Statistical Mechanical Meaning of the Thermodynamic Quantities of AIT

2019 ◽  
pp. 75-82
Author(s):  
Kohtaro Tadaki
Keyword(s):  
Thermodynamic Quantities ◽  
Statistical Mechanical

Isotope effect on the thermodynamic quantities of gaseous uranium hexafluoride

1976 ◽  
Vol 54 (1) ◽  
pp. 160-165 ◽  
Author(s):  
Jan Bron
Keyword(s):  
Partition Function ◽  
Quantum Correction ◽  
Isotope Effects ◽  
Uranium Atom ◽  
Uranium Hexafluoride ◽  
Thermodynamic Quantities ◽  
Heavy Isotope ◽  
Statistical Mechanical ◽  
Lower Temperature ◽  
The Masses

For gaseous UF6 changes in the thermodynamic quantifies ΔG (= ΔA), ΔH (= ΔU), ΔCp (= ΔCv), and ΔS upon isotopic substitution can be determined by using the spectroscopically determined geometry and force field. The differences ΔG etc. are defined as (G238 – Gx), where 238 and x (x = 235, 234, 233, and 232) are the masses of the central uranium atom. The changes in the thermodynamic quantities are related to the logarithm of the partition function ratio of the UF6 species compared. The logarithm of the partition function ratio can be conveniently expressed as a series in temperature and hence, by using statistical mechanical relationships, the changes in thermodynamic quantities can be expressed as a series in temperature.Since these changes form examples of heavy isotope effects the validity and utility of the first quantum correction can be investigated. Uncertainties and trends in the magnitudes of the differences in the thermodynamic quantities due to uncertainties or changes in spectroscopic parameters are discussed by means of the first quantum correction. It has been found that the first quantum correction has little quantitative value in the lower temperature region, but it can be used in that range to explain some observed trends in the isotope effects. Some of the conclusions can also be applied to kinetic and equilibrium heavy isotope effects.

scholarly journals Thermodynamic efficiency of contagions: a statistical mechanical analysis of the SIS epidemic model

2018 ◽  
Vol 8 (6) ◽  
pp. 20180036 ◽  
Author(s):  
Nathan Harding ◽  
Ramil Nigmatullin ◽  
Mikhail Prokopenko
Keyword(s):  
Mechanical Analysis ◽  
Contact Network ◽  
Thermodynamic Efficiency ◽  
Thermodynamic Quantities ◽  
Sis Model ◽  
Closed Form Solutions ◽  
Sis Epidemic Model ◽  
Novel Approach ◽  
Statistical Mechanical ◽  
Computational Processes

We present a novel approach to the study of epidemics on networks as thermodynamic phenomena, quantifying the thermodynamic efficiency of contagions, considered as distributed computational processes. Modelling SIS dynamics on a contact network statistical-mechanically, we follow the maximum entropy (MaxEnt) principle to obtain steady-state distributions and derive, under certain assumptions, relevant thermodynamic quantities both analytically and numerically. In particular, we obtain closed-form solutions for some cases, while interpreting key epidemic variables, such as the reproductive ratio of a SIS model, in a statistical mechanical setting. On the other hand, we consider configuration and free entropy, as well as the Fisher information, in the epidemiological context. This allowed us to identify criticality and distinct phases of epidemic processes. For each of the considered thermodynamic quantities, we compare the analytical solutions informed by the MaxEnt principle with the numerical estimates for SIS epidemics simulated on Watts–Strogatz random graphs.

scholarly journals A statistical mechanical interpretation of algorithmic information theory III: composite systems and fixed points

2012 ◽  
Vol 22 (5) ◽  
pp. 752-770 ◽  
Author(s):  
KOHTARO TADAKI
Keyword(s):  
Information Theory ◽  
Statistical Mechanics ◽  
Sufficient Conditions ◽  
Thermodynamic Quantity ◽  
Thermodynamic Quantities ◽  
Algorithmic Information Theory ◽  
Algorithmic Information ◽  
Statistical Mechanical ◽  
Mechanical Interpretation ◽  
Partial Randomness

The statistical mechanical interpretation of algorithmic information theory (AIT for short) was introduced and developed in our previous papers Tadaki (2008; 2012), where we introduced into AIT the notion of thermodynamic quantities, such as the partition function Z(T), free energy F(T), energy E(T) and statistical mechanical entropy S(T). We then discovered that in the interpretation, the temperature T is equal to the partial randomness of the values of all these thermodynamic quantities, where the notion of partial randomness is a stronger representation of the compression rate by means of program-size complexity. Furthermore, we showed that this situation holds for the temperature itself as a thermodynamic quantity, namely, for each of the thermodynamic quantities above, the computability of its value at temperature T gives a sufficient condition for T ∈ (0, 1) to be a fixed point on partial randomness. In this paper, we develop the statistical mechanical interpretation of AIT further and pursue its formal correspondence to normal statistical mechanics. The thermodynamic quantities in AIT are defined on the basis of the halting set of an optimal prefix-free machine, which is a universal decoding algorithm used to define the notion of program-size complexity. We show that there are infinitely many optimal prefix-free machines that give completely different sufficient conditions for each of the thermodynamic quantities in AIT. We do this by introducing the notion of composition of prefix-free machines into AIT, which corresponds to the notion of the composition of systems in normal statistical mechanics.

Interionic Pair Potential, hard sphere diameter and entropy of mixing of NaCd compound forming binary molten alloys under the framework of Pseudopotential theory

2014 ◽  
Vol 10 (6) ◽  
pp. 2843-2852
Author(s):  
Sujeet Kumar Chatterjee ◽  
Lokesh Chandra Prasad ◽  
Ajaya Bhattarai
Keyword(s):  
Nearest Neighbor ◽  
Effective Interaction ◽  
Pair Potential ◽  
Sphere Diameter ◽  
Compound Formation ◽  
Pseudopotential Theory ◽  
Energy Of Mixing ◽  
Asymmetric Behaviour ◽  
Statistical Mechanical ◽  
Free Energy Of Mixing

The observed asymmetric behaviour of mixing of  NaCd liquid alloys around equiatomic composition with smaller negative values for free energy of mixing at compound forming concentration, i.e. GMXS = -4.9KJ at Ccd =0.66 has  aroused our interest to undertake a theoretical investigation of this system.A simple statistical mechanical theory based on compound formation model has been used to investigate the energetics of formation of intermetallic compound Cd2Na in the melt through the study of entropy of mixing.Besides, the interionic interactions between component atoms Na and Cd of the alloys have been understood through the study of interionic pair potential фij(r), calculated from pseudopotential theory in the light of CF model.Our study of фij(r) suggest that the effective interaction between Na-Na atoms decreases on alloying with Cd atom, being minimum for compound forming alloy( Cd 0.66 Na 0.34 ).The nearest neighbor distance between Na-Na atoms does not alter on alloying. Like wise Na-Na,  effective interaction between  Cd-Cd atom decreases from pure state to NaCd alloys, being smaller at compound forming  concentration Cd 0.66 Na 0.34.The computed values of SM from pseudopotential theory are positive at all concentrations, but the agreement between theory and experimental is not satisfactory. This might be happening due to parameterisation of σ3 and Ψcompound.

System of thermodynamic quantities in the McMillan-Mayer solution theory

1985 ◽  
Vol 50 (4) ◽  
pp. 791-798 ◽  
Author(s):  
Vilém Kodýtek
Keyword(s):  
Free Energy ◽  
Generating Function ◽  
Simple Form ◽  
Unit Volume ◽  
Thermodynamic Quantities ◽  
Solution Theory ◽  
Pure Solvent ◽  
Second Derivatives ◽  
Definition Of ◽  
Derivatives Of

The McMillan-Mayer (MM) free energy per unit volume of solution AMM, is employed as a generating function of the MM system of thermodynamic quantities for solutions in the state of osmotic equilibrium with pure solvent. This system can be defined by replacing the quantities G, T, P, and m in the definition of the Lewis-Randall (LR) system by AMM, T, P0, and c (P0 being the pure solvent pressure). Following this way the LR to MM conversion relations for the first derivatives of the free energy are obtained in a simple form. New relations are derived for its second derivatives.

Interpretation of Preferential Adsorption Using Random Phase Approximation Theory

1995 ◽  
Vol 60 (10) ◽  
pp. 1641-1652 ◽  
Author(s):  
Henri C. Benoît ◽  
Claude Strazielle
Keyword(s):  
Approximation Theory ◽  
Random Phase Approximation ◽  
Virial Coefficient ◽  
Random Phase ◽  
Second Virial Coefficient ◽  
Solvent Mixture ◽  
Gyration Radius ◽  
Thermodynamic Quantities ◽  
Phase Approximation ◽  
Preferential Adsorption

It has been shown that in light scattering experiments with polymers replacement of a solvent by a solvent mixture causes problems due to preferential adsorption of one of the solvents. The present paper extends this theory to be applicable to any angle of observation and any concentration by using the random phase approximation theory proposed by de Gennes. The corresponding formulas provide expressions for molecular weight, gyration radius, and the second virial coefficient, which enables measurements of these quantities provided enough information on molecular and thermodynamic quantities is available.

scholarly journals The Equilibrium Phase Formation and Thermodynamic Properties of Functional Tellurides in the Ag–Fe–Ge–Te System

Energies ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 1314
Author(s):  
Mykola Moroz ◽  
Fiseha Tesfaye ◽  
Pavlo Demchenko ◽  
Myroslava Prokhorenko ◽  
Nataliya Yarema ◽  
...  
Keyword(s):  
Electromotive Force ◽  
Equilibrium Phase ◽  
Stoichiometric Composition ◽  
Negative Electrode ◽  
Electrochemical Cells ◽  
Thermodynamic Quantities ◽  
Positive Electrodes ◽  
Gibbs Energies ◽  
Buffer Region ◽  
First Time

Equilibrium phase formations below 600 K in the parts Ag2Te–FeTe2–F1.12Te–Ag2Te and Ag8GeTe6–GeTe–FeTe2–AgFeTe2–Ag8GeTe6 of the Fe–Ag–Ge–Te system were established by the electromotive force (EMF) method. The positions of 3- and 4-phase regions relative to the composition of silver were applied to express the potential reactions involving the AgFeTe2, Ag2FeTe2, and Ag2FeGeTe4 compounds. The equilibrium synthesis of the set of phases was performed inside positive electrodes (PE) of the electrochemical cells: (−)Graphite ‖LE‖ Fast Ag+ conducting solid-electrolyte ‖R[Ag+]‖PE‖ Graphite(+), where LE is the left (negative) electrode, and R[Ag+] is the buffer region for the diffusion of Ag+ ions into the PE. From the observed results, thermodynamic quantities of AgFeTe2, Ag2FeTe2, and Ag2FeGeTe4 were experimentally determined for the first time. The reliability of the division of the Ag2Te–FeTe2–F1.12Te–Ag2Te and Ag8GeTe6–GeTe–FeTe2–AgFeTe2–Ag8GeTe6 phase regions was confirmed by the calculated thermodynamic quantities of AgFeTe2, Ag2FeTe2, and Ag2FeGeTe4 in equilibrium with phases in the adjacent phase regions. Particularly, the calculated Gibbs energies of Ag2FeGeTe4 in two different adjacent 4-phase regions are consistent, which also indicates that it has stoichiometric composition.

scholarly journals Chemical and biochemical thermodynamics reunification (IUPAC Technical Report)

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Antonio Sabatini ◽  
Marco Borsari ◽  
Gerard P. Moss ◽  
Stefano Iotti
Keyword(s):  
Chemical Reactions ◽  
Atp Hydrolysis ◽  
Joint Commission ◽  
Chemical Thermodynamics ◽  
Thermodynamic Quantities ◽  
Biochemical Reactions ◽  
Mathematical Transformation ◽  
Biochemical Nomenclature ◽  
Thermodynamic Potentials ◽  
Technical Report

AbstractAccording to the 1994 IUBMB-IUPAC Joint Commission on Biochemical Nomenclature (JCBN) on chemical and biochemical reactions, two categories of thermodynamics, based on different concepts and different formalisms, are established: (i) chemical thermodynamics, which employ conventional thermodynamic potentials to deal with chemical reactions [1], [2], [3]; and (ii) biochemical thermodynamics, which employ transformed thermodynamic quantities to deal with biochemical reactions based on the formalism proposed by Alberty [4], [5], [6], [7]. We showed that the two worlds of chemical and biochemical thermodynamics, which so far have been treated separately, can be reunified within the same thermodynamic framework. The thermodynamics of chemical reactions, in which all species are explicitly considered with their atoms and charge balanced, are compared with the transformed thermodynamics generally used to treat biochemical reactions where atoms and charges are not balanced. The transformed thermodynamic quantities suggested by Alberty are obtained by a mathematical transformation of the usual thermodynamic quantities. The present analysis demonstrates that the transformed values for ΔrG′0 and ΔrH′0 can be obtained directly, without performing any transformation, by simply writing the chemical reactions with all the pseudoisomers explicitly included and the elements and charges balanced. The appropriate procedures for computing the stoichiometric coefficients for the pseudoisomers are fully explained by means of an example calculation for the biochemical ATP hydrolysis reaction. It is concluded that the analysis reunifies the “two separate worlds” of conventional thermodynamics and transformed thermodynamics.

Sign in / Sign up

Export Citation Format

Share Document