Adsorption on Proteins, the Grand Partition Function and First-Order Phase Changes, According to Approximate Statistical Mechanical Theories

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.

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Statistical Mechanical Determination of nanocluster size distributions in the phase coexistence region of a first order phase transition from the isotherms of DMPC monolayers at the air-water interface

Physical Chemistry Chemical Physics ◽

10.1039/d1cp03178c ◽

2021 ◽

Author(s):

Eiji Hatta ◽

Ko Nihei

Keyword(s):

Surface Pressure ◽

Size Distributions ◽

Coexistence Region ◽

First Order ◽

First Order Phase Transition ◽

Air Water Interface ◽

Pressure Area ◽

Statistical Mechanical ◽

First Order Phase

A statistical mechanical deconvolution procedure for the experimentally measured surface pressure –area isotherms has been presented to obtain the surface pressure dependence of the liquid expanded (LE) and liquid condensed...

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Partition Function Zeros at First-Order Phase Transitions: Pirogov–Sinai Theory

Journal of Statistical Physics ◽

10.1023/b:joss.0000037243.48527.e3 ◽

2004 ◽

Vol 116 (1-4) ◽

pp. 97-155 ◽

Cited By ~ 14

Author(s):

M. Biskup ◽

C. Borgs ◽

J. T. Chayes ◽

R. Kotecký

Keyword(s):

Phase Transitions ◽

Partition Function ◽

Partition Function Zeros ◽

First Order ◽

Function Zeros ◽

First Order Phase

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Solid−liquid critical behavior of water in nanopores

Proceedings of the National Academy of Sciences ◽

10.1073/pnas.1422829112 ◽

2015 ◽

Vol 112 (27) ◽

pp. 8221-8226 ◽

Cited By ~ 44

Author(s):

Kenji Mochizuki ◽

Kenichiro Koga

Keyword(s):

Critical Points ◽

Liquid Water ◽

Phase Changes ◽

Dynamics Simulation ◽

Scaling Analysis ◽

Widom Line ◽

First Order ◽

Low Dimensional ◽

Solid Liquid ◽

First Order Phase

Nanoconfined liquid water can transform into low-dimensional ices whose crystalline structures are dissimilar to any bulk ices and whose melting point may significantly rise with reducing the pore size, as revealed by computer simulation and confirmed by experiment. One of the intriguing, and as yet unresolved, questions concerns the observation that the liquid water may transform into a low-dimensional ice either via a first-order phase change or without any discontinuity in thermodynamic and dynamic properties, which suggests the existence of solid−liquid critical points in this class of nanoconfined systems. Here we explore the phase behavior of a model of water in carbon nanotubes in the temperature−pressure−diameter space by molecular dynamics simulation and provide unambiguous evidence to support solid−liquid critical phenomena of nanoconfined water. Solid−liquid first-order phase boundaries are determined by tracing spontaneous phase separation at various temperatures. All of the boundaries eventually cease to exist at the critical points and there appear loci of response function maxima, or the Widom lines, extending to the supercritical region. The finite-size scaling analysis of the density distribution supports the presence of both first-order and continuous phase changes between solid and liquid. At around the Widom line, there are microscopic domains of two phases, and continuous solid−liquid phase changes occur in such a way that the domains of one phase grow and those of the other evanesce as the thermodynamic state departs from the Widom line.

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Wave function of the universe from a matrix-valued first-order formalism

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887815500504 ◽

2015 ◽

Vol 12 (04) ◽

pp. 1550050

Author(s):

Sergey I. Kruglov ◽

Mir Faizal

Keyword(s):

Wave Function ◽

Partition Function ◽

Cosmological Constant ◽

Eigenvalue Equation ◽

Cosmological Constant Problem ◽

First Order ◽

Superspace Formalism ◽

Statistical Mechanical ◽

The Universe ◽

Spacetime Foam

In this paper, the Wheeler–DeWitt equation in full superspace formalism will be written in a matrix-valued first-order formalism. We will also analyze the Wheeler–DeWitt equation in minisuperspace approximation using this matrix-valued first-order formalism. We will note that this Wheeler–DeWitt equation, in this minisuperspace approximation, can be expressed as an eigenvalue equation. We will use this fact to analyze the spacetime foam in this formalism. This will be done by constructing a statistical mechanical partition function for the Wheeler–DeWitt equation in this matrix-valued first-order formalism. This will lead to a possible solution for the cosmological constant problem.

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