scholarly journals The Equilibrium Statistical Mechanics of a One-dimensional Self-gravitational System

1979 ◽  
Vol 32 (3) ◽  
pp. 289 ◽  
Author(s):  
Y Fukui ◽  
T Morita
Keyword(s):  
Mechanical Properties ◽  
Statistical Mechanics ◽  
Infinite Number ◽  
Virial Expansion ◽  
Gravitational System ◽  
Equilibrium Statistical Mechanics ◽  
One Dimensional ◽  
Statistical Mechanical ◽  
Number Of Particles

It is shown that the exact statistical mechanical properties of a one-dimensional self-gravitational system in. the limit of an infinite number of particles are easily obtained with the aid of the virial expansion.

Linear Response Theory

2006 ◽  
Author(s):  
Abraham Nitzan
Keyword(s):  
Statistical Mechanics ◽  
Linear Response ◽  
Ad Hoc ◽  
Linear Response Theory ◽  
Perturbative Expansion ◽  
General Nature ◽  
Response Theory ◽  
Equilibrium Statistical Mechanics ◽  
Standard Application ◽  
Statistical Mechanical

Equilibrium statistical mechanics is a first principle theory whose fundamental statements are general and independent of the details associated with individual systems. No such general theory exists for nonequilibrium systems and for this reason we often have to resort to ad hoc descriptions, often of phenomenological nature, as demonstrated by several examples in Chapters 7 and 8. Equilibrium statistical mechanics can however be extended to describe small deviations from equilibrium in a way that preserves its general nature. The result is Linear Response Theory, a statistical mechanical perturbative expansion about equilibrium. In a standard application we start with a system in thermal equilibrium and attempt to quantify its response to an applied (static- or time-dependent) perturbation. The latter is assumed small, allowing us to keep only linear terms in a perturbative expansion. This leads to a linear relationship between this perturbation and the resulting response. Let us make these statements more quantitative. Consider a system characterized by the Hamiltonian Ĥ0.

THERMODYNAMICS OF q-MODIFIED BOSONS

1996 ◽  
Vol 10 (06) ◽  
pp. 683-699 ◽  
Author(s):  
P. NARAYANA SWAMY
Keyword(s):  
Mechanical Properties ◽  
Phase Transition ◽  
Equation Of State ◽  
Partition Function ◽  
Statistical Mechanics ◽  
Specific Heat ◽  
Thermodynamic Functions ◽  
Bose Condensation ◽  
Grand Partition Function ◽  
Statistical Mechanical

Based on a recent study of the statistical mechanical properties of the q-modified boson oscillators, we develop the statistical mechanics of the q-modified boson gas, in particular the Grand Partition Function. We derive the various thermodynamic functions for the q-boson gas including the entropy, pressure and specific heat. We demonstrate that the gas exhibits a phase transition analogous to ordinary bose condensation. We derive the equation of state and develop the virial expansion for the equation of state. Several interesting properties of the q-boson gas are derived and compared with those of the ordinary boson which may point to the physical relevance of such systems.

The virial expansion re-visited: A new interpretation

2015 ◽  
Vol 29 (34) ◽  
pp. 1530014
Author(s):  
F. Y. Wu ◽  
R. Aaron
Keyword(s):  
Statistical Mechanics ◽  
Particle Density ◽  
Research Area ◽  
Virial Expansion ◽  
Expansion Formula ◽  
Mayer Expansion ◽  
Gas System ◽  
Gas Molecule ◽  
New Interpretation ◽  
Number Of Particles

A central topic in statistical mechanics, a research area Professor Hao Bailin devoted himself throughout the years, is the study of the state of matter. For a gas system the study begins with an understanding of the equation of state relating the pressure [Formula: see text], volume [Formula: see text] and the temperature [Formula: see text]. In 1901 Onnes introduced the virial expansion [Formula: see text] as an empirical formula expressing [Formula: see text] in a power series of particle density [Formula: see text], where [Formula: see text] is the number of particles. A first-principle understanding of the virial expansion was provided years later by the advent of the Mayer cluster expansion in statistical mechanics in the 1930s. However, following Onnes the virial expansion has since been generally regarded as an expansion in density. Here we re-visit the virial expansion using the Mayer expansion, and show that the virial expansion should be considered as an expansion in specific volume, the ratio of the effective volume of a gas molecule and its allotted mean volume. This consideration is illustrated in the case of the hard sphere gas.

Statistical mechanics of a one-dimensional Coulomb system with a uniform charge background

1963 ◽  
Vol 59 (4) ◽  
pp. 779-787 ◽  
Author(s):  
R. J. Baxter
Keyword(s):  
Statistical Mechanics ◽  
Positive Charge ◽  
Charged Particles ◽  
Real System ◽  
Coulomb System ◽  
Dimensional System ◽  
One Dimensional ◽  
Uniform Background ◽  
Statistical Mechanical ◽  
Exact Description

AbstractThis paper obtains an exact description of the statistical mechanics of a one-dimensional system of charged particles moving in a uniform neutralizing background of positive charge. These results are compared with the behaviour of a one-dimensional system of equal numbers of positive and negative charged particles. Although the thermodynamics of the two systems do differ, the discrepancy is small enough to indicate that the assumption of a uniform background of positive charge, common in statistical mechanical treatments of a plasma in equilibrium, may provide a good approximation to a real system of discrete charges.

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