On a Principle of Maximal Rate of Entropy Production

Ziegler, Hans; Wehrli, Christoph

doi:10.1515/jnet.1987.12.3.229

Cited by 73 publications

(63 citation statements)

References 7 publications

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“…In the realm of continuum thermodynamic phenomenology (e.g., [10][11][12][13][14][15]), one often simply assumes in a constitutive fashion that a potential representation for evolution-constitutive relations likeḞ P (. .…”

Section: Discussionmentioning

confidence: 99%

“…Although the densities of internal energy and entropy are the principle thermodynamic potentials in the context of the GENERIC, it is interesting to see that the free-energy-like combination ε − θ η appears in both the reversible (39) and irreversible (60) parts of the GENERIC (see also [24]), as well as in the entropy production-rate (64). This is a result of the orthogonality conditions (15). Indeed, (15) 1 induces for example the dependence of L on η in (37), and so that ofẋ| rev on ε − θ η in (39).…”

Section: Summary Of Complete Modelmentioning

confidence: 98%

“…This concept also lies at the heart of so-called generalized standard or standard dissipative materials [9,10]. The evolution-constitutive relations for such internal variables are often formulated with the help of inelastic potentials such as a dissipation potential [11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

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Thermodynamic model formulation for viscoplastic solids as general equations for non-equilibrium reversible–irreversible coupling

Hütter

Svendsen

2012

Continuum Mech. Thermodyn.

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Thermodynamic models for viscoplastic solids are often formulated in the context of continuum thermodynamics and the dissipation principle. The purpose of the current work is to show that models for such material behavior can also be formulated in the form of a General Equation for Non-Equilibrium Reversible-Irreversible Coupling (GENERIC), see, e.g., Grmela and Öttinger (Phys Rev E, 56:6620-6632, 1997), Öttinger and Grmela (Phys Rev E, 56:6633-6655, 1997), Grmela (J Non-Newtonian Fluid Mech, 165:980-986, 2010). A GENERIC combines Hamiltonian-dynamics-based modeling of time-reversible processes with Onsager-Casimir-based modeling of time-irreversible processes. The result is a model for the approach of non-equilibrium systems to thermodynamic equilibrium. Originally developed to model complex fluids, it has recently been applied to anisotropic inelastic solids in Eulerian (Hütter and Tervoort, in J Non-Newtonian Fluid Mech, 152:45-52, 2008; Hütter and Tervoort, in J Non-Newtonian Fluid Mech, 152:53-65, 2008; Hütter and Tervoort, in Adv Appl Mech, 42:254-317, 2008) and Lagrangian (Hütter and Svendsen, in J Elast 104:357-368, 2011) settings, as well as to damage mechanics. For simplicity, attention is focused in the current work on the case of thermoelastic viscoplasticity. Central to this formulation is a GENERIC-based form for the viscoplastic flow rule. A detailed comparison with the formulation based on continuum thermodynamics and the dissipation principle is given.

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Section: Discussionmentioning

confidence: 99%

Section: Summary Of Complete Modelmentioning

confidence: 98%

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Thermodynamic model formulation for viscoplastic solids as general equations for non-equilibrium reversible–irreversible coupling

Hütter

Svendsen

2012

Continuum Mech. Thermodyn.

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“…(5), while τ is a little bit larger than λ/v, as discussed after Eq. (15). Also, c is a little bit larger than k B ; for example, for an ideal gas c = 3 2 k B .…”

Section: Entropy Production and Thermal Conductivity Of Dilute Gasmentioning

confidence: 99%

Entropy production and thermal conductivity of a dilute gas

Zhang¹

2011

Physica A: Statistical Mechanics and its Applications

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It is known that the thermal conductivity of a dilute gas can be derived by using kinetic theory. We present here a new derivation by starting with two known entropy production principles: the steepest entropy ascent (SEA) principle and the maximum entropy production (MEP) principle. A remarkable feature of the new derivation is that it does not require the specification of the existence of the temperature gradient. The known result is reproduced in a similar form.

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“…22,29,30 This divergence of principle was pointed out previously 1 for the case of chemical kinetics.…”

Section: ■ Dissipative Reaction−diffusion Systemsmentioning

confidence: 53%

Dissipation Potentials for Reaction-Diffusion Systems

Goddard

2014

Ind. Eng. Chem. Res.

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This work considers strongly dissipative reaction–diffusion systems with constitutive equations given by Edelen’s dissipation potentials, whose existence is tantamount to nonlinear Onsager symmetry. As the main goal of this work, it is shown that the associated extremum principle yields the relevant steady-state species balances and concentration fields for well-mixed reactors as well as for spatially inhomogeneous reactions accompanied by diffusion. The above principle is contrasted briefly with the popular notion of maximum entropy production. Potential applications of the theory to a wide range of reaction–diffusion systems are discussed, and questions are raised as to the possible breakdown of strong dissipation and nonlinear Onsager symmetry arising from reversible chemical or chemomechanical couplings.

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On a Principle of Maximal Rate of Entropy Production

Cited by 73 publications

References 7 publications

Thermodynamic model formulation for viscoplastic solids as general equations for non-equilibrium reversible–irreversible coupling

Thermodynamic model formulation for viscoplastic solids as general equations for non-equilibrium reversible–irreversible coupling

Entropy production and thermal conductivity of a dilute gas

Dissipation Potentials for Reaction-Diffusion Systems

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