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 Copyright © 2019 by Modern Scientific Press Company, Florida, USA Int. J. Modern Theo. Physics, 2019, 8(1): 17-32 18 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 i1 , (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. Copyright © 2019 by Modern Scientific Press Company, Florida, USA Int. J. Modern Theo. Physics, 2019, 8(1): 17-32 21 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 .