Abstract:
We discuss the condition for the validity of equilibrium quantum statistical mechanics in the light of recent developments in the understanding of classical and quantum chaotic motion. In particular, the ergodicity parameter is shown to provide the conditions under which quantum statistical distributions can be derived from the quantum dynamics of a classical ergodic Hamiltonian system.

Abstract:
We demonstrate the equilibration of isolated macroscopic quantum systems, prepared in non-equilibrium mixed states with significant population of many energy levels, and observed by instruments with a reasonably bound working range compared to the resolution limit. Both properties are fulfilled under many, if not all, experimentally realistic conditions. At equilibrium, the predictions and limitations of Statistical Mechanics are recovered.

Abstract:
We propose a new approach concerning the introduction of time-irreversibility in statistical mechanics. It is based on a transition function defined in terms of path integral and verifying a time-irreversible equation. We show first how dynamic processes may enter in the description of equilibrium states. In order to do that a characteristic time is associated with closed paths. For large isolated systems at equilibrium or for systems in contact with a thermostat our results are identical with those obtained with the Gibbs ensemble methods. For a model used in the microscopic approaches of the brownian motion no new basic assumption is required to predict a transition from a quantum state to a classical one exhibiting a time-irreversible behavior. This demonstration is sufficient to show that very well accepted approximations can lead to time-irreversible behaviors for a large class of systems. The difference between our work and the system+reservoir approaches is underlined. Here equilibrium states and irreversible processes are described on the same footing representing a progress in the question of time-irreversibility in statistical physics. The transition function is also used for describing a small system for which there is no thermodynamics. By adding to the transition function a second one characterizing the reverse motion we may describe time-reversible systems. In a simple case we replace two real valued transition functions by a complex function verifying a Schrodinger like equation. From this we see how to break the time-reversibility of this equation and how to investigate the connection quantum mechanics-thermodynamics from a very fundamental point of view.

Abstract:
In this article, we work out the microscopic statistical foundation of the supergravity description of the simplest 1/2 BPS sector in the AdS(5)/CFT(4). Then, all the corresponding supergravity observables are related to thermodynamical observables, and General Relativity is understood as a mean-field theory. In particular, and as an example, the Superstar is studied and its thermodynamical properties clarified.

Abstract:
We show that most of the empirical or semi-empirical isotherms proposed to extend the Langmuir formula to sorption (adsorption, chimisorption and biosorption) on heterogeneous surfaces in the gaseous and liquid phase belong to the family and subfamily of the Burr_{XII} cumulative distribution functions. As a consequence they obey relatively simple differential equations which describe birth and death phenomena resulting from mesoscopic and microscopic physicochemical processes. Using the probability theory, it is thus possible to give a physical meaning to their empirical coefficients, to calculate well defined quantities and to compare the results obtained from different isotherms. Another interesting consequence of this finding is that it is possible to relate the shape of the isotherm to the distribution of sorption energies which we have calculated for each isotherm. In particular, we show that the energy distribution corresponding to the Brouers-Sotolongo (BS) isotherm [1] is the Gumbel extreme value distribution Finally we propose a generalized GBS isotherm, calculate its relevant statistical properties and recover all the previous results by giving well defined values to its coefficients. In the course of the discussion we make contact with the Tsallis nonextensive theory [2] and the noninteger order reaction and fractal kinetics theory [3]. In the spirits of the present and previous publications, we propose an alternative formula to include fractality in the Michealis-Menten enzyme catalysis theory. Finally we suggest that the stochastic cluster model introduced by K.Weron [4] to account for the universal character of relaxation in disordered systems should be relevant for other phenomena in particular for heterogeneous sorption

Abstract:
An optimization methodology of empirical electronic theory (EET) for solids and molecules has been developed by employing a statistical model in this study. The current paper calculates the hybridization states of different atoms in some crystal structures and succeeds in predicting valence states of atoms. The prediction of γ -Fe hybridization states based on statistics is found to be in reasonable agreement with early measurements. Through calculating Cr alloy austenite and Cr alloy martensite, the statistical results proved stable for each atom, and it is found that the valence electron structure of an atom depends on its element type and location in the crystal cell; finally, wear resistant steel with 1 wt% C is designed by using a statistical model which is consistent with traditional empirical design. An optimization methodology of empirical electronic theory (EET) for solids and molecules has been developed by employing a statistical model in this study. The current paper calculates the hybridization states of different atoms in some crystal structures and succeeds in predicting valence states of atoms. The prediction of γ -Fe hybridization states based on statistics is found to be in reasonable agreement with early measurements. Through calculating Cr alloy austenite and Cr alloy martensite, the statistical results proved stable for each atom, and it is found that the valence electron structure of an atom depends on its element type and location in the crystal cell; finally, wear resistant steel with 1 wt% C is designed by using a statistical model which is consistent with traditional empirical design.

Abstract:
It is proved in the paper that the non-conservative dissipative force and asymmetry of time reversal can be naturally introduced into classical statistical mechanics after retarded electromagnetic interaction between charged microparticles is considered. In this way, the rational dynamic foundation for classical statistical physics can established and the revised Liouville equation is obtained. The micro-canonical ensemble, the canonical ensemble, the distribution of near-independent subsystem, the distribution law of the Maxwell- Boltzmann and the Maxwell distribution of velocities are achieved directly from the Liouville equation without using the hypothesis of equal probability. The micro-canonical ensemble is considered unsuitable as the foundation of equivalent state theory again, for most of equivalent states of isolated systems are not the states with equal probabilities actually. The reversibility paradoxes in the processes of non-equivalent evolutions of macro-systems can be eliminated completely, and the united description of statistical mechanics of equivalent and nonequivalent states is reached. The revised BBKGY series equations and hydromechanics equations are reduced, the non-equivalent entropy of general systems is defined and the principle of entropy increment of the non-equivalent entropy is proved at last.

Abstract:
Based on the concept of ensemble, it is proved in the manuscript that the probability amplitude function can also been used to describe the classical statistical system. The motion equations of probability amplitude functions of classical statistical system are obtained, which are similar to that in quantum mechanics. It is also proved in the meantime that microsystems that obey quantum mechanics can also be described in the forms of classical statistical mechanics and deterministic classical mechanics. The quantum revised formula of classical interaction force and the revised Liouville's equations are also obtained. In this way, the transformation of two descriptive forms between classical mechanics and quantum mechanics is achieved. A new and rational interpretation about quantum mechanics, including the meaning of wave function, the potential barrier penetration of microparticles, the Uncertainty relation, the wave-particle duality, the essence of spin and the Bell's inequality and so on, is provided in the paper. Based on the transformation, two fundamental hypotheses are put forward as the basic postulates of classical statistical physics. The equal probability hypothesis in the equilibrium states is given up. The united description of nonequilibrium state mechanics and equilibrium state statistical mechanics is reached, and the so-called reversibility paradox can also be eliminated.

Abstract:
Recently, ontological study has been one of the key concerns of geographic information science, a number of studies have been conducted in both of philosophical and knowledge engineering approach. Some studies pointed out the importance of human cognition and social context for development of ontologies. This paper presents empirical investigation of common sense of land use categories for development of suitable ontologies for each cultural or speech communities. Distinctions and characteristics in perceiving land use categories were described by a psychological method that was submitted to Japanese graduate and undergraduate students. In addition the results were analyzed using corresponddence analysis, a statistical technique for categorical data. This analysis serves to clarify the dominant determining factors for land use categories.

Abstract:
This introductory article presents the special Discussion and Debate volume "From black swans to dragon-kings, is there life beyond power laws?" published in Eur. Phys. J. Special Topics in May 2012. We summarize and put in perspective the contributions into three main themes: (i) mechanisms for dragon-kings, (ii) detection of dragon-kings and statistical tests and (iii) empirical evidence in a large variety of natural and social systems. Overall, we are pleased to witness significant advances both in the introduction and clarification of underlying mechanisms and in the development of novel efficient tests that demonstrate clear evidence for the presence of dragon-kings in many systems. However, this positive view should be balanced by the fact that this remains a very delicate and difficult field, if only due to the scarcity of data as well as the extraordinary important implications with respect to hazard assessment, risk control and predictability.