A Note on the Principle of Maximum Dissipation Rate

2006 ◽  
Vol 74 (5) ◽  
pp. 923-926 ◽  
Author(s):  
F. D. Fischer ◽  
J. Svoboda
Keyword(s):  
Convex Functions ◽  
Dissipation Rate ◽  
Direct Consequence ◽  
Dissipation Function ◽  
Internal Variables ◽  
Entropy Production Rate ◽  
Kinetic Rate ◽  
Rate Laws ◽  
Thermodynamic Forces ◽  
Principle Of Maximum

The Principle of Maximum Dissipation Rate (PMD) can be exploited to derive homogeneous kinetic rate laws for the internal variables. A “normality structure” expressing the rates of the internal variables as normal to convex functions (entropy production rate, dissipation function as flow potentials) in the space of the conjugate thermodynamic forces is a direct consequence of the PMD. This paper can be considered as a note to Yang et al., 2005, ASME J. Appl. Mech., 72, pp. 322–329.

Internal Variable Theory Formulated by One Extended Potential Function

2020 ◽  
Vol 45 (3) ◽  
pp. 311-318
Author(s):  
Qiang Yang ◽  
Zhuofu Tao ◽  
Yaoru Liu
Keyword(s):  
Potential Function ◽  
Internal Variable ◽  
The State ◽  
Internal Variables ◽  
State Variables ◽  
Kinetic Rate ◽  
Variable Theory ◽  
Rate Laws ◽  
Flow Potential ◽  
Internal Variable Theory

AbstractIn the kinetic rate laws of internal variables, it is usually assumed that the rates of internal variables depend on the conjugate forces of the internal variables and the state variables. The dependence on the conjugate force has been fully addressed around flow potential functions. The kinetic rate laws can be formulated with two potential functions, the free energy function and the flow potential function. The dependence on the state variables has not been well addressed. Motivated by the previous study on the asymptotic stability of the internal variable theory by J. R. Rice, the thermodynamic significance of the dependence on the state variables is addressed in this paper. It is shown in this paper that the kinetic rate laws can be formulated by one extended potential function defined in an extended state space if the rates of internal variables do not depend explicitly on the internal variables. The extended state space is spanned by the state variables and the rate of internal variables. Furthermore, if the rates of internal variables do not depend explicitly on state variables, an extended Gibbs equation can be established based on the extended potential function, from which all constitutive equations can be recovered. This work may be considered as a certain Lagrangian formulation of the internal variable theory.

On the relation between the principle of maximum dissipation and inelastic evolution given by dissipation potentials

2007 ◽  
Vol 464 (2089) ◽  
pp. 117-132 ◽  
Author(s):  
Klaus Hackl ◽  
Franz Dieter Fischer
Keyword(s):  
Variational Formulation ◽  
Evolution Equations ◽  
Minimum Principle ◽  
Internal Variables ◽  
Dissipation Potential ◽  
Thermodynamic Forces ◽  
Principle Of Maximum

We study the evolution of systems described by internal variables. After the introduction of thermodynamic forces and fluxes, both the dissipation and dissipation potential are defined. Then, the principle of maximum dissipation (PMD) and a minimum principle for the dissipation potential are developed in a variational formulation. Both principles are related to each other. Several cases are shown where both principles lead to the same evolution equations for the internal variables. However, also counterexamples are reported where such an equivalence is not valid. In this case, an extended PMD can be formulated.

A study on the principle of maximum dissipation for coupled and non-coupled non-isothermal processes in materials

2010 ◽  
Vol 467 (2128) ◽  
pp. 1186-1196 ◽  
Author(s):  
Klaus Hackl ◽  
Franz Dieter Fischer ◽  
Jiri Svoboda
Keyword(s):  
Heat Flux ◽  
Evolution Equations ◽  
Mathematical Structure ◽  
Dissipation Function ◽  
Internal Variables ◽  
Efficient Tool ◽  
Equilibrium Processes ◽  
Rigorous Treatment ◽  
Isothermal Processes ◽  
Principle Of Maximum

Onsager’s principle of maximum dissipation (PMD) has proven to be an efficient tool to derive evolution equations for the internal variables describing non-equilibrium processes. However, a rigorous treatment of PMD for several simultaneously acting dissipative processes is still open and presented in this paper. The coupling or uncoupling of the processes is demonstrated via the mathematical structure of the dissipation function. Examples are worked out for plastic deformation and heat flux.

Geochemical and Biogeochemical Reaction Modeling

2021 ◽  
Author(s):  
Craig M. Bethke
Keyword(s):  
Wide Spectrum ◽  
Worked Examples ◽  
Surface Complexation Modeling ◽  
Kinetic Rate ◽  
University Teachers ◽  
Rate Laws ◽  
Partial Pressures ◽  
Scientists And Engineers ◽  
Scientific Practical ◽  
Geochemical Reaction

An indispensable primer and reference textbook, the third edition of Geochemical and Biogeochemical Reaction Modeling carries the reader from the field's origins and theoretical underpinnings through to a collection of fully worked examples. A clear exposition of the underlying equations and calculation techniques is balanced by real-world example calculations. The book depicts geochemical reaction modeling as a vibrant field of study applicable to a wide spectrum of issues of scientific, practical, and societal concern. The new edition offers a thorough description of surface complexation modeling, including two- and three-layer methods; broader treatment of kinetic rate laws; the effect of stagnant zones on transport; and techniques for determining gas partial pressures. This handbook demystifies and makes broadly accessible an elegant technique for portraying chemical processes in the geosphere. It will again prove to be invaluable for geochemists, environmental scientists and engineers, aqueous and surface chemists, microbiologists, university teachers, and government regulators.

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.

On the different formalisms for the transport equations of thermoelectricity: A review

2015 ◽  
Vol 40 (3) ◽  
Author(s):  
José A. Manzanares ◽  
Miikka Jokinen ◽  
Javier Cervera
Keyword(s):  
Entropy Production ◽  
Transport Equations ◽  
Dissipation Function ◽  
Point Of View ◽  
Entropy Production Rate ◽  
Systematic Classification ◽  
Seebeck Coefficients ◽  
Primary Focus

AbstractResearchers in thermoelectricity with backgrounds in non-equilibrium thermodynamics, thermoelectric engineering or condensed-matter physics tend to use different choices of flux densities and generalized forces. These choices are seldom justified from either the dissipation function or the entropy production rate. Because thermoelectric phenomena are a primary focus in several emerging fields, particularly in recent energy-oriented developments, a review of the different formalisms employed is judged timely. A systematic classification of the transport equations is presented here. The requirements on valid transport equations imposed by the invariance of the entropy production are clearly explained. The effective Peltier and Seebeck coefficients, and the thermal conductivity, corresponding to the different choices of flux densities and generalized forces, are identified. Emphasis is made on illustrating the compatibility of apparently disparate formalisms. The advantages and drawbacks of these formalisms are discussed, especially from the point of view of the experimental determination of their thermoelectric coefficients.

scholarly journals It is not the entropy you produce, rather, how you produce it

2010 ◽  
Vol 365 (1545) ◽  
pp. 1317-1322 ◽  
Author(s):  
Tyler Volk ◽  
Olivier Pauluis
Keyword(s):  
Entropy Production ◽  
Production Rate ◽  
Thought Experiment ◽  
Biological Evolution ◽  
Irreversible Thermodynamics ◽  
Entropy Production Rate ◽  
Chemical Systems ◽  
Principle Of Maximum Entropy ◽  
Relative Contribution ◽  
Principle Of Maximum

The principle of maximum entropy production (MEP) seeks to better understand a large variety of the Earth's environmental and ecological systems by postulating that processes far from thermodynamic equilibrium will ‘adapt to steady states at which they dissipate energy and produce entropy at the maximum possible rate’. Our aim in this ‘outside view’, invited by Axel Kleidon, is to focus on what we think is an outstanding challenge for MEP and for irreversible thermodynamics in general: making specific predictions about the relative contribution of individual processes to entropy production. Using studies that compared entropy production in the atmosphere of a dry versus humid Earth, we show that two systems might have the same entropy production rate but very different internal dynamics of dissipation. Using the results of several of the papers in this special issue and a thought experiment, we show that components of life-containing systems can evolve to either lower or raise the entropy production rate. Our analysis makes explicit fundamental questions for MEP that should be brought into focus: can MEP predict not just the overall state of entropy production of a system but also the details of the sub-systems of dissipaters within the system? Which fluxes of the system are those that are most likely to be maximized? How it is possible for MEP theory to be so domain-neutral that it can claim to apply equally to both purely physical–chemical systems and also systems governed by the ‘laws’ of biological evolution? We conclude that the principle of MEP needs to take on the issue of exactly how entropy is produced.

Polythermal, Fixed, and Sliding Paths

1996 ◽  
Author(s):  
Craig M. Bethke
Keyword(s):  
Mass Transfer ◽  
Equilibrium System ◽  
Reaction Paths ◽  
Governing Equations ◽  
Kinetic Rate ◽  
Reaction Progress ◽  
Rate Laws ◽  
Reaction Models ◽  
Temperature Path

In this chapter we consider how to construct reaction models that are somewhat more sophisticated than those discussed in the previous chapter, including reaction paths over which temperature varies and those in which species activities and gas fugacities are buffered. The latter cases involve the transfer of mass between the equilibrium system and an external buffer. Mass transfer in these cases occurs at rates implicit in solving the governing equations, rather than at rates set explicitly by the modeler. In Chapter 14 we consider the use of kinetic rate laws, a final method for defining mass transfer in reaction models. Polythermal reactions paths are those in which temperature varies as a function of reaction progress, ξ. In the simplest case, the modeler prescribes the temperatures T0 and Tf at the beginning and end of the reaction path. The model then varies temperature linearly with reaction progress. This type of model is sometimes called a “sliding temperature” path. The calculation procedure for a sliding temperature path is straightforward. In taking a reaction step, the model evaluates the temperature to be attained at the step’s end.

Sign in / Sign up

Export Citation Format

Share Document