If we suppose the energy of the particle to be , the energy  which is the energy of the particle measured by the observer can be given by

 @@@@@@@@@@,                     (13)

From the equation,  and Eq.(3), the increased rate of entropy by the one step computation is given for subliminal particles as

 ,                  (14)

where (: speed of the particle for computation).

The calculation result of Eq.(14) for the case of 50MPS (i.e.) and  is shown in Fig.2.



           Figure.2 Increase rate of entropy for the subliminal particle.


From which, it is seen that entropy of computation is increased per steps by the computation using subluminal particles such as electrons.

For superluminal particles, we have from Eq.(11) as


,                (15)


By this equation, the increase rate of entropy per steps of computation by using superluminal particles can be shown as Fig.3.


         Figure.3 Increase rate of entropy for the superluminal particle.


From this figure, it is seen that negative entropy is appeared for the superluminal particle.


For the point , the increase rate of entropy can be shown as


   Figure.4 Increase rate of entropy for the superluminal particle at .


From these figures, it is seen that entropy becomes negative value for the observer by using superluminal particles.


Superluminal particle inside microtubles

S.R. Hameroff suggested in his paper that a centriole cylinder composed of microtubules functions as a waveguide for evanescent photons, which can allow quantum signal processing [12]. Georgiev also proposed the idea that consciousness can be the result of quantum computation via applied laser-like pulses in quantum gates within the brain cortex [13,14].  Musha and Caligiuri have shown that super-radiant emissions could be used to signal qubits in a fashion similar to standing wave lasers in an ion trap computation by using evanescent photons and metamaterial [15].


Specifically the characteristic of a negative refractive index, in which the generation of evanescent photons is enhanced, and they can propagate lossless inside the neurons, according to these properties of the metamaterial [16,17].


From analysis of the amplification of evanescent waves through a rectangular waveguide filled with a metamaterial, of cross section size gh, J.D.Baena et al.[18] has shown that the propagation of electromagnetic waves along this wave guide is only possible if , where .


           Figure.5 Structure of the neuron and the microtuble


From this equation, the wavelength for the case where electromagnetic waves propagate through the waveguide becomes

                        .                               (16)

 As the average size of microtubules is about , we can see Eq.(16) is satisfied for photons of super radiant emission.


Each microtuble is a hollow cylindrical tube of tublin proteins as shown in Fig.5, which outer core diameter is 25 nm. Microtubules are comprised of subunits of the protein, named tubulin [12]. Proteins contain hydrophobic (water repellent) pockets and these pockets contain atoms with electrons called  electrons. Microtubules are one of the cytoskeletal filament systems in eukaryotic cells. The microtubule cytoskeleton is involved in the transport of material within cells, carried out by motor proteins that move on the surface of the microtubule.


Microtubules are very important in a number of cellular processes. They are involved in maintaining the structure of the cell and, together with microfilaments and intermediate filaments, they form the cytoskeleton.


They also make up the internal structure of cilia and flagella. They provide platforms for intracellular transport and are involved in a variety of cellular processes, including the movement of secretory vesicles, organelles, and intracellular macromolecular assemblies.


If the microtubules are composed of a metamaterial, the super-radiant emission can be used similar to the use of standing wave lasers in ion trap computation and they can be applied for the manipulation of water qubits inside the microtubule[19].

   Figure.6  Quantum computation conducted inside the microtubule.


According to their hypothesis of quantum brain, microtuble quantum states link to those of other neurons by the quantum coherent photon tunneling (which has superluminal speed) through membranes in biological systems, functioning in a way that resemble to an ion trap computer [20].


Therefore it seems highly plausible that macroscopic quantum ordered dynamic systems of evanescent photons in the brain could play an essential role for quantum computations to exist in the brain. From this, it is seen that negative entropy will appear inside the brain when it functions as shown in the preceding calculations.


Result and Discussion

E.Schrödinger, contrary to the general tendency dictated by the second law of thermodynamics, which states that the entropy of an isolated system tends to increase – decreases or keeps constant its entropy by feeding on negative entropy. The problem of organization in living systems increasing despite the second law is known as the Schrödinger paradox. Schrödinger asked the question: "How does the living organism avoid decay?"


Organisms inherit the ability to create unique and complex biological structures; it is unlikely for those capabilities to be reinvented or to be taught to each generation.


But, from the theoretical analysis, negative entropy will appear inside the living systems if the activity of them relates to superluminal evanescent photons.


If this assumption is true, the life has negative entropy as claimed by E. Schrödinger.


From this consideration, the human mind might be consisted of superluminal particles, those have negative entropy.



 The author considered on the negative entropy and it is seen that the negentropy can be observed in the computational steps by using superluminal particles.


If the microtuble structure inside the living systems can operate as a quantum computer by using superluminal evanescent photons, the life has negative entropy as claimed by Schrödinger in his book.



1.E. Schrödinger, What is Life – the Physical Aspect of the Living Cell, Cambridge University Press, 1944

2. L.Brillouin, Negentropy Principle of Information, J. of Applied Physics, v. 24(9), pp. 1152–1163(1953)

3. R.P.Feynman, Feynman Lectures on Computation, Penguin Books, 1999, New York.

4. Lloyd S., Ultimate physical limit to computation, Nature, vol.406, 2000; 1047-1054.

5. T.Musha, Superluminal Effect for Quantum Computation that Utilizes Tunneling Photons, Physics Essays, Vol.18, No.4, 2005; 525-529.

6. E.Recami., A birdfs-eye view of the experimental status-of-the-art for superluminal motions, Foundation of Physics 32, 2001; 1119-1135.

7. J.Brown, Faster than the speed of light, New Scientist. 146, 1995; 26-30.

8. A.M.Steinberg, P.G.Kwait and R.Y.Chiao, Measurement of the single-photon tunneling time, Physical Review Letters, 71(5), 1993; 708-711.

9. L.J.Wang, A.Kuzmich and A.Dogariu, Gain-assisted superluminal light propagation, Nature 406, 2000; 277-279.

10. T.Musha, Possibility of Hypercomputation by Using Superluminal Elementary particles, Advances in Computer Science and Engineering, 8(1), 2012, 57-67, also in; Possibility of Hypercomputation from the Standpoint of Superluminal Particles, Theory and Applications of Mathematics & Computer Science, Vol.3, No.2. 2013; 120-128.

11. M.Park and Y.Park, On the foundation of the relativistic dynamics with the tachyon, Nuovo Cimento, Vol.111B, N.11, 1996; 1333-1368.

12. S.R.Hameroff, Information Processing in microtubules, J. Theor. Biol. 98, 1982; 549-561.

13. D.D.Georgiev, Bose-Einstein condensation of tunneling photons in the brain cortex as a mechanism of conscious action. Available online: http://cogprint/3539/01/tunneling.pdf (31 Mar. 2004).

14. D.D.Georgiev, Quantum computation in the neuronal microtubules: quantum gates, ordered  water and superradiance. Available online: (16 Apr. 2004).

15. T.Musha, L.M.Caligiuri, Possible existence of superluminal photons inside microtubles and resulting explanation for brain mechanism, American Journal of Oprics and Photonics, 3(5), 2015, pp.54-57.

16. L.M.Caliguiri, T.Musha, Quantum vacuum dynamics, coherence, superluminal photons and hypercomputation in brain microtubles, Applied Numerical Mathematics and Scientific Computation, 2014, pp.105-115.

17. L.M.Caligiuri, T.Musha, Superradiant coherent photons and hypercomputation in brain microtubles considered as metamaterials, International Journal of Circuits, Systems and Signal Processing, Vol.9, 2015,pp.192-204.

18. Baena, J.D., Jelinek L., Marques R and Medina F., 2005. Near-perfect tunneling and amplification of evanescent electromagnetic waves in a waveguide filled by a

   metamaterial: Theory and experiments, Physical Review B.72 075116-1-8.

19. T.Musha, Possibility to realize an accelerated Turing machine, Computer Review Journal, Vol.3, 2019, pp.203-217.

20. T.Musha, Superluminal Particles and Hypercomputation, Lambert Academic Publishing, Germany,2013.




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