Quantum macrostatistical picture of nonequilibrium steady states

We employ a quantum macrostatistical treatment of irreversible processes to prove that, in nonequilibrium steady states, (a) the hydrodynamical observables execute a generalised Onsager-Machlup process and (b) the spatial correlations of these observables are generically of long range. The key assumptions behind these results are a nonequilibrium version of Onsager's regression hypothesis, together with certain hypotheses of chaoticity and local equilibrium for hydrodynamical fluctuations.Comment: TeX, 13 page

Simulational Study on Dimensionality-Dependence of Heat Conduction

Heat conduction phenomena are studied theoretically using computer simulation. The systems are crystal with nonlinear interaction, and fluid of hard-core particles. Quasi-one-dimensional system of the size of $L_x\times L_y\times L_z(L_z\gg L_x,L_y)$ is simulated. Heat baths are put in both end: one has higher temperature than the other. In the crystal case, the interaction potential $V$ has fourth-order non-linear term in addition to the harmonic term, and Nose-Hoover method is used for the heat baths. In the fluid case, stochastic boundary condition is charged, which works as the heat baths. Fourier-type heat conduction is reproduced both in crystal and fluid models in three-dimensional system, but it is not observed in lower dimensional system. Autocorrelation function of heat flux is also observed and long-time tails of the form of $\sim t^{-d/2}$, where $d$ denotes the dimensionality of the system, are confirmed.Comment: 4 pages including 3 figure

Irreversibility in a simple reversible model

This paper studies a parametrized family of familiar generalized baker maps, viewed as simple models of time-reversible evolution. Mapping the unit square onto itself, the maps are partly contracting and partly expanding, but they preserve the global measure of the definition domain. They possess periodic orbits of any period, and all maps of the set have attractors with well defined structure. The explicit construction of the attractors is described and their structure is studied in detail. There is a precise sense in which one can speak about absolute age of a state, regardless of whether the latter is applied to a single point, a set of points, or a distribution function. One can then view the whole trajectory as a set of past, present and future states. This viewpoint is then applied to show that it is impossible to define a priori states with very large "negative age". Such states can be defined only a posteriori. This gives precise sense to irreversibility -- or the "arrow of time" -- in these time-reversible maps, and is suggested as an explanation of the second law of thermodynamics also for some realistic physical systems.Comment: 15 pages, 12 Postscript figure

INTEGRATIVE MUSICAL PSYCHOLOGY

Introduction. In recent decades, diverse scientific directions have been actively developed at the interface between various fields of knowledge, including social sciences and humanities. Interdisciplinary research provides a high-quality “unification” of achievements of different sciences and gains fundamental value, since they allow full information on this or that studied subject or phenomenon to be received and options of optimum solutions for difficult research tasks to be obtained. However, there are two problem zones in an integrative trend of knowledge – ontological and epistemological origin.The aim of the research was to reveal the potential of interdisciplinary research and integration of diverse directions from several disciplines by the example of musical psychology. Methodology and research methods. The provisions of the system-integrative approach and the concept of “meta-individual world” (MIW) were employed. The MIW theory justifies the heterogeneous, multi-qualitative, multi-determined nature of poly-systems. Results and scientific novelty. The subject field of musical psychology is outlined and characterised. It is shown that now it is shattered into multi-directional components from the field of psychology and musicology, which links are poorly articulated. The reason is not only in heterogeneity of basic psychological and musicological concepts, but also in the discrepancy of ontological status of objects and objects of two key structural components of the sphere under discussion. Nevertheless, there is urgent necessity for their cross-disciplinary integration and elimination of epistemological dualism in the development of scientific industry. The theoretical and logical grounds for the introduction of the concepts of  “musicological” and “psychological” musical psychology are obviously provided. Differences between them are shown: if the first is turned to a piece of music, then the second – to mentality of a composer and a musician. However, they generate unequal phenomenology and lie outside to each other, although they move in the opposite direction. Therefore, the need for creation of integrative musical psychology (IMP) as psychogenetics, psychophysiology, ethnopsychology or behavioural geography is recognised. As the integrative prototype, it is proposed to use the concept of MIW, which supports the pluralistic view on IMP, i.e. IMP considers individuality (personality, mentality, consciousness) and world (external realities, social groups, culture, art) in a coherent manner. The authors proposed the idea of musical psychology transcendence – bidirectional transitions from one its subject field to another. The main point of existence of such transitions consists in the emergence of the phenomena of otherness as the form (way) of overcoming gaps between subject areas of “psychological” and “musicological” musical psychology. The present research concretises and justifies the ways of formation and development of IMP and contributes to the methodology of social sciences and humanities.Practical significance. The research materials are of practical importance for education of graduates of musical and art specialties. In the teaching and educational process, it is necessary to use the potential of two aspects of musical psychology, but not separately, in order to form and develop in students the skills of transcendental perception and analysis of pieces of music. Введение. В последние десятилетия в науке, в том числе в ее общественно-гуманитарной области, активно развиваются направления на стыке различных отраслей знания. Междисциплинарные исследования, благодаря которым происходит качественное соединение достижений разных наук, приобретают фундаментальное значение, поскольку они позволяют получить максимально полные сведения о том или ином изучаемом предмете либо явлении и найти варианты оптимальных решений для сложных исследовательских задач. Однако в интегративном тренде знаний обнаруживаются, по крайней мере, две проблемные зоны – онтологического и эпистемологического происхождения. Цель исследования, которому посвящена статья, – раскрыть на примере музыкальной психологии потенциал междисциплинарного исследования и интеграции разнокачественных образований из нескольких дисциплин. Методология и методики. В работе использовались положения системно-интегративного подхода к изучению человека и концепции «метаиндивидуального мира» (МИМ), базирующейся на представлениях о гетерогенной, многокачественной, многодетерминированной природе полисистем. Результаты и научная новизна. Очерчено и охарактеризовано предметное поле музыкальной психологии. Показано, что в настоящее время оно раздроблено на разнонаправленные составляющие из области психологии и музыкознания, связи между которыми слабо артикулированы. Причина заключается не только в разнородности базовых психологических и музыковедческих понятий, но и в несовпадении онтологического статуса объектов и предметов двух ключевых структурных компонентов обсуждаемой сферы. Вместе с тем явственно ощущается потребность их междисциплинарной интеграции и устранения эпистемологического дуализма в развитии научной отрасли. Впервые теоретически и логически сформулированы основания для введения понятий «музыковедческой» и «психоведческой» музыкальных психологий. Показаны различия между ними: если первая обращена к собственно музыкальному произведению, то вторая – к психике композитора и музыканта. И хотя они порождают неодинаковые феноменологии и внеположны друг другу, но движутся во встречном направлении. Поэтому акцентируется необходимость построения интегративной музыкальной психологии (ИМП) по типу психогенетики, психофизиологии, этнопсихологии или поведенческой географии. В качестве интеграционного прототипа предлагается концепция МИМ, которая допускает плюралистический взгляд на ИМП и в которой индивидуальность (личность, психика, сознание) и мир (внешние реалии, социальные группы, культура, искусство) рассматриваются в едином ключе. Выдвигается идея трансцендентности музыкальной психологии – двунаправленных переходов из одного ее предметного поля в другое. Главный смысл наличия таких переходов состоит в появлении феноменов инобытия как формы (способа) преодоления разрывов между предметными областями «психоведческой»и «музыковедческой» музыкальной психологии. Изложенное исследование конкретизирует пути становления и укрепления ИМП и вносит свою лепту в методологию гуманитарно-общественных наук в целом. Практическая значимость. Материалы публикации имеют важное прикладное значение для подготовки выпускников музыкальных и искусствоведческих специальностей. В учебно-воспитательном процессе следует использовать потенциал двух аспектов музыкальной психологии совместно, а не по отдельности, формируя и развивая у студентов умения и навыки трансцендентного восприятия и анализа музыкальных произведений

On the Geometry and Entropy of Non-Hamiltonian Phase Space

We analyze the equilibrium statistical mechanics of canonical, non-canonical and non-Hamiltonian equations of motion by throwing light into the peculiar geometric structure of phase space. Some fundamental issues regarding time translation and phase space measure are clarified. In particular, we emphasize that a phase space measure should be defined by means of the Jacobian of the transformation between different types of coordinates since such a determinant is different from zero in the non-canonical case even if the phase space compressibility is null. Instead, the Jacobian determinant associated with phase space flows is unity whenever non-canonical coordinates lead to a vanishing compressibility, so that its use in order to define a measure may not be always correct. To better illustrate this point, we derive a mathematical condition for defining non-Hamiltonian phase space flows with zero compressibility. The Jacobian determinant associated with time evolution in phase space is altogether useful for analyzing time translation invariance. The proper definition of a phase space measure is particularly important when defining the entropy functional in the canonical, non-canonical, and non-Hamiltonian cases. We show how the use of relative entropies can circumvent some subtle problems that are encountered when dealing with continuous probability distributions and phase space measures. Finally, a maximum (relative) entropy principle is formulated for non-canonical and non-Hamiltonian phase space flows.Comment: revised introductio

Chaotic Properties of Dilute Two and Three Dimensional Random Lorentz Gases I: Equilibrium Systems

We compute the Lyapunov spectrum and the Kolmogorov-Sinai entropy for a moving particle placed in a dilute, random array of hard disk or hard sphere scatterers - i.e. the dilute Lorentz gas model. This is carried out in two ways: First we use simple kinetic theory arguments to compute the Lyapunov spectrum for both two and three dimensional systems. In order to provide a method that can easily be generalized to non-uniform systems we then use a method based upon extensions of the Lorentz-Boltzmann (LB) equation to include variables that characterize the chaotic behavior of the system. The extended LB equations depend upon the number of dimensions and on whether one is computing positive or negative Lyapunov exponents. In the latter case the extended LB equation is closely related to an "anti-Lorentz-Boltzmann equation" where the collision operator has the opposite sign from the ordinary LB equation. Finally we compare our results with computer simulations of Dellago and Posch and find very good agreement.Comment: 48 pages, 3 ps fig

Free Energy Functional for Nonequilibrium Systems: An Exactly Solvable Case

We consider the steady state of an open system in which there is a flux of matter between two reservoirs at different chemical potentials. For a large system of size $N$, the probability of any macroscopic density profile $\rho(x)$ is $\exp[-N{\cal F}(\{\rho\})]$; ${\cal F}$ thus generalizes to nonequilibrium systems the notion of free energy density for equilibrium systems. Our exact expression for $\cal F$ is a nonlocal functional of $\rho$, which yields the macroscopically long range correlations in the nonequilibrium steady state previously predicted by fluctuating hydrodynamics and observed experimentally.Comment: 4 pages, RevTeX. Changes: correct minor errors, add reference, minor rewriting requested by editors and refere

Chaotic Scattering Theory, Thermodynamic Formalism, and Transport Coefficients

The foundations of the chaotic scattering theory for transport and reaction-rate coefficients for classical many-body systems are considered here in some detail. The thermodynamic formalism of Sinai, Bowen, and Ruelle is employed to obtain an expression for the escape-rate for a phase space trajectory to leave a finite open region of phase space for the first time. This expression relates the escape rate to the difference between the sum of the positive Lyapunov exponents and the K-S entropy for the fractal set of trajectories which are trapped forever in the open region. This result is well known for systems of a few degrees of freedom and is here extended to systems of many degrees of freedom. The formalism is applied to smooth hyperbolic systems, to cellular-automata lattice gases, and to hard sphere sytems. In the latter case, the goemetric constructions of Sinai {\it et al} for billiard systems are used to describe the relevant chaotic scattering phenomena. Some applications of this formalism to non-hyperbolic systems are also discussed.Comment: 35 pages, compressed file, follow directions in header for ps file. Figures are available on request from [email protected]

Hamiltonian evolutions of twisted gons in \RP^n

In this paper we describe a well-chosen discrete moving frame and their associated invariants along projective polygons in \RP^n, and we use them to write explicit general expressions for invariant evolutions of projective $N$-gons. We then use a reduction process inspired by a discrete Drinfeld-Sokolov reduction to obtain a natural Hamiltonian structure on the space of projective invariants, and we establish a close relationship between the projective $N$-gon evolutions and the Hamiltonian evolutions on the invariants of the flow. We prove that {any} Hamiltonian evolution is induced on invariants by an evolution of $N$-gons - what we call a projective realization - and we give the direct connection. Finally, in the planar case we provide completely integrable evolutions (the Boussinesq lattice related to the lattice $W_3$-algebra), their projective realizations and their Hamiltonian pencil. We generalize both structures to $n$-dimensions and we prove that they are Poisson. We define explicitly the $n$-dimensional generalization of the planar evolution (the discretization of the $W_n$-algebra) and prove that it is completely integrable, providing also its projective realization