Structure of fluids from the statistical mechanics point of view

2003 ◽  
Vol 106 (2-3) ◽  
pp. 123-130 ◽  
Author(s):  
G.A. Martynov
Keyword(s):  
Statistical Mechanics ◽  
Point Of View ◽  
Structure Of Fluids

Numerical Analysis of Conservative Maps: A Possible Foundation of Nonextensive Phenomena

2004 ◽  
Author(s):  
Fulvio Baldovin
Keyword(s):  
Statistical Mechanics ◽  
High Energy Physics ◽  
Financial Analysis ◽  
Initial Conditions ◽  
Research Area ◽  
Distribution Functions ◽  
Point Of View ◽  
Dissipative Systems ◽  
Definition Of ◽  
Low Dimensional

We discuss the sensitivity to initial conditions and the entropy production of low-dimensional conservative maps, focusing on situations where the phase space presents complex (fractal-like) structures. We analyze numerically the standard map as a specific example and we observe a scenario that presents appealing analogies with anomalies detected in long-range Hamiltonian systems. We see how the Tsallis nonextensive formalism handles this situation both from a dynamical and from a statistical mechanics point of view…. In recent years, the Tsallis extension of the Boltzmann-Gibbs (BG) statistical mechanics [9, 26], usually referred to as nonextensive (NE) statistical mechanics, has become an intense and exciting research area (see, e.g., Tsallis [25]). The q-exponential distribution functions that emerge as a consequence of the NE formalism have been applied to an impressive variety of problems, ranging from turbulence, to high-energy physics, epilepsy, protein folding, and financial analysis. Yet, the foundation of this formalism, as well as the definition of its area of applicability, is still not completely understood, and it stands as a present challenge in the affirmation of the whole proposal. An intensive effort is currently being made to investigate this point, precisely in trying to understand: (1) which mechanisms lead to a crisis of the BG formalism; and (2) in these cases, does the NE formalism provide a "way out" to some of the problems? A possible approach to these questions comes from the study of the underlying dynamics that gives the basis for a statistical mechanic treatment of the system. This idea is not new. Einstein, in his critical remark about the validity of the Boltzmann principle [10], was one of the first to call attention to the relevance of a dynamical foundation of statistical mechanics. Another fundamental contribution is Krylov's seminal work [14] on the mixing properties of dynamical systems. In one-dimensional (dissipative) systems, intensive effort has been made to analyze the properties of the systems at the edge of chaos, i.e., at the critical poin that marks the transition between chaoticity and regularity [6, 8, 16, 19, 18, 23, 27].

Statistical Interpretation of Entropy

1993 ◽  
Author(s):  
Greg M. Anderson ◽  
David A. Crerar
Keyword(s):  
Statistical Mechanics ◽  
Thermodynamic Model ◽  
Point Of View ◽  
Statistical Interpretation ◽  
Conservation Of Energy ◽  
Heat Engines ◽  
Lower Temperature ◽  
Intuitive Grasp ◽  
The Individual ◽  
Classical Thermodynamics

As we have seen, thermodynamics is based for the most part on the idea of the conservation of energy (First Law) and the concept of entropy (Second Law). The conservation of energy gives little problem intuitively, but it is quite another story with entropy. Entropy can be considered from the point of view of idealized heat engines operating in cycles, or by deriving some of its inherent properties (Chapter 5). We will see how it is measured and tabulated in Chapter 7. This is all very useful, but doesn't help much in gaining an intuitive grasp of entropy, such as we have for the other thermodynamic parameters. Just what is entropy, anyway? There may not be any definitive short answer to this question. If we had to rely on classical thermodynamics for an answer, we would talk at some length about the availability of energy, e.g., the fact that in spite of the tremendous quantity of energy in the ocean, we cannot use any of it to power a ship or to do anything else; the ocean's thermal energy is unavailable unless we provide a reservoir for heat at a lower temperature. This is of course perfectly true, and many useful discussions of the meaning of entropy follow this line of thought, but somehow after all these discussions, the entropy remains somewhat elusive. There is, however, another way to think of entropy that is by far the most useful, and that is from the statistical/probability point of view. This requires that we consider matter from the point of view of the individual particles (atoms, molecules, ions) rather than as macroscopic, homogeneous bodies, and is therefore not a part of classical thermodynamics, but of statistical mechanics. In this chapter we present the rudiments of this approach, not so that the reader can become proficient in statistical thermodynamics (a considerably more thorough introduction is required for that) but to show how entropy is related to statistical considerations. Statistical mechanics does not exactly explain what entropy is, but rather provides a model, quite different from the thermodynamic model, that contains a parameter identical to the entropy of the thermodynamic model in every measurable respect.

On the relationship between free energy difference calculations by thermodynamic integration and harmonic frequency analysis

2009 ◽  
Vol 87 (3) ◽  
pp. 496-501
Author(s):  
Jason Jechow ◽  
Tom Ziegler
Keyword(s):  
Free Energy ◽  
Statistical Mechanics ◽  
Frequency Analysis ◽  
Helmholtz Free Energy ◽  
Energy Difference ◽  
Thermodynamic Integration ◽  
Point Of View ◽  
Harmonic Frequency ◽  
Free Energy Difference ◽  
The Relationship

Harmonic frequency analysis (HFA), based on statistical mechanics, is a widely used and powerful tool for evaluating free energy changes between molecular states. It has, as such, been employed extensively to evaluate the free energy of reaction and activation for chemical processes. Alternatively, free energy differences can be calculated using thermodynamic integration (TI). In TI, the force on a constrained reaction coordinate is calculated, and this force from a to b is integrated to obtain the Helmholtz free energy change ΔAab. Although HFA and TI clearly are related from a fundamental statistical mechanics point-of-view, the relationship is not immediately obvious when one considers the quite different procedures applied in the two methods. This article provides a detailed analysis and proof of the relation between HFA and TI.

scholarly journals THERMODYNAMIC AND STATISTICAL MECHANICS INCONSISTENCIES IN QUASIPARTICLE MODELS

2013 ◽  
Vol 28 (02) ◽  
pp. 1350006 ◽  
Author(s):  
VISHNU M. BANNUR
Keyword(s):  
Statistical Mechanics ◽  
Phenomenological Models ◽  
Quark Gluon Plasma ◽  
Gluon Plasma ◽  
Point Of View ◽  
Nucl Phys ◽  
Large Temperature ◽  
Lattice Data ◽  
Lattice Gauge ◽  
Quasiparticle Model

Here we reanalyze various quasiparticle models of quark gluon plasma from the statistical mechanics and thermodynamics point of view. We investigate the statistical mechanics and thermodynamics inconsistencies involved in these models and their consequences in the observables. Quasiparticle models are phenomenological models with few parameters and by adjusting them all models fit the results of lattice gauge simulation of gluon plasma [G. Boyd et al., Phys. Rev. Lett.75, 4169 (1995); G. Boyd et al., Nucl. Phys. B469, 419 (1996)]. However, after fixing two of the three parameters of the model by physical arguments, only one quasiparticle model, which is consistent with both statistical mechanics and thermodynamics, fits the Bielefeld lattice data [G. Boyd et al., Phys. Rev. Lett.75, 4169 (1995); G. Boyd et al., Nucl. Phys. B469, 419 (1996)]. The same model also fits the recent lattice results of Wuppertal–Budapest group [S. Borsanyi et al., arXiv:1204.6184v1 [hep-lat]], which deals with precision SU(3) thermodynamics for a large temperature range, reasonably well.

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