Maximal Rate Of Entropy Production Research Articles

Flexibility of enzymatic transitions as a hallmark of optimized enzyme steady-state kinetics and thermodynamics

We investigate the relations between the enzyme kinetic flexibility, the rate of entropy production, and the Shannon information entropy in a steady-state enzyme reaction. All these quantities are maximized with respect to enzyme rate constants. We show that the steady-state, which is characterized by the most flexible enzymatic transitions between the enzyme conformational states, coincides with the global maxima of the Shannon information entropy and the rate of entropy production. This steady-state of an enzyme is referred to as globally optimal. This theoretical approach is then used for the analysis of the kinetic and the thermodynamic performance of the enzyme triose-phosphate isomerase. The analysis reveals that there exist well-defined maxima of the kinetic flexibility, the rate of entropy production, and the Shannon information entropy with respect to any arbitrarily chosen rate constant of the enzyme and that these maxima, calculated from the measured kinetic rate constants for the triose-phosphate isomerase are lower, however of the same order of magnitude, as the maxima of the globally optimal state of the enzyme. This suggests that the triose-phosphate isomerase could be a well, but not fully evolved enzyme, as it was previously claimed. Herein presented theoretical investigations also provide clear evidence that the flexibility of enzymatic transitions between the enzyme conformational states is a requirement for the maximal Shannon information entropy and the maximal rate of entropy production.

A thermodynamic basis for the derivation of the Darcy, Forchheimer and Brinkman models for flows through porous media and their generalizations

In this study we use a general thermodynamic framework which appeals to the criterion of maximal rate of entropy production to obtain popular models due to Darcy and Brinkman and their generalizations, to describe flow of fluids through porous solids. Such a thermodynamic approach has been used with great success to describe various classes of material response and here we demonstrate its use within the context of mixture theory to obtain the classical models for the flow of fluids through porous media and more general models which are all consistent with the second law of thermodynamics.

COLLECTIVE BEHAVIOR OF BIOPHYSICAL SYSTEMS WITH THERMODYNAMIC FEEDBACK LOOPS: A CASE STUDY FOR A NONLINEAR MARKOV MODEL — THE TAKATSUJI SYSTEM

We study order–disorder transitions and the emergence of collective behavior using a particular mean field model: the dynamic Takatsuji system. This model satisfies linear non-equilibrium thermodynamics and can be described in terms of a nonlinear Markov process defined by a nonlinear Fokker–Planck equation, that is, an evolution equation that is nonlinear with respect to its probability density. We discuss quantitatively the impact of a feedback loop that involves a macroscopic, thermodynamic variable. We demonstrate by means of semi-analytical methods and numerical simulations that the feedback loop increases the magnitude of order, increases the gap between the free energy of the ordered and disordered states, and increases the maximal rate of entropy production that can be observed during the order–disorder transition.

Physical foundations of evolutionary theory

The theory of evolution by natural selection is herein subsumed by the 2nd law of thermodynamics. The mathematical form of evolutionary theory is based on a re-examination of the probability concept that underlies statistical physics. Probability regarded as physical must include, in addition to isoenergic combinatorial configurations, also energy in conditional circumstances. Consequently, entropy as an additive logarithmic probability measure is found to be a function of the free energy, and the process toward the maximum entropy state is found equivalent to evolution toward the free energy minimum in accordance with the basic maxim of chemical thermodynamics. The principle of increasing entropy when given as an equation of motion reveals that expansion, proliferation, differentiation, diversification, and catalysis are all ways for a system to evolve toward the stationary state in its respective surroundings. Intriguingly, the equation of evolution cannot be solved when there remain degrees of freedom to consume the free energy, and hence evolutionary trajectories of a nonHamiltonian system remain intractable. Finally, when to-and-from flows of energy are balanced between a system and its surroundings, the system is at the Lyapunov-stable stationary state. The principle of maximal energy dispersal, equivalent to the maximal rate of entropy production, gives rise to the ubiquitous characteristics, conventions, and regularities found in nature, where thermodynamics makes no demarcation line between animate and inanimate.

Economies Evolve by Energy Dispersal

Economic activity can be regarded as an evolutionary process governed by the 2nd law of thermodynamics. The universal law, when formulated locally as an equation of motion, reveals that a growing economy develops functional machinery and organizes hierarchically in such a way as to tend to equalize energy density differences within the economy and in respect to the surroundings it is open to. Diverse economic activities result in flows of energy that will preferentially channel along the most steeply descending paths, leveling a non-Euclidean free energy landscape. This principle of 'maximal energy dispersal‘, equivalent to the maximal rate of entropy production, gives rise to economic laws and regularities. The law of diminishing returns follows from the diminishing free energy while the relation between supply and demand displays a quest for a balance among interdependent energy densities. Economic evolution is dissipative motion where the driving forces and energy flows are inseparable from each other. When there are multiple degrees of freedom, economic growth and decline are inherently impossible to forecast in detail. Namely, trajectories of an evolving economy are non-integrable, i.e. unpredictable in detail because a decision by a player will affect also future decisions of other players. We propose that decision making is ultimately about choosing from various actions those that would reduce most effectively subjectively perceived energy gradients.

Relationship between normality structure and orthogonality condition

The nonlinear generalization of the phenomenological equations along with Onsager [Reciprocal relations in irreversible processes, I, II. Physical Review 37 (1931) 405] reciprocal relations includes the normality structure of Rice [Inelastic constitutive relations for solids: an integral variable theory and its application to metal plasticity. Journal of the Mechanics and Physics of Solids 19 (1971) 433; Continuum mechanics and thermodynamics of plasticity in relation to microscale deformation mechanisms. In: Argon, A.S. (Ed.), Constitutive Equations in Plasticity. MIT Press, Cambridge, MA, 1975, pp. 23–79] and the orthogonality condition of Ziegler [An Introduction to Thermomechanics. North-Holland, Amsterdam, 1977] and Ziegler and Wehrli [The derivation of constitutive relations from the free-energy and the dissipation function. Advances in Applied Mechanics 25 (1987a) 183–238; On a principle of maximal rate of entropy production. Journal of Non-Equilibrium Thermodynamics 12 (1987b) 229–243]. The normality structure is generally not consistent with the orthogonality condition due to the different potential functions. The aim of this paper is to examine whether or not the two theories conflict with each other and to establish the consistency condition between the two theories. It is shown in this paper that monotonic increasing and homogeneous kinetic rate laws of local internal variables are thermo-dynamically admissible within the normality structure. The homogeneity property of the kinetic rate laws is the necessary and sufficient consistency condition between the normality structure and orthogonality condition. The thermodynamic processes obeying the orthogonality condition belong to a subset of these processes covered by the normality structure, so the normality structure possesses much more generality than the orthogonality condition.

A Thermomechanical Modeling and Simulation of Viscoplastic Large Deformation Behavior for Polymeric Materials. 1st Report, Non-Coaxiality of Constitutive Equation Originated in Strain Rate Dependence.

Polymeric materials have various characteristics of deformation, e.g., strain rate dependence (viscoplasticity) at room temperature, strain localization just after initial yielding and propagation of a localized region with strain hardening. Viscoplasticity has been usually represented by a constitutive equation of plasticity with a hardening law including a plastic strain rate. However, such a modeling is not thermodynamically consistent with the hardening law dependent on strain rate. In this paper, a strain rate tensor is introduced into free energy and a thermodynamic force conjugate to this rate is newly defined. On the basis of the principle of increase of entropy and one of maximal entropy production rate, a non-coaxial constitutive equation of viscoplasticity is derived as a flow rule in which a dissipation function plays the role of plastic potential. It is shown that a strain rate dependent constitutive equation must be always non-coaxial in a thermodynamically consistent theory.

A Thermomechanical Modeling and Simulation of Viscoplastic Large Deformation Behavior for Polymeric Materials. 2nd Report, Vertex Model Based on Flow Rule and Its Finite Element Analysis.

In the previous paper, a strain rate tensor is introduced into free energy and a thermodynamic force conjugate to this rate is newly defined. On the basis of the principle of increase of entropy and one of maximal entropy production rate, a non-coaxial constitutive equation associated with a plastic deformation rate is derived as a flow rule in which a dissipation function plays the role of plastic potential. Material moduli in this equation, however, are still not expressed as functions of hardening law. In this paper, the constitutive equation is newly generalized into corner theory which permits an existence of a vertex on dissipation surface. A non-coaxial angle of a plastic deformation rate is related to the non-coaxial angle of a stress rate by use of strain rate sensitivity. Furthermore, a finite element analysis is carried out for a plane strain tension of homopolymer. Some remarkable numerical results of strain localization for homopolymer are discussed in detail.

Thernromechanical Discussions on Constitutive Equations for Plastic Spin and Back Stress in a Theory of Dislocation Drift Rate.

A thermomechanical theory of elastoplasticity, including kinematic hardening at finite strain, is developed by introducing the concept of dislocation density tensor. The theory is self-consistent and is based on two fundamental principles, the principle of increase of entropy and the maximal entropy production rate. The thermomechanically consistent constitutive equations for plastic deformation rate, plasticspin and dislocation drift rate are rigorously derived. Constitutive equation of the plastic spin is directly obtained by taking account of a work associating with plastic spin and deriving stress. An expression for the back stress is given as a balance equation expressing equilibrium between internal stress and microstress conjugate to the dislocation density tensor. Moreover, it is shown that the present theory is sufficiently consistent with the theory of non-Riemannian plasticity.

A Thermodynamical Theory of Plastic Spin and Internal Stress With Dislocation Density Tensor

A thermodynamical theory of elastoplasticity including kinematic hardening and dislocation density tensor is developed. The theory is self-consistent and is based on two fundamental principles of thermodynamics, i.e., the principle of increase of entropy and maximal entropy production rate. The thermodynamically consistent governing equations of plastic spin and back stress are rigorously derived. An expression for the plastic spin tensor is obtained from the constitutive equation of dislocation drift rate tensor and an expression for the back stress tensor is given as a balance equation expressing an equilibrium between internal stress and microstress conjugate to the dislocation density tensor. Moreover, it is shown that, in order to obtain a thermodynamically consistent theory for kinematic hardening, the free energy density should have the dislocation density tensor as one of its arguments.

A thermodynamical theory of gradient elastoplasticity with dislocation density tensor. I: Fundamentals

A thermodynamical theory of gradient elastoplasticity, including kinematic hardening, is developed by introducing the concept of dislocation density tensor. The theory is self-consistent and is based on two fundamental principles, the principle of increase of entropy and the maximal entropy production rate. Thermodynamically consistent constitutive equations for plastic stretching, plastic spin and back stress are rigorously derived. Also, an expression for the plastic spin is obtained from the constitutive equation of dislocation drift rate and an expression for the back stress is given as a balance equation expressing equilibrium between internal stress and microstress conjugate to the dislocation density tensor. Moreover, it is shown that the present gradient theory yields a symmetric stress tensor. Some generalities and utility of this theory are discussed and comparisons with other gradient theories are given.

Thermomechanical Derivation of Noncoaxial Plastic Constitutive Equations Considering Spins of Objective Stress Rates.

Elasto-plastic constitutive equations which take into account yield-vertex effects are important in the study of localization instabilities of plastic deformations. However, they have never been discussed thermomechanically. In this paper, a method of deriving the above equations is proposed which is based on the second law of thermodynamics and the principle of maximal entropy production rate. Elastic strain as a strain measure which is conjugate to the objective stress rate is separated from total strain so that the Clausius-Duhem inequality, in which the Gibbs function is introduced as an elastic potential, can be always satisfied. The strain rate and stress rate are expressed by the same objective rate in the rate form of the elastic constitutive equation obtained. The plastic constitutive equation is derived using the principle of maximal dissipation rate. Since this equation is regarded as a flow rule in which the complementary dissipation function assumes the role of a plastic potential, it is indicated that the yield-vertex can exist on the dissipation surface. Furthermore, the spin which should be used in the objective stress rate is selected by taking into account not only usual requirements but also thermomechanical ones.

Thermomechanical Derivation of Noncoaxial Plastic Constitutive Equations Considering Spins of Objective Stress Rates.

Elastoplastic constitutive equations which take into account yield vertex effects are important in the study of localization instabilities of plastic deformations. However, they have never been discussed thermomechanically. In the present paper, a method of deriving the above equations is proposed which is based on the second law of thermodynamics and the principle of maximal entropy production rate. Elastic strain as a strain measure which is conjugate to objective stress rate is separated from total strain so that the Clausius-Duhem inequality, in which the Gibbs function is introduced as an elastic potential, can be always satisfied. The strain rate and stress rate are expressed by the same objective rate in the rate form of the elastic constitutive equation obtained. The plastic constitutive equation is derived using the principle of maximal dissipation rate. Since this equation is regarded as a flow rule in which the complementary dissipation function assumes the role of a plastic potential, it is indicated that the yield vertex can exist on the dissipation surface. Furthermore, the spin used in the objective stress rate is selected by taking into account not only conventional requirements but also thermomechanical ones.

General principles governing irreversible processes

The orthogonality condition proposed by Ziegler as a generalization of Onsager’s relations and the equivalent principle of maximal rate of entropy production are derived from the postulate suggested by physics that forces are determined by their power and from the exclusion of gyroscopic forces.

Chemical reactions and the principle of maximal rate of entropy production

The author shows that the so-called standard equation of Chemical Kinetics is compatible with the principle of maximal rate of entropy production, but incompatible with Thermodynamics. The principle, on the other hand, is free of this defect and may be used to establish an improved version of the standard equation.

Chemical reactions and the principle of maximal rate of entropy production

Chemical reactions and the principle of maximal rate of entropy production