Absolute entropy and free energy of fluids using the hypothetical scanning method. I. Calculation of transition probabilities from local grand canonical partition functions

2003 ◽  
Vol 119 (23) ◽  
pp. 12084-12095 ◽  
Author(s):  
Agnieszka Szarecka ◽  
Ronald P. White ◽  
Hagai Meirovitch
Keyword(s):  
Free Energy ◽  
Transition Probabilities ◽  
Partition Functions ◽  
Scanning Method ◽  
Absolute Entropy ◽  
Grand Canonical

scholarly journals Confinement and Mayer cluster expansions

2014 ◽  
Vol 29 (15) ◽  
pp. 1450077 ◽  
Author(s):  
Jean-Emile Bourgine
Keyword(s):  
Free Energy ◽  
Equations Of Motion ◽  
Partition Functions ◽  
Young Tableaux ◽  
Cluster Expansions ◽  
Short Range Potential ◽  
Alternative Expression ◽  
Generalized Matrix ◽  
Nekrasov Partition Functions ◽  
Grand Canonical

In this paper, we study a class of grand-canonical partition functions with a kernel depending on a small parameter ϵ. This class is directly relevant to Nekrasov partition functions of 𝒩 = 2 SUSY gauge theories on the 4d Ω-background, for which ϵ is identified with one of the equivariant deformation parameter. In the Nekrasov–Shatashvili limit ϵ→0, we show that the free energy is given by an on-shell effective action. The equations of motion take the form of a TBA equation. The free energy is identified with the Yang–Yang functional of the corresponding system of Bethe roots. We further study the associated canonical model that takes the form of a generalized matrix model. Confinement of the eigenvalues by the short-range potential is observed. In the limit where this confining potential becomes weak, the collective field theory formulation is recovered. Finally, we discuss the connection with the alternative expression of instanton partition functions as sums over Young tableaux.

scholarly journals Enhancing Water Sampling in Free Energy Calculations with Grand Canonical Monte Carlo

2020 ◽  
Author(s):  
Gregory Ross ◽  
Ellery Russell ◽  
Yuqing Deng ◽  
Chao Lu ◽  
Edward Harder ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Free Energy ◽  
Drug Discovery ◽  
Free Energy Calculations ◽  
Data Sets ◽  
Grand Canonical Monte Carlo ◽  
Enhanced Sampling ◽  
Computational Performance ◽  
Energy Perturbation ◽  
Grand Canonical

<div>The prediction of protein-ligand binding affinities using free energy perturbation (FEP) is becoming increasingly routine in structure-based drug discovery. Most FEP packages use molecular dynamics (MD) to sample the configurations of proteins and ligands, as MD is well-suited to capturing coupled motion. However, MD can be prohibitively inefficient at sampling water molecules that are buried within binding sites, which has severely limited the domain of applicability of FEP and its prospective usage in drug discovery. In this paper, we present an advancement of FEP that augments MD with grand canonical Monte Carlo (GCMC), an enhanced sampling method, to overcome the problem of sampling water. We accomplished this without degrading computational performance. On both old and newly assembled data sets of proteinligand complexes, we show that the use of GCMC in FEP is essential for accurate and robust predictions for ligand perturbations that disrupt buried water. <br></div>

scholarly journals Atomic Physics Data for Stellar Atmospheres Research

2003 ◽  
Vol 210 ◽  
pp. 261-272
Author(s):  
Charles R. Cowley ◽  
Saul J. Adelman ◽  
Donald J. Bord
Keyword(s):  
Cross Sections ◽  
Transition Probabilities ◽  
Stellar Atmospheres ◽  
Partition Functions ◽  
Line Broadening ◽  
Data Bases ◽  
Stellar Spectra ◽  
Atomic Ions ◽  
Excitation Cross Sections ◽  
Nuclear Effects

The review will cover the following topics: (1) Ionization energies; (2) Partition functions; (3) Sources of data for atomic and ionic wavelengths, transition probabilities, and broadening parameters, including nuclear effects (hfs and isotope shifts); (4) Opacities from photoionization of abundant elements (atoms and atomic ions) with emphasis on integration of TOPBASE material; and (5) Data bases for diatomic molecules. We emphasize topics of direct relevance to the synthesis of stellar spectra, primarily within the domain where LTE is useful. Additional parameters, such as line-broadening parameters, or excitation cross sections are not reviewed.

scholarly journals Equivalence of the Grand Canonical Partition Functions of Particles with Different Statistics

1997 ◽  
Vol 12 (15) ◽  
pp. 1095-1099 ◽  
Author(s):  
S. Chaturvedi ◽  
P. K. Panigrahi ◽  
V. Srinivasan ◽  
R. MacKenzie
Keyword(s):  
Partition Function ◽  
Single Particle ◽  
Particle Energy ◽  
Partition Functions ◽  
Bose System ◽  
Particle Spectrum ◽  
Single Particle Energy ◽  
Grand Partition Function ◽  
System Of Particles ◽  
Grand Canonical

It is shown that the grand partition function of an ideal Bose system with single particle spectrum εi=(2n+k+3/2)ℏω is identical to that of a system of particles with single particle energy εi=(n+1/2)ℏω and obeying a particular kind of statistics based on the permutation group.

scholarly journals THE ABELIAN HIGGS MODEL AS AN ENSEMBLE OF VORTEX LOOPS

1999 ◽  
Vol 14 (27) ◽  
pp. 4347-4363 ◽  
Author(s):  
DMITRI ANTONOV
Keyword(s):  
Landau Theory ◽  
Higgs Model ◽  
Partition Functions ◽  
Ginzburg Landau ◽  
Translation Invariant ◽  
Abelian Higgs Model ◽  
Vortex Dipoles ◽  
Vortex Loops ◽  
Small Vortex ◽  
Grand Canonical

In the London limit of the Ginzburg–Landau theory (Abelian Higgs model), vortex dipoles (small vortex loops) are treated as a grand canonical ensemble in the dilute gas approximation. The summation over these objects with the most general rotation and translation-invariant measure of integration over their shapes leads to effective sine–Gordon theories of the dual fields. The representations of the partition functions of both grand canonical ensembles are derived in the form of the integrals over the vortex dipoles and the small vortex loops, respectively. By virtue of these representations, the bilocal correlator of the vortex dipoles (loops) is calculated in the low-energy limit. It is further demonstrated that once the vortex dipoles (loops) are considered as such an ensemble rather than individual ones, the London limit of the Ginzburg–Landau theory (Abelian Higgs model) with external monopoles is equivalent up to the leading order in the inverse UV cutoff to the compact QED in the corresponding dimension with the charge of Cooper pairs changed due to the Debye screening.

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