Information, Entropy Decrease and Simulations of Astrophysical Evolutions

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Chang YF* Research Article Department of Physics, Yunnan University, China Volume 5 Issue 2

Received Date: June 23, 2021 Chang YF, Department of Physics, Yunnan University, Kunming *Corresponding author: Published Date: July 21, 2021 650091, China, Email: [email protected] DOI: 10.23880/psbj-16000181

Abstract

Entropy is a great development in science. We proposed that entropy decrease due to internal interactions in the isolated

system is possible. We define the entangled scale, which mainly involves the number n and entangled degree. Since coherence, entanglement and correlation are all internal interactions in information systems, we discuss quantitatively entropy decrease along coherence, and entropy increase only for incoherence. From beginning quantum heat engine, we must systematically study quantum thermodynamics. Based on some astrophysical simulation models, they shown that the universe evolves from be an isolated system only using internal gravitational interactions. disorder to structures, which correspond to entropy decrease. This is consistence with theoretical result. The simulation must

Keywords: Entropy; Information; Coherence; Astrophysics; Evolution; Simulation

Introduction Recently, we emphasized that preconditions of entropy increase are 1) for isolated systems; 2) various internal Great scientist Eddington said: “The law that entropy interactions in system must be neglected; 3) they must always increases holds, I think, the supreme position be thermal equilibrium processes. We proposed possible andamong tend the to laws disorder of Nature” in isolated [1]. Sosystem. far, entropy Its any as violation a great systems,entropy decreaseand research due to various fluctuation possible magnified entropy and decreases internal development in science points out that it is always increase interactions (these are namely Maxwell demon) in isolated

variousseems needsubsystems Maxwell of an demon isolated [2,3]. system, We proposedentropy decrease that if spontaneouslyin physics, which an order include structure, phase and transformation it may be process from of interactions, fluctuations and their magnified exist among entropydisorder decrease. uniformity We to proposed order state. that The entropy solidification decrease formsexists necessarily in self-assembly as isolated system, and discussed in the isolated system is possible [4,5], which includes the molecular motor and entropy decreases in biology. We internalphysics [6-9], energy, chemistry system entropy,[10,11], biologyand nonlinear [12-14], interactions, astronomy etc.,[15,16] an isolated and social system sciences may [17-19].form a self-organized For attractive structure process, for universal evolution of any natural and social systems. proposed quantitatively a total formula of entropy change

with lower entropy. Some possible entropy decreases are As long as we break through the bondage of the second law calculated quantitatively [6,9]. It agrees probably with the of thermodynamics, the rich and complex world is full of first basic theorem proposed by Clarke AC (1917-2008). examples of entropy decrease [20]. In this paper, we discuss

Information, Entropy Decrease and Simulations of Astrophysical Evolutions Phys Sci & Biophys J 2 Physical Science & Biophysics Journal possibly entropy decrease for entanglement, coherence in systems, and for some astrophysical simulation models. The quantum entangled state possesses some characters, Information and Entanglement interaction.for example, coherency, nonlocality, quantum teleportation and superluminal, we think that it should be a new fifth Classical information theory studies non-interference information in the same channel, i.e., information is Based on the classification of the timelike and spacelike independence of all subsystem, i.e., additive entropy. Wang, intervals, one does not add any hypothesis, we necessarily independent. This corresponds to that base of entropy is the andderived the thesuperluminal two symmetrical v >c general types of Lorentz topologically transformation separated structures: the subliminal v1) of entangled mutations increase information, and constantly increasing particles or systems, and entangled degree (d=1, 2, 3...). In two dimensional space, it is: biological complexity. setl (n,d) = ni + dj . (2)

Now the quantum entangled state is approved by some If this scale changes, its rate will be experiments [23-25]. A classical example is the Which Way (WW) experiments by double-path interferometer and atom (3) ∂s ∂s interferometer, etc [26-29]. It is difficult that determinant Moreover, there are also etl and etl electron, neutron, photon pass through which way. This ∂n ∂d implies the complementarity (the mutually exclusive nature number, the larger the general spatial scale, the. Theentanglement larger the of theMonroe, wave and et particle al. completed concepts) [30].the superposition and is less easy.

schr and so entanglement of Beryllium [31]. Polzik, et al. proposed entangled.the method Quantum for entanglement entanglement of of two macroscopic quantum objects states and Similar,information. we may definite the coherence scale contains[32]. Further, entangled it will spin be ofthat Cs hundredsgas about 10of 12millions atoms for of 0.5ms.atoms on. Further, we should discuss the corresponding entropy Moreover, there are also uncertainties about information,

If it is fermion, it will violate Pauli Exclusion Principle (PEP) can[7,33-37], be related and toshort macromolecular time corresponds formation, to high atomic energy; groups, if it is such as conservation of information is inconsistent with the chemistry,boson, it will biological correspond composition, to BEC atetc., high until temperature. the unity of manThis hairrousQuantum law of black Theory hole. and Entropy Decrease basic problems in particle physics. and nature. In short, we need to be studied in depth many In quantum statistics the free energy corrected to Maxwell-Boltzmann (MB) value is [44]: Chang YF. Information, Entropy Decrease and Simulations of Astrophysical Evolutions. Copyright© Chang YF. Phys Sci & Biophys J 2021, 5(2): 000181. 3 Physical Science & Biophysics Journal

exist, should be one of entropy decrease. any In condensation the Ginzburg-Landau process, intheory which the attractive difference interactions in the free energies of the superconducting and normal states:

(4)

Correspondingly, the entropy is: (9) where and later the upper sign corresponds to Fermi-Dirac (FD) statistics and the lower sign corresponds to Bose- Einstein (BE) statistics. Correspondingly, the entropy is: (10) (5) Tc . >0 for Fermi gases, and dS<0 for Such dS<0 for T< Therefore, The occurrence of superfluidity in a Fermi system is due leadBose togases, the i.e.,occurrence the entropy of an in BEadditional statistics effective is smaller repulsion than in to the Cooper effect, the formation of bound states (pairing) MB statistics. In FD statistics the quantum exchange effects by mutually attracting particles. We predict that entropy will anddecrease its fountain for the effect Cooper must suppose effect, that further, the helium for BEC, does not for between the particles, and in BE statistics there is an effective superconductivity and superfluidity. The superfluid helium attraction between the particles [44]. This is consistent with entropy decrease for attractive process [4,5]. zero-entropy,carry entropy, butso that this the cannot second hold law becauseof thermodynamics zero-entropy is not violated [45]. It shows that superfluidity will possess The second virial coefficient may be calculated with He3 the entropy allowance for the quantization of the binary interaction of corresponds to absolute zero according to the third law of ∆S = Sl − S s the gas particles, and the2 atoms2 obey3 / 2 BE statistics. The free thermodynamics. For the liquid or solid 8N  π  −1/ 2 energy is [44]:= −   difference [45] is >0 (for higher temperature), F Fid   Z intT V  m  Correspondingly, the entropy is: . (6) =0 (for T=0.3K), <0 (for lower temperature). Such a solid state with higher entropy should be disorder than a liquid condition.state in lower In temperature.the evolutionary Of course, process the andabove the examples phase are not already under the thermodynamic equilibrium states. (7) transformation, the systems cannot be in thermal equilibrium When there is a critical point, a continuous transformation

This is smaller than entropy of ideal gases [7]. states,can be effectedand internal between symmetries any two statesare different, of the substance so entropies [44]. It is known that entropy is measurement of disorder in areInteractions also different. between In thethe unsymmetricalmolecules are different phase, the for entropythe two a system [45]. In phase transformation the crystallization of an over-cooling liquid or of a supersaturated solution is statesurely and an theordering superconductive process. The state cooling is: principle is entropy is [44]: reduced. The difference of entropies between the normal At the transformation point itself,(11) this expression

becomes S0 Tc , dS=S-S0 Tc , dS=S-S0<0. A symmetrical state is more order than unsymmetrical state. (8) . For T> >0; but for T<

S s is entropy of the normal state, and S s is one of the At a critical point of phase transformation of the second kind, ∂H c wheresuperconductive state. Such dS<0 for < 0 . A there is [7]: a> ∂T superconducting state is more order than a normal state. η (for 0), (12) the Landau-Devonshire theory and the Landau-de Gennes superconducting state is a condensation process. Generally, wheretheory of phaseis an order transformation. parameter. These results are similar in This phase transformation from the normal state to the

transformation.In a system When with the internal order interactions,parameter of a the system fluctuation comes coherence, and if they are 0, the system will have not the tocan a thresholdbe magnified, value, for a phaseexample, transformation in those processes occurs, ofand phase self- as:quantum coherence. For the density ensemble, entropy of the ensemble is defined organization will take place. Simultaneously, the entropy will For the diagonal density (15) decrease continuously, and a final state with lower entropy will be reached. In this case various microscopic states are not equally probability. If entropy is seen as a degree of freedom,In phase the interactiontransformation, will reduce structures the degreeand symmetries of freedom. are For a pure ensemble (16) different, corresponding internal energies and entropies are  0 ... 0 ... 0  also different. At a critical point of phase transformation,   ......  ρ =  0 ... 1 ... 0    entropy can increase or decrease, i.e., possesses two-direction ......  property. This corresponds to reversibility of transformation  . (17)  0 ... 0 ... 0  between order and disorder. Of course, the general phase transformation is an open system. But, if input energy is interrupted at the critical point, it will become an isolated For a completely chaotic mixed ensemble maysystem. be screenedAlthough completely.in an isolated It issystem very easilythe gravitational that strong field and S=0 is the maximum order.  1 ... 0 ... 0  cannot be screened completely, but the electromagnetic field   ......  1 weak interactions as short-distanceC = TdS ones/T isare anomalous, screened. i.e., ρ =  0 ... 1 ... 0  V N   ......  The specific heat   . (18)  0 ... 0 ... 1  entropy is anomalous. This implies entropy decrease [4-20]. A nucleation in phase transformation for solids, which may be formed due to thermal fluctuation, is an ordered process. independent, and S is the maximum. inThe dynamics second of law phase of thermodynamics transformations. is corrected, it will be S=klnN is the equally probability and the statistics conducive to develop freely theories on nucleation and grow From complete chaos to order, entropy decreases. It corresponds to the non-diagonal density, and has coherent, and is partially ordered and entropy decrease. (13) For the diagonal matrix The second law of thermodynamics is based on an isolated system and statistical independence [45]. If For Eq.(14) fluctuations magnified due to internal interactions exist in 0, | ρ | becomes smaller. Interference reduces entropy the system,Coherence entropy and will Entropydecrease possibly Decrease [4-20]. decrease. is the maximum, and density always greater than Assume that are the given set of standard

In quantum information there are correlation, orthogonal bases in the d-dimensional Hilbert space. If the entanglement and coherence [46,47], which are generally all internal interactions in systems, and not only for quantum. coherent.density operators of the quantum system can be diagonalized, Let {|0>,|1>} as a set of bases in a two-dimensional the quantum state will be incoherent, otherwise it is quantum Hilbert space, whose density matrix is:

Here the principal diagonal (14) Quantum coherence and quantum entanglement represent two fundamental features of nonclassical systems are two nonnegative real entanglementthat can each be and characterized coherence within by studying an operational their combined resource theory. Chitambar, et al. unified the resource theories of |0> and |1>, respectively; the secondary diagonal ρ01, ρ10 are behavior in the operational setting of local incoherent numbers, which represent the probability of the ground state two complex numbers, which represent the quantum operations and classical communication (LIOCC) [48]. Chang YF. Information, Entropy Decrease and Simulations of Astrophysical Evolutions. Copyright© Chang YF. Phys Sci & Biophys J 2021, 5(2): 000181. 5 Physical Science & Biophysics Journal

The incoherent operation does not cause the coherence cases, it will improve the efficiency of quantum heat engines. increase of the quantum state, that is, the incoherent We must systematically study quantum thermodynamics. operation may reduce the coherence of the quantum state on Fromany quantum this it may state. be extendedThe incoherent to the andgeneral decoherence state. should enhancesHackermuler, along increasing et al. discussed temperature, decoherence namely decoherence of matter correspond to the entropy increase without interaction. waves by thermal emission of radiation [71]. Decoherence Recently, coherence, incoherence and correlation, the same result. In the human body and parapsychology, a ρ is a highis associated temperature with is temperature dizzy. T. Entanglement should be density operator of d-dimensional Hilbert space, such its relativeentanglement entropy are coherence discussed and widely system [49-68]. entropy Let satisfy the Simulation of Evolutional Universe following uncertain relation: Cr (ρ) + S(ρ) ≤ log2 d It is namely that the relative entropy coherence of any modernIt is astronomyknown that is stars the evolutionalare formed simulation, from nebula especially, through ρ does not exceed the information. (19) function: gravitational self-interactions. Now an important way of quantum state for the evolution of universe [72]. So far, there are some well- Cr (ρ) ≤ It (ρ) known astrophysical simulation models. system, the less coherence; conversely,. (20) the more coherence of This shows that the larger the entropy of the quantum In 2005, the Max Planck Institute for Astrophysics completed Millennium Simulation Project [73-76]. This is the the quantum system, the smaller the entropy of the quantum square box (about 2.3 billion light-years) with a side length of system. In a word, entropy decreases along coherence, and evolution500/h, in whichof a multi-body h is the Hubble system constant. composed It contains of 10 21603billion entropy increases only for incoherence. This is impossible dark matter particles, i.e., it is equivalent to simulating the that entropy always increases for coherence and incoherence. structure is very similar to some spatial distribution of It is completely consistent with my theory [4-20]. particles. This created an image of a cosmic network, whose

ModernThe smart actuator materials is a are material sometimes that called can change“life in the its galaxies (Figure 1). characteristics according to the changing system state [58]. non-living world” [59]. This may even be related to animism. This might make Maxwell demon [2,3]. and perhaps produce results violating the entropy increase Cellular automata may aggregate automatically [60,61], principle [4-20]. can Theobtain internal entropy interactions, decrease and and self-organization their fluctuation based and amplifications can form structures and derive order, and on the nonequilibrium statistical physics. An example is Vicsek model [66,67]. Biological evolution is mainly self- interactions [68].

Scully, et al. designed a photonic gas heater [69]. For this case, the second law of thermodynamics is violated on the surface, and the efficiency of heat engine may be greater than that of the Carnot cycle. Quan, et al., studied a new quantum heat engine (QHE), which is assisted by a Maxwell’s demon. The QHE requires three steps: thermalization, quantum measurement, and quantum feedback controlled by the essentialMaxwell demon.role of the They demon derived is explicitly the positive-work demonstrated condition in this and operation efficiency of this composite QHE. The Figure 1: Millennium Simulation Project. macroscopic QHE [70]. If Maxwell demon exists in quantum Chang YF. Information, Entropy Decrease and Simulations of Astrophysical Evolutions. Copyright© Chang YF. Phys Sci & Biophys J 2021, 5(2): 000181. 6 Physical Science & Biophysics Journal

Further, in 2019 Millennium Simulation is expanded to celestial activity from the big bang to the present, spanning 50403 to reproduce the formation and evolution of galaxies

about 14 billion years. They condensed the whole process cosmologicalunder the cold theories, dark matter and explain model, the statistically results of comparedSDSS, and into a video about 78 seconds long by Arepo simulator with the galactic properties observed, and test current (Figure 4). energy.try to answer fundamental astronomical questions on the evolution of universe, and the nature of dark matter and dark precision galaxy cluster. In 2010 Computational Cosmology In 2009 China developed a “Phoenix” simulation for high-

Consortium of China (C4) launched a large cosmological numerical simulation program, “Pangu Project” (Figure 2).

Figure 4: Simulation on the evolution of universe.

Vogelsberger, et al. proposed a model for cosmological

simulations of galaxy formation physics [77]. They reported a simulation model of the Universe that follows the evolution of both visible and dark matter starting 12 million years after the Big Bang. This simulation covers a region of space big enough to be representative of the whole Universe, and traces 13 billion years of cosmic evolution with 12 billion Figure 2: Large-scale structure of the universe produced resolution elements in a cube of 106.5 megaparsecs (350 by Pangu simulation. scalemillion distribution light years). of Itgalaxy produces clusters a mixture and neutral of galaxy gas shapes in the that fit observations well, and accurately recreates the large-

FIRE simulation, ERIS simulation, Illustris simulation and Universe, as well as the hydrogen and heavy element content Other well-known cosmological simulations include of galaxies [78]. Gibney reviewed this model universe and the cluster of three hundred galaxies simulation, etc recreates evolution of the cosmos [79], and this successful next-generation Illustris simulations, MultiDark simulation, simulation lends weight to standard model of cosmology (Figure 5). (Figure 3).

Figure 3:

In 2012, astrophysicists TNG used Collaboration. computers to simulate the Figure 5: Simulation of large galaxy cluster. most realistic evolution of the universe, which includes all Chang YF. Information, Entropy Decrease and Simulations of Astrophysical Evolutions. Copyright© Chang YF. Phys Sci & Biophys J 2021, 5(2): 000181. 7 Physical Science & Biophysics Journal

invariant cosmological hydrodynamical simulations on a

Brook, et al. studied galaxy formation using simulations variations in the input physics on the cosmic distribution [80].In 2014, astronomers announced that after three months moving mesh [88]. Wiersma, et al. predicted the effect of calculation used 8000 CPU connected, a computer simulation etof metalsal. researched by simulations the formation [89]. Genel, of discet al. galaxies discussed in tracerhigh- particles in astrophysical fluid simulations [90]. Marinacci, of the evolution of the universe was born and evolved from dark matter (Figure 6). resolution moving-mesh cosmological simulations [91]. processes of the celestial evolutions must be order, and Since entropy is a measurement of disorder [45], some becomes an order star due to the internal gravitational interactionentropy decrease in systems. [4,15]. For instance, a disorder nebula

Almost all matter in interstellar space can be considered to be plasma, an ionized gas consisting of electrons, ions, and

neutral atoms or molecules [92]. The entropy of plasma is

Figure 6: Simulation of the evolution of the universe. (21)

γ = cP / cV ,γ ≈ 4 / 3 for the polyatomic gases. In completed and state-of-the-art galaxy evolution simulation. On 12 October 2020, scientists have released a newly where an isolated system of plasma, the ions will attract electrons TNG50 is the most detailed large-scale cosmic evolution to neutral atoms. Since the plasma is often taken to be in simulation, which allowing researchers to study in detail densitylocal thermodynamic ρ equilibrium [92], and the total mass of how galaxies are formed (Figure 7). an isolated system is constant, temperature T and average are invariant. Therefore, the final ionicity changes smaller, so that the final entropy decreases [4,15]. General celestial bodies originate from nebula. For classically The galaxy may be regarded as an isolated system [93].

isolated gas, entropy is [45]:

(22) becomes smaller or the temperature decreases. EntropyTherefore, of the ideal entropy gases should is: decrease when the volume Figure 7: Large-scale cosmic evolution simulation.

(23) These simulations agree well with observations of the evolutionalMoreover, Universe Springel, [81,82]. et al. used cosmological smoothed For an equal-temperature process T=constant, particle hydrodynamics simulations as a hybrid multiphase (24) V f < Vi , i.e., for the of the galaxy population in hydrodynamical simulations attractive process. Conversely, the entropy increases dS>0, model for star formation [83]. Saro, et al. discussed properties This decreases dS<0, when V f > Vi of clusters [84]. Libeskind, et al. researched satellite when . The entropy of non-ideal gases is [44]: systems around galaxies in hydrodynamic simulations [85]. etSijacki, al. searched et al. proposed substructures a unified inmodel hydrodynamical for AGN feedback cluster in (25) cosmological simulations of structure formation [86]. Dolag, times volume of atom, b>0. It corresponds to the existence of This is smaller than one of ideal gases, since b is four simulations [87]. Springel, et al. discussed the Galilean- Chang YF. Information, Entropy Decrease and Simulations of Astrophysical Evolutions. Copyright© Chang YF. Phys Sci & Biophys J 2021, 5(2): 000181. 8 Physical Science & Biophysics Journal

interaction of the gas molecules, and average forces between 3. computation: a review. Iut J Theor Phys 21: 905-940. molecules are attractive [94]. pp:Leff 502. HS, Rex AF (1990) Maxwell’s Demon: Entropy, According to the second law of thermodynamics, all Information, Computing. Taylor & Francis, CRC Press, systems in Nature will tend to “heat death” [94], But, world 4. is not pessimistic always [4,15]. In some cases, internal produce various ordered stable stars and celestial bodies. Chang YF (1997) Possible decrease of entropy due to interactions are very important. The gravitational interactions 99. Various stable objects and their formations from particles to internal interactions in isolated systems. Apeiron 4: 97- 5. implied a possibility of entropy decrease. stars are accompanied with internal interactions, which have Chang YF (2005) Entropy, fluctuation magnified and 6. internal interactions. Entropy 7(3): 190-198.

When a black hole absorbs matter, its mass and entropy isolatedChang YFsystems (2012) and “Negative some possible temperature” tests in physics, fallacy, increase. Conversely, if a black hole evaporates matter [95], sufficient-necessary condition on entropy decrease in so its mass and entropy should decrease. Both are all open possibly.systems. SuchFurther, thermodynamics this is impossible of black that hole both should contrary be the chemistry and biology. International Review of Physics theory of dissipation structure, whose entropy decreases 6: 469-475. violation of Pauli exclusion principle, nonlinear collection and evaporation of black hole are all entropy 7. Chang YF (2013) Unified quantum statistics, possible increase. For opposite black hole and white hole, one is entropy increase, so another must be entropy decrease [16]. equations and some basic problems of entropy. 8. evolves from disorder to structures and their structures International Review of Physics 7(4): 299-306. Various computer simulations show that the universe ofChang microstructure. YF (2015) Entropy International decrease Journal in isolated of Modern system should be entropy decrease. And the simulation must be an and its quantitative calculations in thermodynamics grow all under the gravitational interactions [96]. This 9. Theoretical Physics 4(1): 1-15. gravitationalisolated system, interactions. because no matter can be added. They are entropy decrease in isolated systems and its tests. systems bound by their own gravity, i.e., only using internal Chang YF (2019) Self-organization, critical phenomena, Moreover, famous economist Schelling described a International Journal of Modern Theoretical Physics 8: 10. 17-32. model with two red and white agents, which evolved from entropy decrease in isolated system. International ofthe metal initial alloys, high mixingand is justto separate opposite from to the each process other usual[97,98]. as Chang YF (2013) Chemical reactions and possible This is similar to the separation of water-oil in a liquid or 11. Journal of Modern Chemistry 4(3): 126-136. a typical example of entropy increase. The corresponding isolated system and transformation of internal energy. magnetization and the orienting fields can produce similar Chang YF (2014) Catalyst theory, entropy decrease in effects. The interactions are stronger in social science, which 12. interactions.will be more Interconnection deviation from is thea typical uniformity. and clear The feature various of International Journal of Modern Chemistry 6(2): 74-86. relations and feedback within the system are internal NeuroQuantologyChang YF (2013) Possible11: 189-196. entropy decrease in biology entropy changes. and some new research of biothermodynamics. modern society [98]. This also leads to the complexity of the 13. biology. NeuroQuantology 14: 589-596. Chang YF (2016) Bioinformation and twistor theory in decreaseIn a word,in some coherence, isolated systems. entanglement and astrophysical 14. simulation models are shown the possibility of entropy thermodynamics. International Journal of Research References Chang YF (2018) Entropy change in biological 1. 15. Studies in Biosciences 6(6): 5-12. gravitational collapse, entropy decrease in astronomy, Eddington AE (1928) The Nature of the Physical World. Chang YF (2013) Grand unified theory applied to 2. New York: Macmillan, pp: 74. singularity and quantum fluctuation. International Bennett CH (1982) The thermodynamics of Journal of Modern Applied Physics 3(1): 8-25. Chang YF. Information, Entropy Decrease and Simulations of Astrophysical Evolutions. Copyright© Chang YF. Phys Sci & Biophys J 2021, 5(2): 000181. 9 Physical Science & Biophysics Journal

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