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 Causality and stability conditions of a conformal charged fluid

2020 ◽  
Vol 2020 (8) ◽  
Author(s):  
Farid Taghinavaz
Keyword(s):  
Chemical Potential ◽  
Second Law Of Thermodynamics ◽  
Dense Medium ◽  
Wave Number ◽  
Second Law ◽  
Stability Conditions ◽  
Charged Fluid ◽  
Large Wave ◽  
The Stability ◽  
Large Wave Number

Abstract In this paper, I study the conditions imposed on a normal charged fluid so that the causality and stability criteria hold for this fluid. I adopt the newly developed General Frame (GF) notion in the relativistic hydrodynamics framework which states that hydrodynamic frames have to be fixed after applying the stability and causality conditions. To do this, I take a charged conformal matter in the flat and 3 + 1 dimension to analyze better these conditions. The causality condition is applied by looking to the asymptotic velocity of sound hydro modes at the large wave number limit and stability conditions are imposed by looking to the imaginary parts of hydro modes as well as the Routh-Hurwitz criteria. By fixing some of the transports, the suitable spaces for other ones are derived. I observe that in a dense medium having a finite U(1) charge with chemical potential μ0, negative values for transports appear and the second law of thermodynamics has not ruled out the existence of such values. Sign of scalar transports are not limited by any constraints and just a combination of vector transports is limited by the second law of thermodynamic. Also numerically it is proved that the most favorable region for transports $$ {\tilde{\upgamma}}_{1,2}, $$ γ ˜ 1 , 2 , coefficients of the dissipative terms of the current, is of negative values.

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.

Connections Between Stability, Convexity of Internal Energy, and the Second Law for Compressible Newtonian Fluids

2005 ◽  
Vol 72 (2) ◽  
pp. 299-300 ◽  
Author(s):  
Stephen E. Bechtel ◽  
Francis J. Rooney ◽  
M. Gregory Forest
Keyword(s):  
Convex Function ◽  
Bulk Modulus ◽  
Specific Heat ◽  
Internal Energy ◽  
Linear Stability ◽  
Specific Volume ◽  
Second Law Of Thermodynamics ◽  
Second Law ◽  
Isothermal Bulk Modulus ◽  
Rest State

In this note we provide proofs of the following statements for a compressible Newtonian fluid: (i) internal energy being a convex function of entropy and specific volume is equivalent to nonnegativity of both specific heat at constant volume and isothermal bulk modulus; (ii) convexity of internal energy together with the second law of thermodynamics imply linear stability of the rest state; and (iii) linear stability of the rest state together with the second law imply convexity of internal energy.

scholarly journals Entropy in universes evolving from initial to final de Sitter eras

2014 ◽  
Vol 10 (S306) ◽  
pp. 388-390
Author(s):  
José P. Mimoso ◽  
Diego Pavón
Keyword(s):  
Thermodynamic Equilibrium ◽  
Apparent Horizon ◽  
Second Law Of Thermodynamics ◽  
Concave Function ◽  
Scale Factor ◽  
Cosmological Models ◽  
Second Law ◽  
De Sitter ◽  
Expansion Phase ◽  
Conventional Radiation

AbstractThis work studies the behavior of entropy in recent cosmological models that start with an initial de Sitter expansion phase, go through the conventional radiation and matter dominated eras to be followed by a final de Sitter epoch. In spite of their seemingly similarities (observationally they are close to the Λ-CDM model), different models deeply differ in their physics. The second law of thermodynamics encapsulates the underlying microscopic, statistical description, and hence we investigate it in the present work. Our study reveals that the entropy of the apparent horizon plus that of matter and radiation inside it, increases and is a concave function of the scale factor. Thus thermodynamic equilibrium is approached in the last de Sitter era, and this class of models is thermodynamically correct. Cosmological models that do not approach equilibrium appear in conflict with the second law of thermodynamics. (Based on Mimoso & Pavon 2013)

Application of Nonequilibrium Thermodynamics in Second Law Analysis

1991 ◽  
Vol 113 (1) ◽  
pp. 33-39 ◽  
Author(s):  
Z. F. Sun ◽  
C. G. Carrington
Keyword(s):  
Heat Transfer ◽  
Nonequilibrium Thermodynamics ◽  
Local Thermodynamic Equilibrium ◽  
Second Law ◽  
Second Law Analysis ◽  
Exergy Balance ◽  
The Relationship ◽  
Heat Transfer By Radiation ◽  
Dissipation Processes ◽  
Generation Procedure

We examine the exergy balance of a multi-component fluid subject to viscous dissipation processes, heat transfer by conduction, heat transfer by radiation, matter diffusion and chemical reactions. The differential equations for exergy balance in the fluid formalize the relationship between the exergy input/output approach to second law analysis and the entropy generation procedure using the Gouy-Stodola theorem. The balance relations for mass, momentum, energy and entropy are used to establish the validity conditions for the exergy balance equations. In particular, we define the role and significance of the assumption of local thermodynamic equilibrium. The general functions and restrictions of nonequilibrium thermodynamics within second law analysis are also discussed.

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’.

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