scholarly journals Contact Temperature as an Internal Variable of Discrete Systems in Non-Equilibrium

2018 ◽  
pp. 607-620 ◽  
Author(s):  
Wolfgang Muschik
Keyword(s):  
Discrete Systems ◽  
Internal Variable ◽  
Contact Temperature ◽  
Non Equilibrium

scholarly journals Discrete systems in thermal physics and engineering: a glance from non-equilibrium thermodynamics

2021 ◽  
Author(s):  
W. Muschik
Keyword(s):  
Discrete Systems ◽  
Embedding Theorem ◽  
Contact Temperature ◽  
State Function ◽  
Thermal Physics ◽  
Temperature Changes ◽  
Primitive Concept ◽  
Equilibrium Processes ◽  
Cyclic Processes ◽  
Non Equilibrium

AbstractNon-equilibrium processes in Schottky systems generate by projection onto the equilibrium subspace reversible accompanying processes for which the non-equilibrium variables are functions of the equilibrium ones. The embedding theorem which guarantees the compatibility of the accompanying processes with the non-equilibrium entropy is proved. The non-equilibrium entropy is defined as a state function on the non-equilibrium state space containing the contact temperature as a non-equilibrium variable. If the entropy production does not depend on the internal energy, the contact temperature changes into the thermostatic temperature also in non-equilibrium, a fact which allows to use temperature as a primitive concept in non-equilibrium. The dissipation inequality is revisited, and an efficiency of generalized cyclic processes beyond the Carnot process is achieved.

scholarly journals Second Law and Non-Equilibrium Entropy of Schottky Systems --Doubts and Verification--

2018 ◽  
Author(s):  
Wolfgang Muschik
Keyword(s):  
Open Systems ◽  
Embedding Theorem ◽  
Contact Temperature ◽  
Second Law ◽  
Molar Entropy ◽  
Primitive Concept ◽  
Historical Remark ◽  
Clausius Inequality ◽  
Non Equilibrium

Meixner's historical remark in 1969 "... it can be shown that the concept of entropy in the absence of equilibrium is in fact not only questionable but that it cannot even be defined...." is investigated from today's insight. Several statements --such as the three laws of phenomenological thermodynamics, the embedding theorem and the adiabatical uniqueness-- are used to get rid of non-equilibrium entropy as a primitive concept. In this framework, Clausius inequality of open systems can be derived by use of the defining inequalities which establish the non-equilibrium quantities contact temperature and non-equilibrium molar entropy which allow to describe the interaction between the Schottky system and its controlling equilibrium environment.

Material’s Chemical Reaction Progression Variables Fluctuating and Detailed Equilibrium Principle

2012 ◽  
Vol 424-425 ◽  
pp. 861-864
Author(s):  
Qing Hua Zou
Keyword(s):  
Chemical Reaction ◽  
Equilibrium Equation ◽  
Internal Variable ◽  
Local System ◽  
Mean Square ◽  
Mean Square Deviation ◽  
Variable Chemical ◽  
The Mean ◽  
The Stability ◽  
Non Equilibrium

The paper derived and gave the mean square deviation formula relating to the internal variable (chemical reaction progression variable) fluctuating of the linear non–equilibrium local system, and also rendered the condition of the stability. Furthermore, It discussed the related relations among the corresponding mean square deviation, the detailed equilibrium equation, the relax time and other thermal mechanics variables

scholarly journals Kluitenberg–Verhás Rheology of Solids in the GENERIC Framework

2019 ◽  
Vol 44 (3) ◽  
pp. 247-259 ◽  
Author(s):  
Mátyás Szücs ◽  
Tamás Fülöp
Keyword(s):  
General Equation ◽  
Rheological Model ◽  
Soft Rock ◽  
Internal Variable ◽  
Equilibrium Thermodynamics ◽  
Practical Applications ◽  
Generic Framework ◽  
Ground Conditions ◽  
Model Family ◽  
Non Equilibrium

Abstract The internal variable methodology of non-equilibrium thermodynamics, with a symmetric tensorial internal variable, provides an important rheological model family for solids, the so-called Kluitenberg–Verhás model family [Cs. Asszonyi et al., Contin. Mech. Thermodyn. 27, 2015]. This model family is distinguished not only by theoretical aspects but also on experimental grounds (see [Cs. Asszonyi et al., Period. Polytech., Civ. Eng. 60, 2016] for plastics and [W. Lin et al., Rock Engineering in Difficult Ground Conditions (Soft Rock and Karst), Proceedings of Eurock’09, 2009; K. Matsuki, K. Takeuchi, Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 30, 1993; K. Matsuki, Int. J. Rock Mech. Min. Sci. 45, 2008] for rocks). In this article, we present and discuss how the internal variable formulation of the Kluitenberg–Verhás model family can be presented in the non-equilibrium thermodynamical framework GENERIC (General Equation for the Non-Equilibrium Reversible–Irreversible Coupling) [H. C. Öttinger, Beyond Equilibrium Thermodynamics, 2005; M. Grmela, J. Non-Newton. Fluid Mech. 165, 2010; M. Grmela, H. C. Öttinger, Phys. Rev. E 56, 1997; H. C. Öttinger, M. Grmela, Phys. Rev. E 56, 1997], for the benefit of both thermodynamical methodologies and promising practical applications.

scholarly journals Second Law and Non-Equilibrium Entropy of Schottky Systems—Doubts and Verification–

Entropy ◽  
2018 ◽  
Vol 20 (10) ◽  
pp. 740 ◽  
Author(s):  
Wolfgang Muschik
Keyword(s):  
Open Systems ◽  
Embedding Theorem ◽  
Contact Temperature ◽  
Second Law ◽  
Molar Entropy ◽  
Primitive Concept ◽  
Historical Remark ◽  
Clausius Inequality ◽  
Non Equilibrium

Meixner’s historical remark in 1969 “... it can be shown that the concept of entropy in the absence of equilibrium is in fact not only questionable but that it cannot even be defined....” is investigated from today’s insight. Several statements—such as the three laws of phenomenological thermodynamics, the embedding theorem and the adiabatical uniqueness—are used to get rid of non-equilibrium entropy as a primitive concept. In this framework, Clausius inequality of open systems can be derived by use of the defining inequalities which establish the non-equilibrium quantities contact temperature and non-equilibrium molar entropy which allow to describe the interaction between the Schottky system and its controlling equilibrium environment.

Fluctuating of Chemical Reaction Progression Variable

2011 ◽  
Vol 347-353 ◽  
pp. 927-930
Author(s):  
Qing Hua Zou
Keyword(s):  
Chemical Reaction ◽  
Equilibrium Equation ◽  
Internal Variable ◽  
Local System ◽  
Mean Square ◽  
Mean Square Deviation ◽  
Variable Chemical ◽  
The Mean ◽  
The Stability ◽  
Non Equilibrium

Abstract: The paper derived and gave the mean square deviation formula relating to the internal variable (chemical reaction progression variable) fluctuating of the linear non–equilibrium local system, and also rendered the condition of the stability. Furthermore, It discussed the related relations among the corresponding mean square deviation, the detailed equilibrium equation, the relax time and other thermal mechanics variables.

scholarly journals Non-equilibrium temperatures and heat transport in nanosystems with defects, described by a tensorial internal variable

2016 ◽  
Vol 7 (2) ◽  
pp. 81-97 ◽  
Author(s):  
Liliana Restuccia
Keyword(s):  
Heat Flux ◽  
Heat Transport ◽  
Energy Flux ◽  
Constitutive Relations ◽  
Internal Variable ◽  
Nonequilibrium Steady States ◽  
Solid Matrix ◽  
Isotropic Case ◽  
External Energy ◽  
Non Equilibrium

AbstractThe paper deals with the meaning of non-equilibrium temperatures in nanosystems with an internal variable, describing defects inside them, and implications on heat transport. In equilibrium all definitions of temperature lead to the same value, but in nonequilibrium steady states they lead to different values, giving information on different degrees of freedom. We discuss the caloric and entropic non-equilibrium temperatures and the relations among them, in defective nanosystems (crystals with dislocations or porous channels, carbon nanotubes in a solid matrix and so on), crossed by an external energy flux. Here, we present a model for nanocrystals with dislocation defects submitted to an external energy flux. The dislocations may have a strong influence on the effective thermal conductivity, and their own dynamics may be coupled in relevant way to the heat flux dynamics. In the linear case the constitutive relations, the rate equations for the internal variable and the heat flux are worked out and a generalized telegraphic heat equation is derived in the anisotropic and isotropic case, describing the thermal disturbances with finite velocity.

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