THE VARIATIONAL PRINCIPLE FOR THE PACKING ENTROPY OF NONAUTONOMOUS DYNAMICAL SYSTEMS

Let(X,φ) be a nonautonomous dynamical system.In this paper,we introduce the notions of packing topological entropy and measure-theoretical upper entropy for nonautonomous dynamical systems.Moreover,we establish the variational principle between the packing topological entropy and the measure-theoretical upper entropy.

Surface Elevation Distribution of Sea Waves Based on the Maximum Entropy Principle

A probability density function of surface elevation is obtained through improvement of the method introduced by Cieslikiewicz who employed the maximum entropy principle to investigate the surface elevation distribution. The density function can be easily extended to higher order according to demand and is non-negative everywhere, satisfying the basic behavior of the probability, Moreover because the distribution is derived without any assumption about sea waves, it is found from comparison with several accepted distributions that the new form of distribution can be applied in a wider range of wave conditions, In addition, the density function can be used to fit some observed distributions of surface vertical acceleration although something remains unsolved.

Analyses of an air conditioning system with entropy generation minimization and entransy theory

In this paper,based on the generalized heat transfer law,an air conditioning system is analyzed with the entropy generation minimization and the entransy theory.Taking the coefficient of performance（denoted as COP） and heat flow rate Qout which is released into the room as the optimization objectives,we discuss the applicabilities of the entropy generation minimization and entransy theory to the optimizations.Five numerical cases are presented.Combining the numerical results and theoretical analyses,we can conclude that the optimization applicabilities of the two theories are conditional.If Qout is the optimization objective,larger entransy increase rate always leads to larger Qout,while smaller entropy generation rate does not.If we take COP as the optimization objective,neither the entropy generation minimization nor the concept of entransy increase is always applicable.Furthermore,we find that the concept of entransy dissipation is not applicable for the discussed cases.

Generalized uncertainty principle and tunneling radiation of the SAdS_5 black hole

After considering the generalized uncertainty principle, we discuss the quantum tunneling radiation of a fivedimensional Sehwarzschild anti de Sitter black hole. The radiation spectrum and the correction value of the Bekenstein-- Hawking entropy are derived. In a five-dimensional black hole the one order correction term in the Bekenstein-Hawking entropy correction term is proportional to the third power of the area, and the logarithmic correction term is a twoorder small quantity. The correction term is related to the dimension constant introduced in the generalized uncertainty principle. Because the black hole entropy is not divergent, the lowest value of the five-dimensional Schwarzschild anti de Sitter black hole horizon radius is obtained. After considering the generalized uncertainty principle, the radiation spectrum is still consistent with normalization theory.

Band structure,Fermi surface,elastic,thermodynamic,and optical properties of AlZr3,AlCu3,and AlCu2Zr:First-principles study

The electronic properties（Fermi surface,band structure,and density of states（DOS）） of Al-based alloys AlM3（M=Zr and Cu） and AlCu2Zr are investigated using the first-principles pseudopotential plane wave method within the generalized gradient approximation（GGA）.The structural parameters and elastic constants are evaluated and compared with other available data.Also,the pressure dependences of mechanical properties of the compounds are studied.The temperature dependence of adiabatic bulk modulus,Debye temperature,specific heat,thermal expansion coefficient,entropy,and internal energy are all obtained for the first time through quasi-harmonic Debye model with phononic effects for T = 0 K-100 K.The parameters of optical properties（dielectric functions,refractive index,extinction coefficient,absorption spectrum,conductivity,energy-loss spectrum,and reflectivity） of the compounds are calculated and discussed for the first time.The reflectivities of the materials are quite high in the IR-visible-UV region up to ~ 15 eV,showing that they promise to be good coating materials to avoid solar heating.Some of the properties are also compared with those of the Al-based Ni3 Al compound.

Entropy of a rotating and charged black string to all orders in the Planck length

By using the entanglement entropy method, this paper calculates the statistical entropy of the Bose and Fermi fields in thin films, and derives the Bekenstein-Hawking entropy and its correction term on the background of a rotating and charged black string. Here, the quantum field is entangled with quantum states in the black string and thin film to the event horizon from outside the rotating and charged black string. Taking into account the effect of the generalized uncertainty principle on quantum state density, it removes the difficulty of the divergence of state density near the event horizon in the brick-wall model. These calculations and discussions imply that high density quantum states near the event horizon of a black string are strongly correlated with the quantum states in a black string and that black string entropy is a quantum effect. The ultraviolet cut-off in the brick-wall model is not reasonable. The generalized uncertainty principle should be considered in the high energy quantum field near the event horizon. From the viewpoint of quantum statistical mechanics, the correction value of Bekenstein-Hawking entropy is obtained. This allows the fundamental recognition of the correction value of black string entropy at nonspherical coordinates.

Generalized Uncertainty Principle and Thermodynamic Quantities of SAdS_5 Black Hole

Recently,there has been much attention devoted to resolving the quantum corrections to the Bekenstein-Hawking black hole entropy.The different correction leading terms are obtained by the different methods.In this paper,we calculate the correction to SAdS_5 black hole thermodynamic quantity due to the generalized uncertainty principle.Furthermore we derive that the black hole entropy obeys Bekenstein-Hawking area theorem.The entropy has infinitecorrection terms.And every term is finite and calculable.The corrected Cardy-Verlinde formula is derived.In ourcalculation,Bekenstein-Hawking area theorem still holds after considering the generalized uncertainty principle.Wehave not introduced any hypothesis.The calculation is simple.Physics meaning is clear.We note that our results arequite general.It is not only valid for four-dimensional spacetime but also for higher-dimensional SAdS spacetime.

Connection between the Principles of Thermodynamics and the Conservation Laws: Physical Meaning of the Principles of Thermodynamics

It has been shown that the first principle of thermodynamics follows from the conservation laws for energy and linear momentum. And the second principle of thermodynamics follows from the first principle of thermodynamics under realization of the integrating factor (namely, temperature) and is a conservation law. The significance of the first principle of thermodynamics consists in the fact that it specifies the thermodynamic system state, which depends on interaction between conservation laws and is non-equilibrium due to a non-commutativity of conservation laws. The realization of the second principle of thermodynamics points to a transition of the thermodynamic system state into a locally-equilibrium state. Phase transitions are examples of such transitions.

Thermodynamic effects of Bardeen black hole surrounded by perfect fluid dark matter under general uncertainty principle

The thermodynamics of Bardeen black hole surrounded by perfect fluid dark matter is investigated.We calculate the analytical expresses of corresponding thermodynamic variables,e.g.,the Hawking temperature,entropy of the black hole.In addition,we derive the heat capacity to analyze the thermal stability of the black hole.We also compute the rate of emission in terms of photons through tunneling.By numerical method,an obvious phase transition behavior is found.Furthermore,according to the general uncertainty principle,we study the quantum corrections to these thermodynamic quantities and obtain the quantum-corrected entropy containing the logarithmic term.Lastly,we investigate the effects of the magnetic charge g,the dark matter parameter k and the generalized uncertainty principle parameterαon the thermodynamics of Bardeen black hole surrounded by perfect fluid dark matter under general uncertainty principle.

Application of MEP Method to the Study of statistical Properties of Random Waves

The maximum entropy principle (MEP) method and the corresponding probability evaluation method are introduced, and the maximum entropy probability distribution expression is deduced in moment of the second order. Fully developed wave height distribution in deep water and wave height and period distribution for different depths in wind wave channel experiment are obtained from the MEP method, and the results are compared with the distribution and the experimental histogram. The wave height and period distribution for the Lianyungang port is also obtained by the MEP method, and the results are compared with the Weibull distribution and the field histogram.

Thermodynamic Formulation of Living Systems and Their Evolution

The purpose of this review article is to present some of the recent contributions that show the use of thermo-dynamics to describe biological systems and their evolution, illustrating the agreement that this theory pre-sents with the field of evolution. Organic systems are described as thermodynamic systems where entropy is produced by the irreversible processes, considering as an established fact that this entropy is eliminated through their frontiers to preserve life. The necessary and sufficient conditions to describe the evolution of life in the negentropy principle are established. Underlining the fact that the necessary condition requires formulation, which is founded on the principle of minimum entropy production for open systems operating near equilibrium. Other formulations are mentioned, particularly the information theory, the energy inten-siveness hypothesis and the theory of open systems far from equilibrium. Finally suggesting the possibility of considering the lineal formulation as a viable alternative;that is, given the internal constrictions under which a biological system operates, it is possible that the validity of its application is broader than it has been suggested.

Tree Network Formation in Poisson Equation Models and the Implications for the Maximum Entropy Production Principle

This paper presents not only practical but also instructive mathematical models to simulate tree network formation using the Poisson equation and the Finite Difference Method (FDM). Then, the implications for entropic theories are discussed from the viewpoint of Maximum Entropy Production (MEP). According to the MEP principle, open systems existing in the state far from equilibrium are stabilized when entropy production is maximized, creating dissipative structures with low entropy such as the tree-shaped network. We prepare two simulation models: one is the Poisson equation model that simulates the state far from equilibrium, and the other is the Laplace equation model that simulates the isolated state or the state near thermodynamic equilibrium. The output of these equations is considered to be positively correlated to entropy production of the system. Setting the Poisson equation model so that entropy production is maximized, tree network formation is advanced. We suppose that this is due to the invocation of the MEP principle, that is, entropy of the system is lowered by emitting maximal entropy out of the system. On the other hand, tree network formation is not observed in the Laplace equation model. Our simulation results will offer the persuasive evidence that certifies the effect of the MEP principle.

Representation of the Basic Laws of Thermodynamics in Quantum Mechanics

We propose a representation of the basic laws, namely the zeroth, first, second and third law, in quantum thermodynamics. The zeroth law is represented by some parameters () that specify respective quantum states. The parameters are the elements of thermodynamic state space. The introduction of such parameters is based on a probabilistic nature of quantum theory. A quantum analog of the first law can be established by utilizing these parameters. The notion of heat in quantum systems is clarified from the probabilistic point of view in quantum theory. The representation of the second law can be naturally described in terms of these parameters introduced for the respective quantum systems. In obtaining the representation of quantum thermodynamics, consistency between quantum theory and classical thermodynamics should have been preserved throughout our formulation of quantum thermodynamics. After establishing the representation of the second law, the third law is discussed briefly. The relationship between thermodynamic temperatures and the parameters in is also discussed.

Collapse of Entangled State and Entropy Increase in an Isolated System

我们证明纠缠的量状态的倒塌让熵在一个孤立的系统增加。热力学的第二条法律因此在它的很一般的形式被证明。

Motoyosi Sugita—A “Widely Unknown” Japanese Thermodynamicist Who Explored the 4th Law of Thermodynamics for Creation of the Theory of Life

The purpose of this paper is to introduce to you, the Western people, nowadays a “widely unknown” Japanese thermodynamicist by the name of Motoyosi Sugita and his study on the thermodynamics of transient phenomena and his theory of life. This is because although he was one of the top theoretical physicists in Japan before, during and after WWII and after WWII he promoted the establishment of the biophysical society of Japan as one of the founding members, he himself and his studies themselves have seemed to be totally forgotten nowadays in spite that his study was absolutely important for the study of life. Therefore, in this paper I would like to present what kind of person he was and what he studied in physics as a review on the physics work of Motoyosi Sugita for the first time. I will follow his past studies to introduce his ideas in theoretical physics as well as in biophysics as follows: He proposed the bright ideas such as the quasi-static change in the broad sense, the virtual heat, and the field of chemical potential etc. in order to establish his own theory of thermodynamics of transient phenomena, as the generalization of the Onsager-Prigogine’s theory of the irreversible processes. By the concept of the field of chemical potential that acquired the nonlinear transport, he was seemingly successful to exceed and go beyond the scope of Onsager and Prigogine. Once he established his thermodynamics, he explored the existence of the 4th law of thermodynamics for the foundation of theory of life. He applied it to broad categories of transient phenomena including life and life being such as the theory of metabolism. He regarded the 4th law of thermodynamics as the maximum principle in transient phenomena. He tried to prove it all life long. Since I have recently found that his maximum principle can be included in more general maximum principle, which was known as the Pontryagin’s maximum principle in the theory of optimal control, I would like to explain such theories produced by Motoyosi Sugita as detailed as possible. And also I have put short history of Motoyosi Sugita’s personal life in order for you to know him well. I hope that this article helps you to know this wonderful man and understand what he did in the past, which was totally forgotten in the world and even in Japan.

A Generalized Statement of Highest-Entropy Principle for Stable Equilibrium and Non-Equilibrium in Many-Particle Systems

Among all statements of Second Law, the existence and uniqueness of stable equilibrium, for each given value of energy content and composition of constituents of any system, have been adopted to define thermodynamic entropy by means of the impossibility of Perpetual Motion Machine of the Second Kind (PMM2) which is a consequence of the Second Law. Equality of temperature, chemical potential and pressure in many-particle systems are proved to be necessary conditions for the stable equilibrium. The proofs assume the stable equilibrium and derive, by means of the Highest-Entropy Principle, equality of temperature, chemical potential and pressure as a consequence. A first novelty of the present research is to demonstrate that equality is also a sufficient condition, in addition to necessity, for stable equilibrium implying that stable equilibrium is a condition also necessary, in addition to sufficiency, for equality of temperature potential and pressure addressed to as generalized potential. The second novelty is that the proof of sufficiency of equality, or necessity of stable equilibrium, is achieved by means of a generalization of entropy property, derived from a generalized definition of exergy, both being state and additive properties accounting for heat, mass and work interactions of the system underpinning the definition of Highest-Generalized-Entropy Principle adopted in the proof.

A Maximum-Entropy Compound Distribution Model for Extreme Wave Heights of Typhoon-Affected Sea Areas

A new compound distribution model for extreme wave heights of typhoon-affected sea areas is proposed on the basis of the maximum-entropy principle. The new model is formed by nesting a discrete distribution in a continuous one, having eight parameters which can be determined in terms of observed data of typhoon occurrence-frequency and extreme wave heights by numerically solving two sets of equations derived in this paper. The model is examined by using it to predict the N-year return-period wave height at two hydrology stations in the Yellow Sea, and the predicted results are compared with those predicted by use of some other compound distribution models. Examinations and comparisons show that the model has some advantages for predicting the N-year return-period wave height in typhoon-affected sea areas.

Extraction of Information from Crowdsourcing: Experimental Test Employing Bayesian, Maximum Likelihood, and Maximum Entropy Methods

A crowdsourcing experiment in which viewers (the “crowd”) of a British Broadcasting Corporation (BBC) television show submitted estimates of the number of coins in a tumbler was shown in an antecedent paper (Part 1) to follow a log-normal distribution ∧(m,s2). The coin-estimation experiment is an archetype of a broad class of image analysis and object counting problems suitable for solution by crowdsourcing. The objective of the current paper (Part 2) is to determine the location and scale parameters (m,s) of ∧(m,s2) by both Bayesian and maximum likelihood (ML) methods and to compare the results. One outcome of the analysis is the resolution, by means of Jeffreys’ rule, of questions regarding the appropriate Bayesian prior. It is shown that Bayesian and ML analyses lead to the same expression for the location parameter, but different expressions for the scale parameter, which become identical in the limit of an infinite sample size. A second outcome of the analysis concerns use of the sample mean as the measure of information of the crowd in applications where the distribution of responses is not sought or known. In the coin-estimation experiment, the sample mean was found to differ widely from the mean number of coins calculated from ∧(m,s2). This discordance raises critical questions concerning whether, and under what conditions, the sample mean provides a reliable measure of the information of the crowd. This paper resolves that problem by use of the principle of maximum entropy (PME). The PME yields a set of equations for finding the most probable distribution consistent with given prior information and only that information. If there is no solution to the PME equations for a specified sample mean and sample variance, then the sample mean is an unreliable statistic, since no measure can be assigned to its uncertainty. Parts 1 and 2 together demonstrate that the information content of crowdsourcing resides in the distribution of responses (very often log-normal in form), which can be obtained empirically or by appropriate modeling.

On Chien's question to the Hu-Washizu three-field functional and variational principle

There is an open question,namely Chien’s question,in construction of a generalized functional in elasticity,i.e.,why the stress-strain relation can still be derived from the Hu-Washizu generalized variational principle while the Lagrangian multiplier method is applied in vain?This study shows that the generalized variational principle can only be understood and implemented correctly within the framework of thermodynamics.This investigation finds that as long as the functional has one of the combinations(A(ε_(ij))-σ_(ij)ε_(ij))or(B(σ_(ij))-σ_(ij)ε_(ij)),its corresponding variational principle will produce the stress-strain relation without the need to introduce extra constraints by the Lagrangian multiplier method.This research proves that the Hu-Washizu functionalΠ(u_(ij),ε_(ij),σ_(ij))is real three-field functional,and resolves the historic academic controversy on the issue of constructing a three-field functional.