scholarly journals Intrinsic properties of conservation-dissipation formalism of irreversible thermodynamics

2020 ◽  
Vol 378 (2170) ◽  
pp. 20190177 ◽  
Author(s):  
Wen-An Yong
Keyword(s):  
Nonequilibrium Thermodynamics ◽  
Second Law Of Thermodynamics ◽  
Irreversible Thermodynamics ◽  
Irreversible Processes ◽  
Second Law ◽  
Gradient Structure ◽  
Intrinsic Properties ◽  
Theme Issue ◽  
Onsager Relations ◽  
Refined Formulation

This paper proposes four fundamental requirements for establishing PDEs (partial differential equations) modelling irreversible processes. We show that the PDEs derived via the CDF (conservation-dissipation formalism) meet all the requirements. In doing so, we find useful constraints on the freedoms of CDF and point out that a shortcoming of the formalism can be remedied with the help of the Maxwell iteration. It is proved that the iteration preserves the gradient structure and strong dissipativeness of the CDF-based PDEs. A refined formulation of the second law of thermodynamics is given to characterize the strong dissipativeness, while the gradient structure corresponds to nonlinear Onsager relations. Further advantages and limitations of CDF will also be presented. This article is part of the theme issue ‘Fundamental aspects of nonequilibrium thermodynamics’.

scholarly journals Relationships between rational extended thermodynamics and extended irreversible thermodynamics

2020 ◽  
Vol 378 (2170) ◽  
pp. 20190172 ◽  
Author(s):  
David Jou
Keyword(s):  
Nonequilibrium Thermodynamics ◽  
Irreversible Thermodynamics ◽  
Extended Thermodynamics ◽  
Internal Variables ◽  
Second Law ◽  
Hamiltonian Approach ◽  
Theme Issue ◽  
Extended Irreversible Thermodynamics ◽  
Independent Variables ◽  
Rational Extended Thermodynamics

We consider a few conceptual questions on extended thermodynamics, with the aim to contribute to a higher contact between rational extended thermodynamics and extended irreversible thermodynamics. Both theories take a number of fluxes as independent variables, but they differ in the formalism being used to deal with the exploitation of the second principle (rational thermodynamics in the first one and classical irreversible thermodynamics in the second one). Rational extended thermodynamics is more restricted in the range of systems to be analysed, but it is able to obtain a wider number of restrictions and deeper specifications from the second law. By contrast, extended irreversible thermodynamics is more phenomenological, its mathematical formalism is more elementary, but it may deal with a wider diversity of systems although with less detail. Further comparison and dialogue between both branches of extended thermodynamics would be useful for a fuller deployment and deepening of extended thermodynamics. Besides these two approaches, one should also consider the Hamiltonian approach, formalisms with internal variables, and more microscopic approaches, based on kinetic theory or on non-equilibrium ensemble formalisms. This article is part of the theme issue ‘Fundamental aspects of nonequilibrium thermodynamics’.

Thermodynamics as a fundamental science of reliability

2016 ◽  
Vol 230 (6) ◽  
pp. 598-608 ◽  
Author(s):  
Anahita Imanian ◽  
Mohammad Modarres
Keyword(s):  
Energy Dissipation ◽  
Entropy Generation ◽  
Damage Model ◽  
Second Law Of Thermodynamics ◽  
Reliability Function ◽  
Cumulative Damage ◽  
Life Assessment ◽  
Irreversible Processes ◽  
Second Law ◽  
Cumulative Hazard

Cumulative hazard and cumulative damage are important models for reliability and structural integrity assessment. This article reviews a previously developed thermodynamic entropy–based damage model and derives and demonstrates an equivalent reliability function. As such, a thermodynamically inspired approach to developing new definitions of cumulative hazard, cumulative damage, and life models of structures and components based on the second law of thermodynamics is presented. The article defines a new unified measure of damage in terms of energy dissipation associated with multiple interacting irreversible processes that represent the underlying failure mechanisms that cause damage and failure. Since energy dissipation leads to entropy generation in materials, it has been shown and experimentally demonstrated that the use of the total entropy generated in any degradation process is measurable and can ultimately be used to represent the time of failure of structures and components. This description therefore connects the second law of thermodynamics to the conventional models of reliability used in life assessment. Any variability in the entropic endurance to failure and uncertainties about the parameters of the entropic-based damage model lead to the time-to-failure distribution. In comparison with the conventional probabilistic reliability methods, deriving the reliability function in terms of the entropy generation can offer a general and more fundamental approach to representation of reliability. The entropic-based theory of damage and the equivalent reliability approach are demonstrated and confirmed experimentally by applying the complex interactive corrosion-fatigue degradation mechanism to samples of aluminum materials.

scholarly journals A Derivation of the Main Relations of Nonequilibrium Thermodynamics

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Vladimir N. Pokrovskii
Keyword(s):  
Nonequilibrium Thermodynamics ◽  
Second Law Of Thermodynamics ◽  
Thermodynamic System ◽  
Internal Variables ◽  
Second Law ◽  
Basic Principles ◽  
First Law Of Thermodynamics ◽  
Sum Of Products ◽  
Thermodynamic Forces ◽  
Production Of Entropy

The principles of nonequilibrium thermodynamics are discussed, using the concept of internal variables that describe deviations of a thermodynamic system from the equilibrium state. While considering the first law of thermodynamics, work of internal variables is taken into account. It is shown that the requirement that the thermodynamic system cannot fulfil any work via internal variables is equivalent to the conventional formulation of the second law of thermodynamics. These statements, in line with the axioms introducing internal variables can be considered as basic principles of nonequilibrium thermodynamics. While considering stationary nonequilibrium situations close to equilibrium, it is shown that known linear parities between thermodynamic forces and fluxes and also the production of entropy, as a sum of products of thermodynamic forces and fluxes, are consequences of fundamental principles of thermodynamics.

scholarly journals Thermodynamics in Modified Gravity with Curvature Matter Coupling

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
M. Sharif ◽  
M. Zubair
Keyword(s):  
Modified Gravity ◽  
Nonequilibrium Thermodynamics ◽  
Second Law Of Thermodynamics ◽  
Second Law ◽  
Production Term ◽  
Matter Coupling ◽  
Generalized Second Law ◽  
Laws Of Thermodynamics ◽  
Coupling Parameters ◽  
Modified Theory

The first and generalized second laws of thermodynamics are studied inf(R,Lm)gravity, a more general modified theory with curvature matter coupling. It is found that one can translate the Friedmann equations to the form of first law accompanied with entropy production term. This behavior is due to the nonequilibrium thermodynamics in this theory. We establish the generalized second law of thermodynamics and develop the constraints on coupling parameters for two specific models. It is concluded that laws of thermodynamics in this modified theory are more general and can reproduce the corresponding results in Einstein,f(R)gravity, andf(R)gravity with arbitrary as well as nonminimal curvature matter coupling.

scholarly journals Entropy meters and the entropy of non-extensive systems

2014 ◽  
Vol 470 (2167) ◽  
pp. 20140192 ◽  
Author(s):  
Elliott H. Lieb ◽  
Jakob Yngvason
Keyword(s):  
Second Law Of Thermodynamics ◽  
Surface Effects ◽  
Equilibrium States ◽  
Second Law ◽  
Intrinsic Properties ◽  
Mesoscopic Systems ◽  
Entropy Functions ◽  
Non Equilibrium

In our derivation of the second law of thermodynamics from the relation of adiabatic accessibility of equilibrium states, we stressed the importance of being able to scale a system's size without changing its intrinsic properties. This leaves open the question of defining the entropy of macroscopic, but unscalable systems, such as gravitating bodies or systems where surface effects are important. We show here how the problem can be overcome, in principle, with the aid of an ‘entropy meter’. An entropy meter can also be used to determine entropy functions for non-equilibrium states and mesoscopic systems.

scholarly journals Variational principles and nonequilibrium thermodynamics

2020 ◽  
Vol 378 (2170) ◽  
pp. 20190178 ◽  
Author(s):  
P. Ván ◽  
R. Kovács
Keyword(s):  
Symplectic Structure ◽  
Evolution Equations ◽  
Nonequilibrium Thermodynamics ◽  
Variational Principles ◽  
Dissipative Systems ◽  
Second Law ◽  
Theme Issue ◽  
Dissipative Processes ◽  
Variational Techniques ◽  
Lagrange Form

Variational principles play a fundamental role in deriving the evolution equations of physics. They work well in the case of non-dissipative evolution, but for dissipative systems, the variational principles are not unique and not constructive. With the methods of modern nonequilibrium thermodynamics, one can derive evolution equations for dissipative phenomena and, surprisingly, in several cases, one can also reproduce the Euler–Lagrange form and symplectic structure of the evolution equations for non-dissipative processes. In this work, we examine some demonstrative examples and compare thermodynamic and variational techniques. Then, we argue that, instead of searching for variational principles for dissipative systems, there is another viable programme: the second law alone can be an effective tool to construct evolution equations for both dissipative and non-dissipative processes. This article is part of the theme issue ‘Fundamental aspects of nonequilibrium thermodynamics’.

scholarly journals APPLICATION OF THE POSTULATE OF NONEQUILIBRIUM TO CALCULATE THE NONEQUILIBRIUM OF SYSTEMS OF DISSIMILAR GASES AND LIQUIDS

2020 ◽  
Vol 17 (34) ◽  
pp. 998-1011
Author(s):  
Vladimir V RYNDIN
Keyword(s):  
Equilibrium State ◽  
Quantitative Characteristic ◽  
Second Law Of Thermodynamics ◽  
Irreversible Processes ◽  
Second Law ◽  
Nonequilibrium Systems ◽  
Real Property ◽  
Pure Solvent ◽  
Classical Thermodynamics ◽  
Isothermal Mixing

The postulate of nonequilibrium is at the heart of the second law of thermodynamics. According to this postulate, there is a real property of matter – “nonequilibrium,” which characterizes the uneven distribution of matter and motion in space. All processes (reversible and irreversible) can occur only in nonequilibrium systems. As a quantitative characteristic of the nonequilibrium of the system, the maximum work that can be performed during the transition of the nonequilibrium system to the equilibrium state is considered. The only formulation of the second law is given. When real (irreversible) processes occur, the nonequilibrium of the isolated system decreases, and in reversible processes, the nonequilibrium in the system of locally equilibrium subsystems does not change (the increment of one kind of the nonequilibrium entirely compensated by a decrease in the disequilibrium of some other kind). When the system reaches an equilibrium state, the disequilibrium disappears, and all processes cease. The article provides a calculated confirmation of the theoretical provisions of the concept of nonequilibrium and its mathematical apparatus by examples of determining the loss of the nonequilibrium of system when an isothermal mixing of dissimilar gases, and changes of nonequilibrium of system "pure solvent – solution" in the transition of part of the solvent in the solution. The mixing of the same gases leads to the Gibbs paradox, which is also considered in this paper. The concept of nonequilibrium was developed and the quantitative characteristics (measures) of nonequilibrium of the system were introduced allow to study nonequilibrium systems consisting of locally equilibrium subsystems in the sections of classical thermodynamics as simply as individual equilibrium systems.

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