Article

# Spontaneous entropy decrease and its statistical formula

11/2007;
Source: arXiv

ABSTRACT

Why can the world resist the law of entropy increase and produce self-organizing structure? Does the entropy of an isolated system always only increase and never decrease? Can be thermodymamic degradation and self-organizing evolution united? How to unite? In this paper starting out from nonequilibrium entropy evolution equation we proved that a new entropy decrease could spontaneously emerge in nonequilibrium system with internal attractive interaction. This new entropy decrease coexists with the traditional law of entropy increase, both of them countervail each other, so that the total entropy of isolated system can be able to decrease. It not only makes isolated system but also helps open system to produce self-organizing structure. We first derived a statistical formula for this new entropy decrease rate, and compared it both in mathematical form and in microscopic physical foundation with the statistical formula for the law of entropy increase which was derived by us some years ago. Furthermore, we gave the formulas for the time rate of change of total entropy in isolated system and open system. The former is equal to the sum of the formula for the law of entropy increase and the formula for the new entropy decrease rate, the latter is the algebraic sum of the formulas for entropy increase, entropy decrease and entropy flow. All of them manifest the unity of thermodynamic degradation and self-organizing evolution. As the application of the new theoretical formulas, we discussed qualitatively the emergency of inhomogeneous structure in two real isolated systems including clarifying the inference about the heat death of the universe.

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##### Article: On the fundamental equation of nonequilibrium statistical physics—Nonequilibrium entropy evolution equation and the formula for entropy production rate
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ABSTRACT: In this paper the author presents an overview on his own research works. More than ten years ago, we proposed a new fundamental In this paper the author presents an overview on his own research works. More than ten years ago, we proposed a new fundamental equation of nonequilibrium statistical physics in place of the present Liouville equation. That is the stochastic velocity equation of nonequilibrium statistical physics in place of the present Liouville equation. That is the stochastic velocity type’s Langevin equation in 6N dimensional phase space or its equivalent Liouville diffusion equation. This equation is time-reversed asymmetrical. It shows type’s Langevin equation in 6N dimensional phase space or its equivalent Liouville diffusion equation. This equation is time-reversed asymmetrical. It shows that the form of motion of particles in statistical thermodynamic systems has the drift-diffusion duality, and the law of that the form of motion of particles in statistical thermodynamic systems has the drift-diffusion duality, and the law of motion of statistical thermodynamics is expressed by a superposition of both the law of dynamics and the stochastic velocity motion of statistical thermodynamics is expressed by a superposition of both the law of dynamics and the stochastic velocity and possesses both determinism and probability. Hence it is different from the law of motion of particles in dynamical systems. and possesses both determinism and probability. Hence it is different from the law of motion of particles in dynamical systems. The stochastic diffusion motion of the particles is the microscopic origin of macroscopic irreversibility. Starting from this The stochastic diffusion motion of the particles is the microscopic origin of macroscopic irreversibility. Starting from this fundamental equation the BBGKY diffusion equation hierarchy, the Boltzmann collision diffusion equation, the hydrodynamic fundamental equation the BBGKY diffusion equation hierarchy, the Boltzmann collision diffusion equation, the hydrodynamic equations such as the mass drift-diffusion equation, the Navier-Stokes equation and the thermal conductivity equation have equations such as the mass drift-diffusion equation, the Navier-Stokes equation and the thermal conductivity equation have been derived and presented here. What is more important, we first constructed a nonlinear evolution equation of nonequilibrium been derived and presented here. What is more important, we first constructed a nonlinear evolution equation of nonequilibrium entropy density in 6N, 6 and 3 dimensional phase space, predicted the existence of entropy diffusion. This entropy evolution equation plays a leading entropy density in 6N, 6 and 3 dimensional phase space, predicted the existence of entropy diffusion. This entropy evolution equation plays a leading role in nonequilibrium entropy theory, it reveals that the time rate of change of nonequilibrium entropy density originates role in nonequilibrium entropy theory, it reveals that the time rate of change of nonequilibrium entropy density originates together from its drift, diffusion and production in space. From this evolution equation, we presented a formula for entropy together from its drift, diffusion and production in space. From this evolution equation, we presented a formula for entropy production rate (i.e. the law of entropy increase) in 6N and 6 dimensional phase space, proved that internal attractive force in nonequilibrium system can result in entropy decrease production rate (i.e. the law of entropy increase) in 6N and 6 dimensional phase space, proved that internal attractive force in nonequilibrium system can result in entropy decrease while internal repulsive force leads to another entropy increase, and derived a common expression for this entropy decrease while internal repulsive force leads to another entropy increase, and derived a common expression for this entropy decrease rate or another entropy increase rate, obtained a theoretical expression for unifying thermodynamic degradation and self-organizing rate or another entropy increase rate, obtained a theoretical expression for unifying thermodynamic degradation and self-organizing evolution, and revealed that the entropy diffusion mechanism caused the system to approach to equilibrium. As application, evolution, and revealed that the entropy diffusion mechanism caused the system to approach to equilibrium. As application, we used these entropy formulas in calculating and discussing some actual physical topics in the nonequilibrium and stationary we used these entropy formulas in calculating and discussing some actual physical topics in the nonequilibrium and stationary states. All these derivations and results are unified and rigorous from the new fundamental equation without adding any extra states. All these derivations and results are unified and rigorous from the new fundamental equation without adding any extra new assumption. new assumption. Keywordsstochastic velocity type’s Langevin equation in 6N dimensional phase space-drift-diffusion duality-nonequilibrium entropy evolution equation-entropy diffusion-formula for entropy production rate-entropy change from internal interaction-approach to equilibrium-hydrodynamic equation Keywordsstochastic velocity type’s Langevin equation in 6N dimensional phase space-drift-diffusion duality-nonequilibrium entropy evolution equation-entropy diffusion-formula for entropy production rate-entropy change from internal interaction-approach to equilibrium-hydrodynamic equation
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