scholarly journals Non-Equilibrium Thermodynamics View on Kinetics of Autocatalytic Reactions—Two Illustrative Examples

Molecules ◽  
2021 ◽  
Vol 26 (3) ◽  
pp. 585
Author(s):  
Miloslav Pekař
Keyword(s):  
Second Law Of Thermodynamics ◽  
Mass Action ◽  
Rate Equations ◽  
Equilibrium Thermodynamics ◽  
Mass Action Kinetics ◽  
Autocatalytic Reactions ◽  
Chemical Potentials ◽  
Entropic Inequality ◽  
Reaction Stoichiometry ◽  
Non Equilibrium

Autocatalytic reactions are in certain contrast with the linear algebra of reaction stoichiometry, on which rate equations respecting the permanence of atoms are constructed. These mathematical models of chemical reactions are called conservative. Using a non-equilibrium thermodynamics-based theory of chemical kinetics, it is shown how to introduce autocatalytic step into such (conservative) rate equation properly. Further, rate equations based on chemical potentials or affinities are derived, and conditions for the consistency of rate equations with the entropic inequality (the second law of thermodynamics) are illustrated. The theory illustrated here can be viewed as a tool for verifying and generalizing traditional mass-action kinetics by means of modern non-equilibrium thermodynamics, which is able to deal also with such rather problematic cases.

scholarly journals A Non-Equilibrium Thermodynamics-Based View of the Kinetics of Autocatalytic Reactions – a Simple Illustrative Example

2020 ◽  
Author(s):  
Miloslav Pekař
Keyword(s):  
Second Law Of Thermodynamics ◽  
Rate Equations ◽  
Second Law ◽  
Equilibrium Thermodynamics ◽  
Autocatalytic Reactions ◽  
Chemical Potentials ◽  
Entropic Inequality ◽  
Reaction Stoichiometry ◽  
Kinetics Of ◽  
Non Equilibrium

Autocatalytic reactions are in a certain contrast with the linear algebra of reaction stoichiometry, on whose basis rate equations respecting the permanence of atoms are constructed. These mathematical models of chemical reactions are termed conservative.Using a non-equilibrium thermodynamics-based theory of chemical kinetics, this paper demonstrates how to properly introduce an autocatalytic step into a (conservative) rate equation. Further, rate equations based on chemical potentials or affinities are derived, and conditions for the consistency of rate equations with entropic inequality (the second law of thermodynamics) are illustrated.<br><div><br></div>

scholarly journals A Non-Equilibrium Thermodynamics-Based View of the Kinetics of Autocatalytic Reactions – a Simple Illustrative Example

2020 ◽  
Author(s):  
Miloslav Pekař
Keyword(s):  
Second Law Of Thermodynamics ◽  
Rate Equations ◽  
Second Law ◽  
Equilibrium Thermodynamics ◽  
Autocatalytic Reactions ◽  
Chemical Potentials ◽  
Entropic Inequality ◽  
Reaction Stoichiometry ◽  
Kinetics Of ◽  
Non Equilibrium

Autocatalytic reactions are in a certain contrast with the linear algebra of reaction stoichiometry, on whose basis rate equations respecting the permanence of atoms are constructed. These mathematical models of chemical reactions are termed conservative.Using a non-equilibrium thermodynamics-based theory of chemical kinetics, this paper demonstrates how to properly introduce an autocatalytic step into a (conservative) rate equation. Further, rate equations based on chemical potentials or affinities are derived, and conditions for the consistency of rate equations with entropic inequality (the second law of thermodynamics) are illustrated.<br><div><br></div>

Thermodynamics and foundations of mass-action kinetics

2005 ◽  
Vol 30 (1-2) ◽  
pp. 3-113 ◽  
Author(s):  
Miloslav Pekař
Keyword(s):  
Chemical Kinetics ◽  
Reaction Rate ◽  
Chemical Potential ◽  
Kinetic Equations ◽  
Reaction Rates ◽  
Equilibrium States ◽  
Mass Action ◽  
Rate Equations ◽  
Mass Action Kinetics ◽  
Non Equilibrium

A critical overview is given of phenomenological thermodynamic approaches to reaction rate equations of the type based on the law of mass-action. The review covers treatments based on classical equilibrium and irreversible (linear) thermodynamics, extended irreversible, rational and continuum thermodynamics. Special attention is devoted to affinity, the applications of activities in chemical kinetics and the importance of chemical potential. The review shows that chemical kinetics survives as the touchstone of these various thermody-namic theories. The traditional mass-action law is neither demonstrated nor proved and very often is only introduced post hoc into the framework of a particular thermodynamic theory, except for the case of rational thermodynamics. Most published “thermodynamic'’ kinetic equations are too complicated to find application in practical kinetics and have merely theoretical value. Solely rational thermodynamics can provide, in the specific case of a fluid reacting mixture, tractable rate equations which directly propose a possible reaction mechanism consistent with mass conservation and thermodynamics. It further shows that affinity alone cannot determine the reaction rate and should be supplemented by a quantity provisionally called constitutive affinity. Future research should focus on reaction rates in non-isotropic or non-homogeneous mixtures, the applicability of traditional (equilibrium) expressions relating chemical potential to activity in non-equilibrium states, and on using activities and activity coefficients determined under equilibrium in non-equilibrium states.

Tensorielle chemische Potentiale — eine notwendige Erweiterung der Gibbs'schen Thermodynamik / Tensorial Chemical Potentials — a Necessary Extension of Gibbs' Thermodynamics

1975 ◽  
Vol 30 (11) ◽  
pp. 1433-1440 ◽  
Author(s):  
B. Stuke
Keyword(s):  
Chemical Potential ◽  
Spherically Symmetric ◽  
Relaxation Phenomena ◽  
Pressure Tensor ◽  
Equilibrium Thermodynamics ◽  
Equilibrium Conditions ◽  
Chemical Potentials ◽  
Thermodynamic Pressure ◽  
Fundamental Equations ◽  
Non Equilibrium

In a system with a non spherically symmetric pressure tensor, the chemical potential of at least one substance in the system has to be a tensor of the same character as the pressure. The necessary generalization of Gibbs' fundamental equations of thermodynamics is presented. Being already of consequence for equilibrium, this extension is more important for non-equilibrium thermodynamics, in particular for the proper thermodynamic formulation of general relaxation phenomena. Reasons are given why the distinction between dynamic and thermodynamic pressure, originating from the incomplete formulation of customary thermodynamics, is erroneous. Finally a tensorial temperature is introduced which can exist under extreme non-equilibrium conditions, e.g. shock waves

scholarly journals Unified Extended Irreversible Thermodynamics and the Stability of Relativistic Theories for Dissipation

2021 ◽  
Vol 8 ◽  
Author(s):  
Lorenzo Gavassino ◽  
Marco Antonelli
Keyword(s):  
Second Law Of Thermodynamics ◽  
Direct Consequence ◽  
Irreversible Thermodynamics ◽  
Effective Field ◽  
Navier Stokes ◽  
Equilibrium Thermodynamics ◽  
Diffusion Type ◽  
Extended Irreversible Thermodynamics ◽  
First Order ◽  
Non Equilibrium

In a relativistic context, the main purpose of Extended Irreversible Thermodynamics (EIT) is to generalize the principles of non-equilibrium thermodynamics to the domain of fluid dynamics. In particular, the theory aims at modeling any diffusion-type process (like heat as diffusion of energy, viscosity as diffusion of momentum, charge-conductivity as diffusion of particles) directly from thermodynamic laws. Although in Newtonian physics this task can be achieved with a first-order approach to dissipation (i.e. Navier–Stokes–Fourier like equations), in a relativistic framework the relativity of simultaneity poses serious challenges to the first-order methodology, originating instabilities which are, instead, naturally eliminated within EIT. The first part of this work is dedicated to reviewing the most recent progress made in understanding the mathematical origin of this instability problem. In the second part, we present the formalism that arises by promoting non-equilibrium thermodynamics to a classical effective field theory. We call this approach Unified Extended Irreversible Thermodynamics (UEIT), because it contains, as particular cases, EIT itself, in particular the Israel-Stewart theory and the divergence-type theories, plus Carter’s approach and most branches of non-equilibrium thermodynamics, such as relativistic chemistry and radiation hydrodynamics. We use this formalism to explain why all these theories are stable by construction (provided that the microscopic input is correct), showing that their (Lyapunov) stability is a direct consequence of the second law of thermodynamics.

scholarly journals Homo-Oligomerisation in Signal Transduction: Dynamics, Homeostasis, Ultrasensitivity, Bistability

2019 ◽  
Author(s):  
Daniel Koch
Keyword(s):  
Signal Transduction ◽  
Enzyme Regulation ◽  
Monomer Concentration ◽  
Mass Action ◽  
Rate Equations ◽  
Complex Dynamic ◽  
Mass Action Kinetics ◽  
Post Translational Modifications ◽  
Potential Signal ◽  
Reaction Routes

AbstractHomo-oligomerisation of proteins is a ubiquitous phenomenon whose exact role remains unclear in many cases. To identify novel functions, this paper provides an exploration of general dynamical mathematical models of homo-oligomerisation. Simulation and analysis of these models show that homo-oligomerisation on its own allows for a remarkable variety of complex dynamic and steady-state regulatory behaviour such as transient overshoots or homeostatic control of monomer concentration. If post-translational modifications are considered, however, conventional mass-action kinetics leads to thermodynamic inconsistencies due to asymmetric combinatorial expansion of reaction routes. Introducing a conservation principle to balance rate equations re-establishes thermodynamic consistency. Using such balanced models it is shown that oligomerisation can lead to bistability by enabling pseudo-multisite modification and kinetic pseudo-cooperativity via multi-enzyme regulation, thereby constituting a novel motif for bistable modification reactions. Due to these potential signal processing capabilities, homo-oligomerisation could play far more versatile roles in signal transduction than previously appreciated.

Non-Equilibrium Dislocation Dynamics in Semiconductor Crystals and Superlattices

2018 ◽  
Vol 43 (2) ◽  
pp. 163-170 ◽  
Author(s):  
David Jou ◽  
Liliana Restuccia
Keyword(s):  
Mechanical Properties ◽  
Heat Flux ◽  
Relative Orientation ◽  
Dislocation Dynamics ◽  
Rate Equations ◽  
Internal Variables ◽  
Equilibrium Thermodynamics ◽  
Semiconductor Crystals ◽  
Standard Procedures ◽  
Non Equilibrium

AbstractA model for semiconductor crystals and superlattices with dislocations proposed in a previous paper is used here to study the thermal, electrical and mechanical properties of these defective materials. The standard procedures of non-equilibrium thermodynamics with internal variables are applied to derive in the linear approximation constitutive equations as well as rate equations for the dislocation, charges and heat flux fields, containing coupled effects among the different fields. A new dislocation tensor is used to describe the geometry of the dislocation lines, because their relative orientation with respect to the superlattice interfaces is very relevant.

scholarly journals Simple, Accurate and User-Friendly Differential Constitutive Model for the Rheology of Entangled Polymer Melts and Solutions from Non-Equilibrium Thermodynamics

2020 ◽  
Author(s):  
Pavlos Stephanou ◽  
Ioanna Tsimouri ◽  
Vlasis Mavrantzas
Keyword(s):  
Large Scale ◽  
Polymer Melts ◽  
Second Law Of Thermodynamics ◽  
Equilibrium Thermodynamics ◽  
High Shear Rates ◽  
Entangled Polymer ◽  
Conformation Tensor ◽  
Entangled Polymer Melts ◽  
User Friendly ◽  
Non Equilibrium

In a recent reformulation of the Marrucci-Ianniruberto constitutive equation for the rheology of entangled polymer melts in the context of non-equilibrium thermodynamics, rather large values of the convective constraint release parameter \beta_{ccr} had to be used in order not to violate the second law of thermodynamics. In this work, we present an appropriate modification of the model which avoids the splitting of the evolution equation for the conformation tensor into an orientation and a stretching part. Then, thermodynamic admissibility dictates simply that \beta_{ccr}&ge; 0, thus allowing for more realistic values of \beta_{ccr} to be chosen. Moreover, and in view of recent experimental evidence for a transient stress undershoot (following the overshoot) at high shear rates whose origin may be traced back to molecular tumbling, we have incorporated in the model additional terms accounting, at least in an approximate way, for non-affine deformation through a slip parameter \xi. Use of the new model to describe available experimental data for the transient and steady-state shear and elongational rheology of entangled polystyrene melts and solutions shows close agreement. Overall, the modified model proposed here combines simplicity with accuracy, which renders it an excellent choice for managing complex viscoelastic fluid flows in large-scale numerical calculations.

Non-equilibrium Thermodynamical Principles for Chemical Reactions with Mass-Action Kinetics

2017 ◽  
Vol 77 (4) ◽  
pp. 1562-1585 ◽  
Author(s):  
Alexander Mielke ◽  
Robert I. A. Patterson ◽  
Mark A. Peletier ◽  
D. R. Michiel Renger
Keyword(s):  
Chemical Reactions ◽  
Mass Action ◽  
Mass Action Kinetics ◽  
Non Equilibrium

scholarly journals A facilitated diffusion model constrained by the probability isotherm: a pedagogical exercise in intuitive non-equilibrium thermodynamics

2017 ◽  
Vol 4 (6) ◽  
pp. 170429 ◽  
Author(s):  
Brian Chapman
Keyword(s):  
Kinetic Modelling ◽  
Reaction Rates ◽  
Mass Action ◽  
Model Parameters ◽  
Facilitated Diffusion ◽  
Equilibrium Thermodynamics ◽  
New Approach ◽  
Rate Limiting ◽  
Substrate Concentrations ◽  
Non Equilibrium

This paper seeks to develop a more thermodynamically sound pedagogy for students of biological transport than is currently available from either of the competing schools of linear non-equilibrium thermodynamics (LNET) or Michaelis–Menten kinetics (MMK). To this end, a minimal model of facilitated diffusion was constructed comprising four reversible steps: cis- substrate binding, cis → trans bound enzyme shuttling, trans -substrate dissociation and trans → cis free enzyme shuttling. All model parameters were subject to the second law constraint of the probability isotherm, which determined the unidirectional and net rates for each step and for the overall reaction through the law of mass action. Rapid equilibration scenarios require sensitive ‘tuning’ of the thermodynamic binding parameters to the equilibrium substrate concentration. All non-equilibrium scenarios show sigmoidal force–flux relations, with only a minority of cases having their quasi -linear portions close to equilibrium. Few cases fulfil the expectations of MMK relating reaction rates to enzyme saturation. This new approach illuminates and extends the concept of rate-limiting steps by focusing on the free energy dissipation associated with each reaction step and thereby deducing its respective relative chemical impedance. The crucial importance of an enzyme's being thermodynamically ‘tuned’ to its particular task, dependent on the cis- and trans- substrate concentrations with which it deals, is consistent with the occurrence of numerous isoforms for enzymes that transport a given substrate in physiologically different circumstances. This approach to kinetic modelling, being aligned with neither MMK nor LNET, is best described as intuitive non-equilibrium thermodynamics, and is recommended as a useful adjunct to the design and interpretation of experiments in biotransport.

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