Nested sampling of isobaric phase space for the direct evaluation of the isothermal-isobaric partition function of atomic systems

2015 ◽  
Vol 143 (15) ◽  
pp. 154108 ◽  
Author(s):  
Blake A. Wilson ◽  
Lev D. Gelb ◽  
Steven O. Nielsen
Keyword(s):  
Phase Space ◽  
Partition Function ◽  
Direct Evaluation ◽  
Nested Sampling ◽  
Atomic Systems

scholarly journals On Boundedness of Entropy of Photon Gas in Noncommutative Spacetime

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Kazi Ashraful Alam ◽  
Mir Mehedi Faruk
Keyword(s):  
Black Holes ◽  
Distribution Function ◽  
Phase Space ◽  
Partition Function ◽  
Boltzmann Distribution ◽  
Einstein Distribution ◽  
Entropy Bound ◽  
Photon Gas ◽  
Noncommutative Spacetime ◽  
Bose Einstein

Entropy bound for the photon gas in a noncommutative (NC) spacetime where phase space is with compact spatial momentum space, previously studied by Nozari et al., has been reexamined with the correct distribution function. While Nozari et al. have employed Maxwell-Boltzmann distribution function to investigate thermodynamic properties of photon gas, we have employed the correct distribution function, that is, Bose-Einstein distribution function. No such entropy bound is observed if Bose-Einstein distribution is employed to solve the partition function. As a result, the reported analogy between thermodynamics of photon gas in such NC spacetime and Bekenstein-Hawking entropy of black holes should be disregarded.

scholarly journals Phase-space curvature in spin-orbit-coupled ultracold atomic systems

2017 ◽  
Vol 95 (4) ◽  
Author(s):  
J. Armaitis ◽  
J. Ruseckas ◽  
E. Anisimovas
Keyword(s):  
Phase Space ◽  
Spin Orbit ◽  
Atomic Systems ◽  
Space Curvature

scholarly journals Generalised partition functions: inferences on phase space distributions

2016 ◽  
Vol 34 (6) ◽  
pp. 557-564 ◽  
Author(s):  
Rudolf A. Treumann ◽  
Wolfgang Baumjohann
Keyword(s):  
Phase Space ◽  
Partition Function ◽  
Bessel Functions ◽  
Chemical Potential ◽  
Temperature Limit ◽  
Large Temperature ◽  
Partition Functions ◽  
Functional Dependencies ◽  
Boltzmann Factor ◽  
Nonextensive Statistical Mechanics

Abstract. It is demonstrated that the statistical mechanical partition function can be used to construct various different forms of phase space distributions. This indicates that its structure is not restricted to the Gibbs–Boltzmann factor prescription which is based on counting statistics. With the widely used replacement of the Boltzmann factor by a generalised Lorentzian (also known as the q-deformed exponential function, where κ = 1∕|q − 1|, with κ, q ∈ R) both the kappa-Bose and kappa-Fermi partition functions are obtained in quite a straightforward way, from which the conventional Bose and Fermi distributions follow for κ → ∞. For κ ≠ ∞ these are subject to the restrictions that they can be used only at temperatures far from zero. They thus, as shown earlier, have little value for quantum physics. This is reasonable, because physical κ systems imply strong correlations which are absent at zero temperature where apart from stochastics all dynamical interactions are frozen. In the classical large temperature limit one obtains physically reasonable κ distributions which depend on energy respectively momentum as well as on chemical potential. Looking for other functional dependencies, we examine Bessel functions whether they can be used for obtaining valid distributions. Again and for the same reason, no Fermi and Bose distributions exist in the low temperature limit. However, a classical Bessel–Boltzmann distribution can be constructed which is a Bessel-modified Lorentzian distribution. Whether it makes any physical sense remains an open question. This is not investigated here. The choice of Bessel functions is motivated solely by their convergence properties and not by reference to any physical demands. This result suggests that the Gibbs–Boltzmann partition function is fundamental not only to Gibbs–Boltzmann but also to a large class of generalised Lorentzian distributions as well as to the corresponding nonextensive statistical mechanics.

q-STATISTICAL PROPERTIES OF LARGE CRITICAL CLUSTERS

2007 ◽  
Vol 21 (23n24) ◽  
pp. 3947-3953 ◽  
Author(s):  
A. ROBLEDO
Keyword(s):  
Phase Space ◽  
Partition Function ◽  
Saddle Point ◽  
Critical Points ◽  
Order Parameter ◽  
Statistical Properties ◽  
Coarse Grained ◽  
Thermal Systems ◽  
Saddle Point Approximation ◽  
Large Clusters

We consider both static (fractal) and dynamical (intermittent) properties of large clusters of order parameter φ at critical points in thermal systems and highlight their association to q-statistics. These properties, previously obtained through the saddle-point approximation in a coarse-grained partition function, are reexamined by considering a phenomenological scheme based on sub-occupation of φ-phase space.

Phase–space noncommutativity and the thermodynamics of the Landau system

2017 ◽  
Vol 32 (20) ◽  
pp. 1750102
Author(s):  
Aslam Halder ◽  
Sunandan Gangopadhyay
Keyword(s):  
Phase Space ◽  
Partition Function ◽  
Equivalent System ◽  
Noncommutative Phase Space ◽  
Nc System ◽  
Space Noncommutativity

Thermodynamics of the Landau system in noncommutative phase–space (NCPS) has been studied in this paper. The analysis involves the use of generalized Bopp-shift transformations to map the noncommutative (NC) system to its commutative equivalent system. The partition function of the system is computed and from this, the magnetization and the susceptibility of the Landau system are obtained. The results reveal that the magnetization and the susceptibility get modified by both the spatial and momentum NC parameters [Formula: see text] and [Formula: see text]. We then investigate the de Hass–van Alphen effect in NCPS. Here, the oscillation of the magnetization and the susceptibility get corrected by both the spatial and momentum NC parameters [Formula: see text] and [Formula: see text].

scholarly journals PHASE SPACE POLARIZATION AND THE TOPOLOGICAL STRING: A CASE STUDY

2008 ◽  
Vol 23 (38) ◽  
pp. 3199-3214 ◽  
Author(s):  
AMIR-KIAN KASHANI-POOR
Keyword(s):  
Phase Space ◽  
Partition Function ◽  
Canonical Form ◽  
Topological String ◽  
Target Space ◽  
Canonical Transformations ◽  
Space Polarization

We review and elaborate on our discussion in hep-th/0606112 on the interplay between the target space and the worldsheet description of the open topological string partition function, for the example of the conifold. We discuss the appropriate phase space and canonical form for the system. We find a map between choices of polarization and the worldsheet description, based on which we study the behavior of the partition function under canonical transformations.

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