Bayesian Statistical Mechanics: Entropy-Enthalpy Compensation and Universal Equation of State at the Tip of Pen

Starikov, E. B.

doi:10.3389/fphy.2018.00002

Cited by 3 publications

(6 citation statements)

References 59 publications

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“…Note that the EEC (exemplified in Figure 2b) is demonstrated on a very intricate path of mathematical conversions for only one coordinate. 43 The deciding role of the EEC effect is played by the Gibbs free energy, 44 which can be calculated using eq 11.…”

Section: Discussionmentioning

confidence: 99%

Isoconversional Methods in Thermodynamic Principles

Mianowski

Urbańczyk

2018

J. Phys. Chem. A

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The thermodynamic aspects of the methods commonly used in thermogravimetric analysis, that is, isothermal and dynamic, are presented. Models for isoconversional variants of dynamic methods are accepted. For the thermal dissociation of the solid phase, the free enthalpy of the system, called the Gibbs free energy state, and the stoichiometric principles according to de Donder's extent of reaction, were proposed as the starting point, binding the dissociative pressure in the gas phase with the rate of solid phase conversion. It was found that the isothermal methods and, surprisingly, the dynamic methods, occur in one system group, although with different energetic activity, whereas isoconversional variants of dynamic methods represent opposite effects in this range. Off-distance, which is formally defined as D = ΔΔ G, was proposed for the quantification of each analyzed case. According to the presented considerations, the isothermal and dynamic methods are dominated by enthalpy, whereas isoconversional methods are dominated by entropy.

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Section: Discussionmentioning

confidence: 99%

Isoconversional Methods in Thermodynamic Principles

Mianowski

Urbańczyk

2018

J. Phys. Chem. A

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“…By way of theoretical considerations, Starikov proved the validity of Equation (3) based on Bayesian statistical mechanics [11]. Equations ( 2) and ( 4) contain thermodynamic activation functions derived from Eyring's theory from 1935 [12].…”

Section: Outline Of the Problemmentioning

confidence: 99%

“…Accepting the general thermokinetic Equation (11), it was proved that the great majority of kinetic equations can be generalized to a single relationship (13), which contains the most important component − E RT . Using the relationship ( 13) and forming the onecolumn matrix according to (26) one obtains a very practical for analysis of experimental data, Equations ( 27)- (31) with the intercept Equations ( 16), (19), (20), allowing us to determine the Arrhenius equation parameters and the initial (Equations ( 17) and ( 19)) or isokinetic temperature (Equation ( 1)).…”

Section: Isokinetics and Initial Temperaturementioning

confidence: 99%

Isokinetic and Compensation Temperature in the Analysis of Thermal Dissociation of the Solid Phase under Dynamic Conditions

Mianowski,

Radko,

Bigda

2023

Energies

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Sets of Arrhenius parameters, determined according to known different equations for dynamic conditions, in the vast majority form the Kinetic Compensation Effect (KCE). Converting these data to the simplified components of the Eyring equation comes down to Enthalpy–Entropy Compensation (EEC), which is consistent with the second law of thermodynamics. It has been proved that the impact of the generally known Coats−Redfern solution on the equation in differential form results in an isokinetic form of the equations and a very important coordinate T0;α0 (initial temperature and conversion degree), depending on the heating rate. This makes it possible to determine the parameters of Arrhenius’ law for both in silico and experimental data. An analytical method for determining this coordinate has been proposed. These considerations have given rise to an analysis of the relationship between two temperatures: initial and isokinetic. The sense of isokinetic temperature has been verified by the parameters CQF and K. Going further, it was found that the effects of EEC can be transformed into KCE and vice versa, which means that the two temperatures should be identical, i.e., Tiso=Tc. However, the experimental data indicate that the analyzed temperatures form a sequence T0↔Tiso↔Tc≤Teq, where Teq is the equilibrium temperature.

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“…The intense debate on the nature of the H/S compensation phenomenon in the theoretical and computational community resulted in a rich literature that attempts to unravel this complex problem with simplified models. 7 A seminal theoretical work by Ryde addresses a fundamental question in H/S compensation regarding noncovalent binding, i.e., whether contacts dominated by hydrogen bonds or van der Waals forces can present different H/S compensation profiles owing to the fundamentally different nature of the weak interaction involved. 8 The report discusses this by using model systems fully dominated by either interaction type and considering the effects of molecular size and solvation.…”

Section: Introductionmentioning

confidence: 99%

“…Interestingly, it has been suggested that H/S compensation may be of evolutionary and functional advantage, providing a thermodynamic homeostasis that prevents harsh changes in free energy profiles. The intense debate on the nature of the H/S compensation phenomenon in the theoretical and computational community resulted in a rich literature that attempts to unravel this complex problem with simplified models . A seminal theoretical work by Ryde addresses a fundamental question in H/S compensation regarding noncovalent binding, i.e., whether contacts dominated by hydrogen bonds or van der Waals forces can present different H/S compensation profiles owing to the fundamentally different nature of the weak interaction involved .…”

Section: Introductionmentioning

confidence: 99%

Enthalpy–Entropy Compensation in Biomolecular Recognition: A Computational Perspective

Peccati

Jiménez‐Osés

2021

ACS Omega

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This mini-review provides an overview of the enthalpy–entropy compensation phenomenon in the simulation of biomacromolecular recognition, with particular emphasis on ligand binding. We approach this complex phenomenon from the point of view of practical computational chemistry. Without providing a detailed description of the plethora of existing methodologies already reviewed in depth elsewhere, we present a series of examples to illustrate different approaches to interpret and predict compensation phenomena at an atomistic level, which is far from trivial to predict using canonical, classic textbook assumptions.

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Bayesian Statistical Mechanics: Entropy-Enthalpy Compensation and Universal Equation of State at the Tip of Pen

Abstract: This work has shown the way to put the formal statistical-mechanical basement under the hotly debated notion of enthalpy-entropy compensation. The possibility of writing down the universal equation of state based upon the statistical mechanics is discussed here.

Cited by 3 publications

References 59 publications

Isoconversional Methods in Thermodynamic Principles

Isoconversional Methods in Thermodynamic Principles

Isokinetic and Compensation Temperature in the Analysis of Thermal Dissociation of the Solid Phase under Dynamic Conditions

Enthalpy–Entropy Compensation in Biomolecular Recognition: A Computational Perspective

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