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.

Supradegeneracy and the Second Law of Thermodynamics

2020 ◽  
Vol 45 (2) ◽  
pp. 121-132
Author(s):  
Daniel P. Sheehan
Keyword(s):  
Steady State ◽  
Statistical Mechanics ◽  
Population Inversion ◽  
Laboratory Experiments ◽  
Second Law Of Thermodynamics ◽  
Second Law ◽  
Boltzmann Factor ◽  
Energy Currents ◽  
Non Equilibrium

AbstractCanonical statistical mechanics hinges on two quantities, i. e., state degeneracy and the Boltzmann factor, the latter of which usually dominates thermodynamic behaviors. A recently identified phenomenon (supradegeneracy) reverses this order of dominance and predicts effects for equilibrium that are normally associated with non-equilibrium, including population inversion and steady-state particle and energy currents. This study examines two thermodynamic paradoxes that arise from supradegeneracy and proposes laboratory experiments by which they might be resolved.

The trouble with entropy

1998 ◽  
Vol 59 (4) ◽  
pp. 619-627 ◽  
Author(s):  
M. de HAAN ◽  
C. D. GEORGE
Keyword(s):  
Symmetry Breaking ◽  
Second Law Of Thermodynamics ◽  
The State ◽  
Large System ◽  
Second Law ◽  
Dynamical Description ◽  
Non Equilibrium

An understanding of the mechanisms leading to the symmetry breaking of the dynamical description of a large system with respect to the direction of time is necessary, but not sufficient to ensure the finding of a functional of the state of the system that would satisfy the requirements placed by the Second Law of Thermodynamics upon the non-equilibrium entropy S.

Cosmology in scalar–tensor–vector theory via thermodynamics

2018 ◽  
Vol 33 (24) ◽  
pp. 1850137 ◽  
Author(s):  
Onur Siginc ◽  
Mustafa Salti ◽  
Hilmi Yanar ◽  
Oktay Aydogdu
Keyword(s):  
Apparent Horizon ◽  
Second Law Of Thermodynamics ◽  
Entropy Function ◽  
Second Law ◽  
Generalized Second Law ◽  
Vector Theory ◽  
Theory Of Gravity ◽  
The Universe ◽  
Non Equilibrium

Assuming the universe as a thermodynamical system, the second law of thermodynamics can be extended to another form including the sum of matter and horizon entropies, which is called the generalized second law of thermodynamics. The generalized form of the second law (GSL) is universal which means it holds both in non-equilibrium and equilibrium pictures of thermodynamics. Considering the universe is bounded by a dynamical apparent horizon, we investigate the nature of entropy function for the validity of GSL in the scalar–tensor–vector (STEVE) theory of gravity.

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>

scholarly journals Entropy and the Second Law of Thermodynamics—The Nonequilibrium Perspective

Entropy ◽  
2020 ◽  
Vol 22 (7) ◽  
pp. 793
Author(s):  
Henning Struchtrup
Keyword(s):  
Thermodynamic Equilibrium ◽  
Nonequilibrium Thermodynamics ◽  
Local Thermodynamic Equilibrium ◽  
Thermodynamic Temperature ◽  
Second Law Of Thermodynamics ◽  
Equilibrium States ◽  
Second Law ◽  
Rest State ◽  
The Stability

An alternative to the Carnot-Clausius approach for introducing entropy and the second law of thermodynamics is outlined that establishes entropy as a nonequilibrium property from the onset. Five simple observations lead to entropy for nonequilibrium and equilibrium states, and its balance. Thermodynamic temperature is identified, its positivity follows from the stability of the rest state. It is shown that the equations of engineering thermodynamics are valid for the case of local thermodynamic equilibrium, with inhomogeneous states. The main findings are accompanied by examples and additional discussion to firmly imbed classical and engineering thermodynamics into nonequilibrium thermodynamics.

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’.

Spontaneous changes

2018 ◽  
Author(s):  
Dennis Sherwood ◽  
Paul Dalby
Keyword(s):  
Chemical Reactions ◽  
Equilibrium States ◽  
Phase Changes ◽  
Second Law ◽  
Vacuum Mixing ◽  
Non Equilibrium

To set the scene for the Second Law, this (non-mathematical) chapter explores our experience of spontaneous changes - such as the expansion of a gas into a vacuum, mixing, phase changes and many chemical reactions - demonstrating that they are all irreversible, and proceed unidirectionally from non-equilibrium states to equilibrium states. Furthermore, they all comply with the First Law. The First Law therefore cannot be used as a predictor of spontaneity. What, then, can be used as a predictor?

scholarly journals The Second Law and Entropy Misconceptions Demystified

Entropy ◽  
2020 ◽  
Vol 22 (6) ◽  
pp. 648
Author(s):  
Milivoje M. Kostic
Keyword(s):  
Quantum Physics ◽  
Open Systems ◽  
Second Law Of Thermodynamics ◽  
Second Law ◽  
Mass Energy ◽  
Energy Potential ◽  
Ordered Structures ◽  
Thermodynamic Entropy ◽  
Thermal Disorder ◽  
Non Equilibrium

The challenges and claims of hypothetical violations of the Second Law of thermodynamics have been a topic of many scientific, philosophical and social publications, even in the most prestigious scientific journals. Fascination with challenging the Second Law has further accelerated throughout the development of statistical and quantum physics, and information theory. It is phenomenologically reasoned here that non-equilibrium, useful work-energy potential is always dissipated to heat, and thus thermodynamic entropy (a measure of thermal disorder, not any other disorder) is generated always and everywhere, at any scale without exception, including life processes, open systems, micro-fluctuations, gravity or entanglement. Furthermore, entropy cannot be destroyed by any means at any scale (entropy is conserved in ideal, reversible processes and irreversibly generated in real processes), and thus, entropy cannot overall decrease, but only overall increase. Creation of ordered structures or live species always dissipate useful energy and generate entropy, without exception, and thus without Second Law violation. Entropy destruction would imply spontaneous increase in non-equilibrium, with mass-energy flux displacement against cause-and-effect, natural forces, as well as negate the reversible existence of the very equilibrium. In fact, all resolved challengers’ paradoxes and misleading violations of the Second Law to date have been resolved in favor of the Second Law and never against. We are still to witness a single, still open Second Law violation, to be confirmed.

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