Nested sampling in the canonical ensemble: Direct calculation of the partition function from NVT trajectories

2013 ◽  
Vol 139 (12) ◽  
pp. 124104 ◽  
Author(s):  
Steven O. Nielsen
Keyword(s):  
Partition Function ◽  
Canonical Ensemble ◽  
Direct Calculation ◽  
Nested Sampling

A canonical ensemble derivation of the McMillan-Mayer solution theory

1983 ◽  
Vol 48 (10) ◽  
pp. 2888-2892 ◽  
Author(s):  
Vilém Kodýtek
Keyword(s):  
Free Energy ◽  
Partition Function ◽  
Energy Function ◽  
Special Function ◽  
Helmholtz Free Energy ◽  
Canonical Ensemble ◽  
Free Energy Function ◽  
Solution Theory ◽  
Pure Solvent ◽  
The Common

A special free energy function is defined for a solution in the osmotic equilibrium with pure solvent. The partition function of the solution is derived at the McMillan-Mayer level and it is related to this special function in the same manner as the common partition function of the system to its Helmholtz free energy.

scholarly journals PHASE TRANSITION AND FRAGMENT PRODUCTION IN THE LATTICE GAS MODEL

1999 ◽  
Vol 08 (06) ◽  
pp. 527-544 ◽  
Author(s):  
FRANCESCA GULMINELLI ◽  
PHILIPPE CHOMAZ
Keyword(s):  
Phase Transition ◽  
Gas Phase ◽  
Lattice Gas ◽  
Canonical Ensemble ◽  
Finite Size ◽  
Direct Calculation ◽  
Lattice Gas Model ◽  
Finite Size Scaling ◽  
Finite Size Effects ◽  
Fragment Production

The critical behavior of fragment production is studied within a Lattice Gas Model in the canonical ensemble. Finite size effects on the liquid-gas phase transition are analyzed by a direct calculation of the partition function, and it is shown that phase coexistence and phase transition are relevant concepts even for systems of a few tens of particles. Critical exponents are extracted from the behavior of the fragment production yield as a function of temperature by means of a finite size scaling. The result is that in a finite system well defined critical signals can be found at supercritical (Kertész line) as well as subcritical densities inside the coexistence zone.

Critical Properties of Isobaric Processes of Lennard-Jones Gases

2005 ◽  
Vol 60 (1-2) ◽  
pp. 23-28
Author(s):  
Akira Matsumoto
Keyword(s):  
Heat Capacity ◽  
Free Energy ◽  
Partition Function ◽  
Critical Point ◽  
Gibbs Free Energy ◽  
Canonical Ensemble ◽  
Thermodynamic Quantities ◽  
Lennard Jones ◽  
The Laplace Transform ◽  
Enthalpy And Entropy

The thermodynamic quantities of Lennard-Jones gases, evaluated till the fourth virial coefficient, are investigated for an isobaric process. A partition function in the T-P grand canonical ensemble Y(T,P,N) may be defined by the Laplace transform of the partition function Z(T,V,N) in the canonical ensemble. The Gibbs free energy is related with Y(T,P,N) by the Legendre transformation G(T,P,N) = −kT logY(T,P,N). The volume, enthalpy, entropy, and heat capacity are analytically expressed as functions of the intensive variables temperature and pressure. Some critical thermodynamic quantities for Xe are calculated and drawn. At the critical point the heat capacity diverges to infinity, while the Gibbs free energy, volume, enthalpy, and entropy are continuous. This suggests that a second-order phase transition may occur at the critical point.

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