Self-Organization, Critical Phenomena, Entropy Decrease in Isolated Systems and Its Tests

International Journal of Modern Theoretical Physics, 2019, 8(1): 17-32 International Journal of Modern Theoretical Physics ISSN: 2169-7426 Journal homepage:www.ModernScientificPress.com/Journals/ijmtp.aspx Florida, USA Article Self-Organization, Critical Phenomena, Entropy Decrease in Isolated Systems and Its Tests

Yi-Fang Chang

Department of Physics, Yunnan University, Kunming, 650091, China Email: [email protected]

Article history: Received 15 January 2019, Revised 1 May 2019, Accepted 1 May 2019, Published 6 May 2019.

Abstract: We proposed possible entropy decrease due to fluctuation magnification and internal interactions in isolated systems, and these systems are only approximation. This possibility exists in transformations of internal energy, complex systems, and some new systems with lower entropy, nonlinear interactions, etc. Self-organization and self- assembly must be entropy decrease. Generally, much structures of Nature all are various self-assembly and self-organizations. We research some possible tests and predictions on entropy decrease in isolated systems. They include various self-organizations and self- assembly, some critical phenomena, physical surfaces and films, chemical reactions and catalysts, various biological membranes and enzymes, and new synthetic life, etc. They exist possibly in some microscopic regions, nonlinear phenomena, many evolutional processes and complex systems, etc. As long as we break through the bondage of the second law of thermodynamics, the rich and complex world is full of examples of entropy decrease.

Keywords: entropy decrease, self-assembly, self-organizations, complex system, critical phenomena, nonlinearity, test.

DOI ·10.13140/RG.2.2.36755.53282

1. Introduction

It is well-known that thermodynamics and entropy are origin of investigation on heat engines and their efficiency. From this we cannot obtain the perpetual motion machine. But, now we derived already various chemical energy, nuclear energy, even if the vacuum energy. These energies can be transformed to the macroscopic energy. The second law of thermodynamics is entropy increase in an isolated system. The most particular property is its universality, which may include various systems from microscopic particles, atoms, molecules to macroscopic celestial body, universe, even in philosophy and social sciences. Its infinite generalized conclusion is that all systems in Nature will tend to “heat death” [1]. An important development is that Prigogine proposed the theory of dissipative structure, and discussed time, chaos and the new laws of nature, in which life is associated with entropy production and therefore with irreversible processes [2]. The second law of thermodynamics is based on statistical independence, etc. We proposed that if interactions, fluctuations and its magnified exist among various subsystems of an isolated system, entropy decrease in the isolated system will be possible [3-5], which includes physics [6-8], chemistry [9,10], biology [11], astronomy [12,13] and social sciences [14,15]. For attractive process, internal energy, system entropy, and nonlinear interactions, etc., an isolated system may form a self-organized structure with lower entropy. Some possible entropy decreases are calculated quantitatively [5,8]. Generally, the entropy increase law possesses relativity and approximation, because it must be an isolated system, but which always dependent of some conditions. Complete exact isolated system does not exist in essence, since the gravitational interaction cannot be screened completely.

2. Some Transformations of Internal Energy, and Complex Systems

When internal interaction exists, for example, the kinetic energy is transformed to the potential energy, order of this isolated system may increase, and entropy decrease. Catalyst as substance remained constant in the reaction may regard as an isolated system [10]. So are also the adsorption, fluctuations, and self-assembly, etc. Moreover, enzyme as biological catalyst and membrane, and general entropy decrease in biology are researched [11]. The change of entropy should be a testable science. The first law of thermodynamics points out: the total internal energy U of an isolated system is a constant, and this energy associates with the microscopic components of a system——atoms and molecules. It is usually: U=K+V. (1) Here K is kinetic energy and V is potential energy. For ideal gas V is neglected usually. It agrees completely with entropy increase. It is known that entropy is a measure of the molecular disorder in a

Copyright © 2019 by Modern Scientific Press Company, Florida, USA Int. J. Modern Theo. Physics, 2019, 8(1): 17-32 19 system. For usual cases molecular kinetic energy increases, then disorder and entropy increase. But, when internal interaction in an isolated system exists, for example, the kinetic energy is transformed to the potential energy, then order increases, and the kinetic energy and entropy decrease. This includes the evolution of celestial bodies from nebula to star. It is an assumption that “the entropy of the Universe increases in all natural processes”, then “isolated systems tend toward greater disorder, and entropy is a measure of that disorder” [16]. Entropy increase, i.e., more disorder, always will be unable to derive any complex systems. Complex adaptation system (CAS) is composed of many interacting parts, which are adapted each other in interactions [17,18]. They show nonlinear non-additive effects in many aspects, for example, self-organization, chaos, fractals, etc. Order will obtain entropy decrease. The energy and entropy of a molecule on a surface or interface is different from that inside the body. At least molecules limited by the interface derive entropy decrease [19, 20]. Based on entropy S  (F / T) , the free energy is [20]: 1 F  TV[n(log[nv ]1)  an2 ], (2) 0 2 1 S  V[n(log[nv ]1)  an2 ] . (3) 0 2 If n is invariant, entropy will be 1 1 dS  {[n(log[nv ] 1)  an2 ]}dV   an2dV . (4) 0 2 2 For attractive force, a<0 and dV<0, so dS<0. For repulsive force, a>0 and dV>0, so dS<0.

Let dU/T=dS(U,T), T=f(p,V), then dS is a compound function. dS(t)/dt>0 is a monotone increasing function, dS(t)/dt<0 is a monotone decreasing function. In continuous medium mechanics, the mass force F is divided into internal mass force and external mass force, and both correspond to internal and external works, and further divided into internal and external energies, and internal entropy and external entropy, etc. The internal energy is generally non-additive, for example, the internal energy density of the mixture is [21]:

N 1 2 1 2   [ v   k (vk  v) U]d . (5) 2 k 1 2

When the isolated system tends to equilibrium, the entropy increases. On the contrary, the entropy should decrease due to internal interactions and fluctuations magnified [4, 5]. The appearance of interfaces should be a kind of ordering originated by internal interactions, which are often automatic, so the formations of interface and membrane will be entropy decrease. Both must exist together on internal attraction and repulsion between the two phases in order to form

Copyright © 2019 by Modern Scientific Press Company, Florida, USA Int. J. Modern Theo. Physics, 2019, 8(1): 17-32 20 automatically the separated phase and order. Walls of structures for solute are attraction or repulsion， interactions all are attraction, i.e., the depletion interactions [20]. Grand thermodynamic potential g(n), equation g /n  0 derive double-solution, i.e., the coexistence of two phases may be the  type of soliton [20]. Non-polar Molecules can decrease the entropy of water, and increase the free energy, and the molecules tend to combine to form micelles [20]. Van der Waals (VdW) interactions can be attraction or repulsion [20]. Self-assembly interfaces and memory alloy in applied physics are not entropy increase always. The mixing entropy of vesicles is much larger than that of layered phase, so self-assembly layered entropy decreases [20]. Therefore, conclusion is: the single surfactants layered phase is generally much more stable than spherical vesicle phase [20]. In a word, fluctuations of entropy [20] show entropy can increase or decrease. If the second law of thermodynamics as belief will constrain our ideas and development of science. Generally, the total internal energy is:

U  Ei . (6) i

Here Ei are various internal energies, which include chemical energy, biological energy and nuclear energy, etc. The molecular kinetic energy only is one of Ei , but it determines heat, temperature, and contacts entropy. For the systems with internal interactions, we proposed that the total entropy should be extended to [5] dS  dS a  dS i , (7) where dS a is an additive part of entropy, and dS i is an interacting part of entropy. Eq.(7) is similar to a well known formula:

dS  di S  de S , (8) in the theory of dissipative structure proposed by Prigogine. Non-addible entropy corresponds to the non-extensive statistical mechanics [22-24]. Tsallis proposed the generalized entropy:

W q 1  pi S  i1 , (9) q q 1 It is basis of the generalized Boltzmann-Gibbs (BG) statistics. BG statistics is statistical laws of an idealized thermodynamic system consisting of a large number of particles. It must be assumed that the equal-probability in the isolated system, and the extended quantity neglects the temporal correlation and the spatial correlation, etc.

Eq.(9) becomes BG statistics for q=1, and the parameter q cannot be determined in advance, and q=1 in (9), S=0/0 is not a fix value. We proposed the universal formula on entropy change in any systems for outside and inside:

outside: dS  diS  deS. Systems   a i (10)  inside: dS  dS  dS . From this we derived a total formula of entropy change [15, 8]: a i i   . (11) dS  dS  dS  dS  dSi  dSe  dSe It may be applied to any systems, and obtained a figure on transformation processes between states with higher entropy and lower entropy. The universal law is that nonlinear internal interactions can achieve self-organization, entropy decrease and order. There are different levels: material, chemical, biological, personal (including health), society, religion and so on. If this system is isolated, it will correct and develop the second law of thermodynamics. These examples may include the spontaneous magnetization, and from war to peace, and from chaos to order, etc. In magnetic transformation the action of spin magnetic moment is also an internal interaction. We found that negative temperature, which contradicts usual meaning of temperature and some basic concepts of physics and mathematics, is a fallacy in thermodynamics, and derives necessarily entropy decrease [6]. Gas expands spontaneously, but nebula may aggregate to evolve star. Big Bang and expanding universe are entropy increase, so cosmic microwave background (CMB) is entropy very big. But, attractive force in black hole is also entropy increase, and it will be maximum for black hole. Automatic separation of water and oil is an internal interaction. The oil appears spherical in water should be spontaneous tend to order, entropy tends to minimum. Different liquids may mix and indistinguishable, their entropy increases; but, if those liquids with different specific gravity will be spontaneously separated, so they should be entropy decreases. Typical blackbody radiation should be an isolated system. The simple harmonic oscillator is also an isolated system in which kinetic energy and potential energy are converted each other. Any stable system which deviates and approaches the equilibrium state can be described by harmonic oscillator, so harmonic oscillator is an important fundamental model in classical mechanics, quantum mechanics and statistical physics. Order is contrary to entropy increase, larger entropy is more disorder, which and randomness are consistent. Complexity is proportional to information. Chaos is the unity of order (regularity) and disorder. The relations between these concepts must be determined.

The first and second laws of thermodynamics, i.e., the laws of energy and entropy are the most basic laws of Nature. They control everything that is going on in our universe, including human activities [25]. Various internal energies in isolated systems may be the gravitational interaction, which forms order stars and various celestial bodies from the kinetic energy of nebula motion. The attractive electromagnetic interaction may form some order states. The strong interaction forms various nuclei, and the nuclear energy can transform to macroscopic energy. Various chemical energies may form some order states. Some biological energies may form some order states, for example, molecular motor [11], and information exchange. Molecular aggregation is mainly origin of VdW force. In a word, the transformations of various internal energies may obtain some order states, in which entropy decrease. And these are testable. Inside system the structure decomposed is order decrease and entropy increase, and corresponds to the decomposition force R. But, the structure formed is order increase and entropy decrease, and corresponds to the structure force G. From gravitational force and electromagnetic force to nuclear force they may all form structures, and order increase and entropy decrease. Generally, let the total internal force is:

F  Gi  Rj . (12) i j Here G and R are gravitation and repulsion, respectively. Of course, the weak interaction derives disorder and entropy increase. Therefore, entropy decrease of macroscopic thermodynamics may be obtained in chemistry from the microscopic atomic, molecular and nano-theories. Many fallacies originate from the belief of entropy increases: 1. The negative temperature in which the heat efficiency is even greater than 1 [6]. 2. Entropy of black hole [13]. 3. Superfluid without entropy [26] for jet. 4. Various evolutions always entropy and disorder increase. 5. A pessimistic worldview in the social sciences [1, 4].

3. New System with Lower Entropy

The second law of thermodynamics corresponds completely to the ideal gas. In 2002 Jona- Lasinio, et al., can effectively introduced the entropy in a random system of interacting particles, which is a nonlocal functional. The nonlocal functional corresponds to interaction. The topological thermodynamics should be independent of direction and entropy increase. The exchange theorem is also bidirectional and can be increase or decrease. It can be applied in biology

Copyright © 2019 by Modern Scientific Press Company, Florida, USA Int. J. Modern Theo. Physics, 2019, 8(1): 17-32 23 and various systems. Moreover, there is the holographic entanglement entropy [27-29], which is applied in holographic superconductor [30]. The appearance of macroscopic structure promotes greatly the development of non-equilibrium statistical mechanics. It occurs in fluid convection and sand grain ripples in geological formation, and even the early stages of cosmic expansion. From the early interacting equations between the activator a and the substrate matter s are: a  D a   (a2s  a) , (13) t a a s  D s   (1 a2s) . (14) t s s This may be developed to the nonlinear equation, as the complex Ginzburg-Landau (G-L) equation: A  A  (l  ic )A  (l  ic ) | A |2 A . (15) t 1 3 It is introduced by Newell and Whitehead in 1971. This derives order and structure, for example, the evolutional results of celestial bodies. And the structure determines the nature. First, the total effect of internal interaction is equivalent to an “average field”. Next, the “average field” method is used, this is a power series expanded by the free energy as an order parameter. Then the free energy F is extended S=dF/T, etc., and obtain the relations between S and F. Further, it is developed to the theory of Wilson renormalization group method. In 1993 Wu and Kapral by Willamowski-Rossler model proved that all concentrations are uniform in space under the condition of the limit of the reactants which are well stirred, and their evolution obeys the average field dynamics. In the existence of macroscopic chaos, the thermal fluctuation is amplified, and the inevitable internal noise acts like the external noise, which produces the structure. Politi, et al., suggested that entropy should be developed in the construction of laws that surmounts physics and control organisms [31, 32]. A typical configuration of a system of 40000 particles after about 500 collisions per particle is strongly clustered [33]. This corresponds to the evolution of celestial bodies, which interact and are uneven. Black hole is the simplest system, whose entropy should be minimum. In an isolated system the evolved black hole is an order process of entropy decrease. Generally, final ends of many stars all are the order processes of entropy decrease, no matter what white dwarf, neutron star or black hole, which are only determined by mass of this star. In 1948 Kauzmann discussed the configuration entropy S(T). In 2002 Edwards and Grinev proposed a definition of entropy by temperature X=dV/dS replaced T=dE/dS. It should correspond to new definition of dS=dE/T.

We discussed that since fluctuations can be magnified due to internal interactions under a certain condition, the equal-probability does not hold, and entropy decrease in isolated system is possible [4-15]. Internal interactions bring about inapplicability of the statistical independence, so the statistics and the second law of thermodynamics are possibly different, and a state with smaller entropy will be able to appear. Although in usual statistical physics physicists emphasized that in all closed systems which occur in Nature the entropy never decreases.

4. Entropy Decrease and Nonlinear Interactions

In a well-known computer experiment Fermi, Pasta and Ulam (FPU) in 1950’s studied the vibration of 64 mass particles connected by nonlinear springs arranged as an approximation to a nonlinear vibrating string. The result is not tendency toward thermalization. If the energy was originally put in the lowest frequency mode, it returned almost entirely to that mode after interaction with a few other low-frequency modes. A similar recurrence was observed for the KdV equation with sinusoidal data [34]. This is already a deviation of thermodynamics for the existence of small nonlinearities. It is closely related to solitons. Solitons are stable, localized solitary waves propagated without spreading, which can be qualitatively understood as representing a balance between the effect of nonlinearity and that of dispersion. This nonlinear stability theory with various soliton solutions includes the nonlinear Schrödinger equation, which is related to the Ginzburg-Landau equation of superconductivity, and the self-induced transparency equations [35], etc. Then Friedberg and Lee developed the classical solitons to the non-topological solitons [36], which are the stable bound states in the nonlinear field theory. Solitons were applied to the physical hadrons, and the MIT and SLAC bag models as special limiting cases. For atomic matter waves, bright solitons have been demonstrated for which the effective interaction between atoms in a Bose-Einstein Condensate (BEC) is tuned from repulsive to attractive interaction [37]. A BEC with attraction interactions between the atoms forms stable bright solitons of Li atoms [38]. For repulsive atom-atom interaction, dark solitons have also been observed experimentally [39,40]. A weakly interacting BEC obeys a nonlinear wave equation that supports solitons. At zero temperature, this equation is known as the Gross-Pitaevskii equation: i(/t) [(2 / 2m)2 V  g | |2 ] , (16) where V is the trapping potential, and g describes the strength of the atom-atom interaction. Eiermann, et al., reported on the experimental observation of bright matter wave solitons for Rb atoms with repulsive atom-atom interaction corresponding to self-defocusing medium, which exist only in periodic potentials [41].

The fractal structures with multi-layer self-similarity cannot always entropy increase. Fractional Kramers equation describes diffusion magnified, and satisfies the Einstein relation

K  kBT /(m) , which unites the friction coefficient  and the diffusion coefficient K [42]. The multifractal thermodynamics gives a full and detail description of the scaling behavior and geometrical character of complex fractals. The entropy function (per step) is: 1 S( )  ln ( ) , (17) n where ( ) is the distribution of scaling index lie between  and   d . Further, the generalized entropy function is: 1 G(q,) G(q,) Q(,)  ln (,)  G(q,)  q   , (18) n q  where and  are the two scale indices, and G(q,  )  [ln (q, )]/ n is a generalized free energy. For the invariant set of a dynamical system, a relation [43] G(q  1,   0)  h    , (19) is derived. This connects the measure-theoretic (Kolmogolov-Sinai) entropy, the Lyapunov exponent, the escape rate exponent, and the generalized free energy. When they change, entropy changes also. Chaos must be far-equilibrium states, and relate to the non-equilibrium statistics. In chaos there are the correlation function and super entropy. A periodic vibration is an ordered cycle on time. Further, Prigogine proposed order out of chaos [44]. In experiments, Halperin, et al., found that the solid-He entropy decreases by 80% in an interval at T=1.17mK [45]. Xie, et al., found that the entropy discontinuity decreases ( S =0.13Rln2) as the magnetic field increases, and thermodynamic data not previously available are obtained [46]. In chemical thermodynamics, the entropy of formation is a variant with pressure [47]. In general, any chemical reaction can take place in either direction. In a word, in nonlinear sciences, formations of soliton and fractal should be order. And chaos cannot simply be classified as entropy increase, which includes also rules and Feigenbaum constants. Thermodynamics should be developed combined nonlinearity. Quantum thermodynamics cannot be isolated because of entangled states. And it may be used in biology.

5. Self-Assembly and Self-Organization

Self-Assembly (SA) is a process in which a disordered system of pre-existing components forms an organized structure or pattern as a consequence of specific, local interactions among the components themselves, without external direction. Therefore, it and self-organization must be a

Copyright © 2019 by Modern Scientific Press Company, Florida, USA Int. J. Modern Theo. Physics, 2019, 8(1): 17-32 26 process of entropy decrease [48, 13]. Generally, much structures of Nature all are various self- assembly and self-organizations. A classical example of SA is the artificial self-organization. One of the goals of nanotechnology is to mass-produce micro-building modules that can self-assemble micro machines [49, 50]. When the constitutive components are molecules, the process is molecular self-assembly, which is an autonomous process that forms molecules or polymer under non-external influence. Crane (1950) proposed two basic principles of molecular self-assembly [51]. Self-assembly is defined as the spontaneous and reversible organization of molecular units into ordered structures by non-covalent interactions. The first property of a SA system that this definition suggests is the spontaneity of the SA process: the interactions responsible for the formation of the SA system act on a strictly local level, i.e., nano-structure. The most famous example of SA is the occurrence of the life on Earth. Self- assembled monolayer and molecular self-assembled film are molecules pass through chemical bond, and interact spontaneously to form stable order film with the lowest energy [52]. Other important examples of SA in materials science include the formation of molecular crystals, colloids, lipid bilayers, phase-separated polymers and SA monolayers. The folding of polypeptide chains into proteins and the folding of nucleic acids into their functional forms are examples of SA biological structures. Adleman [53], Winfree, et al. [54] and Ignatova, et al. [55] discussed the SA of DNA structures by the molecular and DNA computation. These self-assembly processes show great progress, in which these must be order and entropy decrease through internal interaction. It is known that near the critical point of continuous phase transition, the intermolecular correlation length can be very large, and any fluctuations can form new phases of any scale in the old phase. This corresponds to the universal scaling law of Wilson critical phenomena. The critical phenomenon can be a kind of crisis described by P. Bak, or it can form a stable self-organizing system.

6. Tests and Predictions of Entropy Decrease in Isolated Systems

We proposed that the applicability of the entropy increase principle should be tested again [4- 15]. If there are interactions among the subsystems in an isolated system, the second law of thermodynamics will be corrected and developed. In this paper we propose systematically some possible tests and predictions on entropy decrease in isolated systems.

They include various self-organizations, self-assembly, and self-reproduction, in which if at a certain time this system is isolated. Entropy decrease is thermodynamic basis of self-organization and ordering process. They include some critical phenomena, for instance, super cold states, “negative temperature”, etc. They include some physical surfaces and films, whose growth process is very complex, but no matter what the layer-by-layer growth (Frank-van der Merwe growth), or island (Volmer-Weber) growth, or reentrant layer-by-layer growth, or mixture (Stranski-Krastanov) growth [56, 57], or self- assembled monolayer growth all relate with interactions. They include some transformations of internal energy [10]. They exist possibly in some microscopic regions. Quantum tunnel effect is namely an internal interaction. Strong interactions and the electromagnetic force of nuclear-electron all are internal interactions, both derive stable nuclei and atoms, etc. They include some chemical reactions and catalysts [9, 10]. They include various biological membranes and enzymes [11], and new synthetic life [58]. They may exist in some nonlinear phenomena and many evolutional processes. They include systems with periodicity, as Lotka-Volterra model, in which entropy oscillates. For these systems with lower entropy the input of negative entropy flow is the external cause, the internal interaction is the essential cause, especially for complexity, self-organizing and critical phenomenon, they originate from fluctuations, mutations and emergence, etc., and connect the conversion of kinetic energy to potential energy. We investigate generally that these systems are isolated under certain conditions, so that tests the second law of thermodynamics. Moreover, they may be as an isolated system for a bigger system. Entropy decrease should exist widely in various complex systems. The main features of complex systems are the whole order or macroscopic order in the global pattern, which generates complexity from simplicity, and the irreducibility between levels [18]. The complex self-adaptive systems and self-organization systems [59-64] are possibly entropy decrease. Constructs and emergences will exist. Entropy decrease should exist in synergetics and hypercycle. Generally, many emergence theories should also be entropy decrease. While hypercycle, etc., may be isolated systems. For the reversible process, dS  (dU  HdJ)/T . (20) If HdJ>dU, there will be dS<0.

For lower temperature T  Tc (here Tc is the Curie temperature), the spontaneous magnetization of ferromagnetics must be order increase in isolated system, and should be entropy decrease. It is origin of the Weiss molecular field theory or the Pauli Exclusion force [65]. Both are all internal interactions.

2 2 Nwg J B Tc  J(J 1) . (21) 30kB J=1/2 for Fe and Ni agrees better with experiments. The initial Universe is origin of quantum fluctuations which do not obey the second law of thermodynamics. Further evolutions of Universe are quantum fluctuations magnified, they should also violate the second law of thermodynamics. But, total direction of evolution is entropy increase. If the primeval matter (universe) was already a complete disorder state of maximum entropy [66], then evolution must be entropy decrease. In general case, entropy decreases dS < 0 for attraction force, and cooperation leads to order. Entropy increases dS > 0 for repulsive force, and struggle leads to disorder. Gravity derives various celestial bodies and structures. Solar luminescence is origin of nuclear fusion and strong interaction. Evolution is phase transformation and symbiosis [67, 68]. This is the development of duality, whose generalization is the balance between gravity and repulsive forces (motion, centrifugal force, etc.), such as nuclear-electron, solar system, positive and negative matter, etc. It can be further developed into multi-duality. Any stable objects and their formations from particles to stars are accompanied with internal interactions inside these objects, which imply a possibility of entropy decrease. Entropy decrease exists more in social sciences and society [14, 15]. Einstein said: “The search and striving for truth and knowledge is one of the highest of man’s virtues.” The pursuit of truth, goodness and beauty as three dimensions of ideal society and life [69] is mainly based on internal interaction, introspection and an order. This is the mathematical and nonlinear whole theory of the emergent theory of complex systems. In fact, as long as we break through the bondage of the second law of thermodynamics, the rich and complex world is full of examples of entropy decrease.

6. Discussions and Conclusions

The preparation of Graphene [70, 71] overturns the Landau-Peierls proof that any two- dimensional crystal is unstable and nonexistent conclusion at finite temperature due to thermodynamic fluctuations.

At present, some physicists already identified with our viewpoint, for example, Tabti, et al., discussed melting of argon cluster [72], and Quarati, et al., researched negentropy in the many-body quantum systems and energy from negentropy of non-Cahotic systems [73,74]. These are surprised: Nuclear fission and nuclear fusion all are entropy increase. In chemistry the exothermic reaction and the endothermic reaction all are entropy increase. Biological creation and biological die all are entropy increase. All change, even these complete opposite change all are entropy increase. According to the uncertainty principle, the smaller scale corresponds to the larger energy fluctuation, so S  E/T  /Tt . Thus, we may discuss the relation between the uncertainty principle and entropy increase. The entropy increase or decrease is not accurate, and it is inversely proportional to time  t. Or we should study entropy and what amount conjugate, both are uncertainty. General relation is one between quantum theory and entropy decrease. Classical mechanics observers and observed objects are independent of each other. The quantum world has developed into a correlation between the two. Similarly, the second law of thermodynamics is developed from the external isolated or open systems to the internal interactions of isolated system. Of course, even the second law of thermodynamics is corrected and developed, astrophysics shows many conclusions, including “heat death” or oscillating universe all is possible. The aim of science is to study the laws of nature: their orderliness, their origin and breakdown. The orderliness is often mathematically reflected in symmetry, periodicity, and so on. It would be too pessimistic if we see disorder alone. New emergences produce new nonlinear relations and new interactions. The network is not a superposition of a single element. Mathematically, it is the principle of nonlinear superposition. The nonlinear terms of different equations have different solutions, and the different coupling of equations have different solutions. Assume that if different levels correspond to different equations, the interactions between different equations correspond to some equations. The nonlinear interaction of a single equation is only a simplified approximation. Neither a one-level epistemology nor a one-level ontology is possible [72]. The basic principles of general evolutionism include principle of blind variation and principle of selection retention [73]. It must have self-organization and adaptability. In a word, according to the misunderstanding second law of thermodynamics, all systems in Nature will tend to “heat death”, any product and structures will be impossible. But, world is not pessimistic always. When internal interactions exist, entropy decrease is possible. So long as different entropy states for any systems exist, entropy should decrease in transition process from a higher

Copyright © 2019 by Modern Scientific Press Company, Florida, USA Int. J. Modern Theo. Physics, 2019, 8(1): 17-32 30 entropy state to a lower entropy state. If this system is isolated, it will correct and develop the second law of thermodynamics. The change of entropy should be a testable science. At least some extensions of the second law of thermodynamics are not universal.

References

[1] J. Rifkin and T. Toward, Entropy——A New World View. New York: Bantam Edition. 1981. [2] I. Prigogine, The End of Certainty: Time, Chaos and the New Laws of Nature. The Free Press. 1997. [3] Yi-Fang Chang, Internal mechanism of isolated systems and new research on limitations of second law of thermodynamics. In: Entropy, Information and Intersecting Science. Yu C.Z. et al., Ed. Yunnan Univ. Press. 1994. p53-60. [4] Yi-Fang Chang, Apeiron. 4(1997):97. [5] Yi-Fang Chang, Entropy. 7(2005):190. [6] Yi-Fang Chang, International Review of Physics. 6(2012):469. [7] Yi-Fang Chang, International Review of Physics. 7(2013):299. [8] Yi-Fang Chang, International Journal of Modern Theoretical Physics. 4(2015):1. [9] Yi-Fang Chang, International Journal of Modern Chemistry. 4(2013):126. [10] Yi-Fang Chang, International Journal of Modern Chemistry. 6(2014):74. [11] Yi-Fang Chang, NeuroQuantology. 11(2013):189. [12] Yi-Fang Chang, International Journal of Modern Applied Physics. 3(2013):8. [13] Yi-Fang Chang, International Journal of Modern Applied Physics. 8(2018):1. [14] Yi-Fang Chang, International Journal of Modern Social Science. 2(2013):94. [15] Yi-Fang Chang, International Journal of Modern Social Science. 4(2015):42. [16] R.A. Serway and J.S. Faughn, College Physics (Sixth Edition). Thomson Learning. 2004. [17] J.H. Holland, Hidden Order: How Adaptation Builds Complexity. Perseus Books. 1996. [18] J.H. Holland, Emergence: From Chaos to Order. Oxford University Press. 1998. [19] J.S. Rowlinson and B. Widom, Molecular Theory of Capillarity. Oxford: Clarendon Press. 1982. [20] S.A. Safran, Statistical Thermodynamics of Surfaces, Interfaces, and Membrane. Westview Press. 2003. [21] L.C. Woods, The Thermodynamics of Fluid Systems. Oxford: Clarendon Press. 1975. [22] C. Tsallis, J.Stat.Phys. 52(1988):479. [23] C. Tsallis, R.S. Mendes and A.R. Plastino, Physica A. 261(1998):534. [24] C. Tsallis, J.Phys: Conf.Ser. 201(2010):012001. [25] J. Hokikian, The Science of Disorder. Los Feliz Publishing. 2006.

[26] L.F. Reichl, A Modern Course in Statistical Physics. Univ. of Texas Press. 1980. [27] S. Ryu and T. Takayanagi, Phys.Rev.Lett. 96(2006):181602. [28] S. Ryu and T. Takayanagi, JHEP. 0608(2006):045. [29] V.E. Hubeny, M. Rangamani and T. Takayanagi, JHEP. 0707(2007):062. [30] T. Albash and C.V. Johnson, JHEP. 1205(2012):079. [31] R. Badii and A. Politi, Complexity: Hierarchical Structures and Scaling Physics. Cambridge University Press. 1997. [32] A. Politi, Complex systems. In: Gordon Fraser ed, The New Physics for the Twenty-First Century. Cambridge University Press. 2006. [33] I. Goldhirsch and G. Zanetti, Phys.Rev.Lett. 70(1993):1611. [34] N.J. Zabusky and M.D. Kruskal, Phys.Rev.Lett. 15(1965):240. [35] A.C. Scott, F.Y.F. Chu and D.W. McLaughlin, Proc.IEEE. 61(1973):1443. [36] R. Friedberg and T.D. Lee, Phys.Rev. D15(1977):1694; D16(1977):1096. [37] L. Khaykovich, F. Schreck, G. Ferrari, et al., Science. 296(2002):1290. [38] K.E. Strecker, G.B. Partridge, A.G. Truscott and R.G. Hulet, Nature. 417(2002): 150. [39] S. Burger, K. Bongs, S. Dettmer, et al., Phys.Rev.Lett. 83(1999):5198. [40] J. Denschlag, J.E. Simsarian, D.L. Ferder, Science. 287(2000):97. [41] B. Eiermann, Ah. Anker, M. Albiez, et al., Phys.Rev.Lett. 92(2004):230401. [42] E. Barkai, R.J. Silbey, J.Phys.Chem. B. 104(2000):3866. [43] M. Kohmoto, Phys.Rev. A37(1988):1345. [44] I. Prigogine and I. Stengers, Order Out of Chaos. New York: Bantam Books Inc. 1984. [45] W.P. Halperin, C.N. Archie, F.B. Rasmussen, et al., Phys.Rev.Lett. 32(1974):927. [46] J.S. Xie, W. Ni, E.D. Adams, et al., Phys.Rev.Lett. 70(1993):1481. [47] J.P. Holman, Thermodynamics(Third Edition). McGraw-Hill. 1980. [48] Yi-Fang Chang, NeuroQuantology. 14(2016):589. [49] W.M. Shih, J.D. Quispe, and G.F. Joyce, Nature. 427(2004):618. [50] F.J. Dyson, A Many-Colored Glass: Reflections on the Place of Life in the Universe. University of Virginia Press. 2007. [51] H.R. Crane, The Scientific Monthly. 70(1950):376. [52] A. Ulman, Thin Films-self-assembled Monolayer of Thiols. San Diego: Academic Press, Inc. 1998. [53] L.M. Adleman, Science. 266(1994):1021. [54] E. Winfree, F. Liu, L.A. Wenzler and N.C. Seeman, Nature. 394 (1998):539. [55] Z. Ignatova, I. Martinez-Perez and K-H. Zimmermann. DNA Computing Model. Springer. 2008.

[56] Z.Y. Zhang and M.G. Lagally, Science. 276(1997):377. [57] J.A. Venables, Physica. 239(1997):35. [58] T.S. Ray, An Approach to the Synthesis of Life. In: C.G. Langton, T. Taylor, J.D. Farmer, S. Rasmussen (eds.), Artificial Life II. Addison-Wesley Publishing Company. 1992. [59] M. Gell-Mann, Complex Adaptive System. In G.A. Cowan, et al. (ed.), Complexity: Metaphors, Models and Reality. David Pines, David Meltzer. 1994. [60] M. Gell-Mann, What is Complexity. John Wiley & Sons. 1995. [61] P. Cilliers, Complexity and Postmodernism: Understanding Complex Systems. London and New York: Routledge. 1998. [62] F. Heylighen, Self-organization, Emergence and the Architecture of Complexity. Transdisciplinary Research Group, Free University of Brussels. 2001. [63] F. Heylighen, The Science of Self-organization and Adaptivity. The Encyclopedia of Life Support Systems. Oxford: EOLSS Publisher. 2002. [64] M. Bunge, Emergence and Convergence: Qualitative Novelty and the Unity of Knowledge. University of Toronto Press. 2003. [65] R.P. Feynman, R.B. Leighton and M. Sands, The Feynman Lectures on Physics. Reading: Addison-Wesley Publishing. 1963. [66] P.C.W. Davies, God and the New Physics. New York: Simon & Schuster. 1983. [67] L. Margulis, Symbiosis in Cell Evolution. San Francisco: Freeman and Co. 1981. [68] J. Silk, A. Szalay and Zeldovich, Scientific American. 249 (1983):72. [69] Yi-Fang Chang, International Journal of Modern Social Science. 7(2018):25. [70] A.K. Geim, K.S. Novoselov, Nature Materials. 6(2007):183. [71] J.C. Meyer, et al., Nature. 446(2007):60. [72] M. Tabti，A. Eddahbi，S. Ouaskit and L. Elarroum, World Journal of Condensed Matter Physics. 2(2012):139. [73] P. Quarati, M. Lissia and A.M. Scarfone, Entropy. 18(2016):63. [74] P. Quarati, A.M. Scarfone and G. Kaniadakis, Entropy. 20(2018):113. [75] P. Checkland, Systems Thinking, Systems Practice. John Wiley & Sons. 1981. [76] D.T. Campbell, Evolutionary Epistemology. In: P.A. Schilpp (ed.), The Philosophy of Karl Popper. The Library of Living Philosophers. 1974.