Maximal Entropy Production Research Articles

Biology: Motion is Function.

In 1966 Francis Crick declared that: “The ultimate aim of the modern movement in biology is to explain all biology in terms of physics and chemistry.” This motivated us to contemplate approaches that unify biology at a fundamental level. Exploration led us to consider the features of energy, entropy, and motion. Overall, it can be considered that motion of matter is the feature of life function. No motion. No function. In initial work we evaluated the hypothesis that the scope for biologic function is mediated mechanistically by a differential for energy transfer. Maximal treadmill running capacity served as a proxy for energy transfer. The span for capacity was estimated “biologically” by application of two-way artificial selection in rats for running capacity. Consistent with our “Energy Transfer Hypothesis” (ETH), low physical health and dysfunction segregated with low running capacity and high physical health and function segregated with high running capacity. The high energy yield of aerobic metabolism is also consonant with the ETH; that is, amongst the elements of the universe, oxygen is second only to fluorine in electronegativity. Although we deem these energy findings possibly correct, they are based on correlation and do not illuminate function via fundamental principles. For consideration of life, Entropy (2nd Law of thermodynamics) can be viewed as an open system that exchanges energy with the universe operating via nonequilibrium thermodynamics. The Principle of Maximal Entropy Production (MEP) states that: If a source of free energy is present, complex systems can intercept the free energy flow, and self-organize to enhance entropy production. The development of Benard convection cells in a water heat gradient demonstrate simplistic operation of MEP. A direct step forward would be to explain the mechanism of the obligatory motion of molecules for life function. Motion may be mediated by operation of “action at a distance” for molecules as considered by the Einstein-Podolsky-Rosen Paradox and confirmed by JS Bell. Magnetism, electricity, and gravity are also examples of action at a distance. We propose that some variant of “action at a distance” as directed by the property of Maximal Entropy Production (MEP) underwrites biologic motion.

Modeling competitive precipitations among iron carbides during low-temperature tempering of martensitic carbon steel

Upon tempering of martensitic carbon steels, transition carbides (TCs), as precipitated precursors that compete for available C atoms among multiple iron carbides, have tremendous influences on the microstructural evolution and the final properties of steels. Although two similar structures of TCs, i.e. the hexagonal ε-Fe2C and the orthorhombic η-Fe2C, were successively identified, they still cannot be clearly distinguished experimentally, so far. It is timely to grasp the corresponding atomic-scale nature to predict the real structure of TCs. Based on the maximal entropy production principle and the atomic-scale computations, a Fokker-Planck type equation (FPE) following a modified multi-scale modeling framework, is solved for competitive precipitations among the potential iron carbides (including ε-Fe2C, η-Fe2C and θ-Fe3C) during the low-temperature tempering of carbon steel. The obtained microstructural evolution path dominated by synergy of thermodynamics and kinetics indicates a precipitation sequence for TCs, i.e. ε → η, which is further verified by the minimum energy path in terms of the solid-state nudged elastic band (SSNEB) method. On this basis, the potential hexagonal-orthorhombic transformation (HOT) of TCs is discussed, by which the probable structure of TCs can be accurately identified in experiment. The current modeling framework is expected to be a worthy paradigm for reference to predict the structural evolution of TCs in engineering materials.

Does maximal entropy production play a role in the evolution of biological complexity? A biological point of view

A considerable literature has developed around the concept that the complexity of biological organisms, and the development of ever increasing complexity during biological evolution, is driven, in some way, by the maximization of entropy production (MEP). Most of these studies deal in very general terms with the living state and do not examine specific biological models. In the present study, we discuss some of the basic postulates of MEP as they are applied to living organisms. It is concluded that the MEP ideas seem to have little relevance either for the development of biological complexity or biological evolution.

Maximum Entropy Production Theorem for Transitions between Enzyme Functional States and Its Applications.

Transitions between enzyme functional states are often connected to conformational changes involving electron or proton transport and directional movements of a group of atoms. These microscopic fluxes, resulting in entropy production, are driven by non-equilibrium concentrations of substrates and products. Maximal entropy production exists for any chosen transition, but such a maximal transitional entropy production (MTEP) requirement does not ensure an increase of total entropy production, nor an increase in catalytic performance. We examine when total entropy production increases, together with an increase in the performance of an enzyme or bioenergetic system. The applications of the MTEP theorem for transitions between functional states are described for the triosephosphate isomerase, ATP synthase, for β-lactamases, and for the photochemical cycle of bacteriorhodopsin. The rate-limiting steps can be easily identified as those which are the most efficient in dissipating free-energy gradients and in performing catalysis. The last step in the catalytic cycle is usually associated with the highest free-energy dissipation involving proton nanocurents. This recovery rate-limiting step can be optimized for higher efficiency by using corresponding MTEP requirements. We conclude that biological evolution, leading to increased optimal catalytic efficiency, also accelerated the thermodynamic evolution, the synergistic relationship we named the evolution-coupling hypothesis.

Modeling Competitive Precipitations Among Iron Carbides During Low-Temperature Tempering of Martensitic Carbon Steel

Upon tempering of martensitic carbon steels, transition carbides (TCs), as precipitated precursors that compete for available C atoms among multiple iron carbides, are usually regarded as either the hexagonal e-Fe2C or the orthorhombic η-Fe2C, both of which have tremendous influences on the microstructural evolution and the final properties of steels, but still cannot be clearly distinguished experimentally, so far. It is timely to grasp the corresponding atomic-scale nature to predict the real structure of the TCs. Based on maximal entropy production principle (MEPP) and atomic-scale computations, a Fokker-Planck type equation (FPE) following a modified multi-scale modeling framework, is solved for competitive precipitations among the potential iron carbides, including e-Fe2C, η-Fe2C and θ-Fe3C, during the low-temperature tempering of carbon steel. The obtained microstructural evolution path dominated by synergy of thermodynamics and kinetics indicates a precipitation sequence for TCs, i.e. e → η, which is further verified by the minimum energy path (MEP) in terms of the solid-state nudged elastic band (SSNEB) method. On this basis, the potential hexagonal-orthorhombic transformation (HOT) of TCs is discussed, by which the probable structure of TCs can be accurately identified in experiment. The current modeling framework is expected to be a worthy paradigm for reference to predict the structural evolution of TCs in engineering materials.

The maximum entropy production requirement for proton transfers enhances catalytic efficiency for β-lactamases

Movement of charges during enzyme catalytic cycle may be due to conformational changes, or to fast electron or proton transfer, or to both events. In each case, entropy production can be calculated using Terrel L. Hill's method, if relevant microscopic rate constants are known. When ranked by their evolutionary distance from putative common ancestor, three β-lactamases considered in this study show correspondingly increased catalytic constant, catalytic efficiency, and overall entropy production. The acylation and deacylation steps with concomitant proton shuttles are the most important contributors to overall entropy production. The maximal entropy production requirement for the ES↔EP or EP↔E + P step leads to optimal rate constants, performance parameters, and entropy production values, which are close to those extracted from experiments and also rank in accordance with evolutionary distances. Concurrent maximization of entropy productions for both proton transfer steps revealed that evolvability potential of different β-lactamases is similarly high. These results may have implications in particular for latent potential of β-lactamases to evolve further and in general for selection of optimized enzymes through natural or directed evolution.

Multi-scale modeling of the complex microstructural evolution in structural phase transformations

Modeling the microstructural evolution in structural phase transformations remains challenging, mostly due to the competitions among the potential product phases and the multi-scale nature. To develop a practical tool for such a scientifically and technologically important issue, a multi-scale framework is proposed, where a coarse graining scheme based on the probability density distribution of the representative volume elements (RVEs) of product phases is coupled with the maximal entropy production principle (MEPP) to model the competitions among the multiple product phases as the selection of dissipative paths, and a Fokker-Planck type equation is obtained for the evolution of multiple microstructural parameters (MPs) for the product phases. Applied to precipitation in Al-Cu alloys, the present model, free of adjustable parameters, predicts a correct sequence of precipitation, i.e. GP zone → θꞌꞌ → θꞌ, and yields the accurate precipitation kinetics for θꞌꞌ and θꞌ as compared with the previous experimental data, thus demonstrating the inherent correlation between the MPs and thermodynamics and kinetics of the transformation. For the complex transformations in engineering alloys, the current framework, starting from the general statistical principles and the MEPP, can incorporate the specific MPs for a given transformation following the same scheme.

Steady State Entanglement beyond Thermal Limits.

Classical engines turn thermal resources into work, which is maximized for reversible operations. The quantum realm has expanded the range of useful operations beyond energy conversion, and incoherent resources beyond thermal reservoirs. This is the case of entanglement generation in a driven-dissipative protocol, which we hereby analyze as a continuous quantum machine. We show that for such machines the more irreversible the process, the larger the concurrence. Maximal concurrence and entropy production are reached for the hot reservoir being at negative effective temperature, beating the limits set by classic thermal operations on an equivalent system.

Photosystem I, when excited in the chlorophyll Qy absorption band, feeds on negative entropy

It is often suggested that Life may lay outside the normal laws of Physics and particularly of Thermodynamics, though this point of view is refuted by many. As the Living State may be thought of as an open system, often far from equilibrium, most attempts at placing Life under the umbrella of the laws of Physics have been based, particularly in recent years, on non-equilibrium Thermodynamics and particularly the Maximum Entropy Production Principle. In this view it is the dissipation of entropy (heat) which permits the ever increasing complexity of Living Systems in biological evolution and the maintenance of this complexity. However, these studies usually consider such biological entities as whole cells, organs, whole organisms and even Life itself at the entire terrestrial level. This requires making assumptions concerning the Living State, which are often not soundly based on observation and lack a defined model structure.The present study is based on an entirely different approach, in which a classical thermodynamic analysis of a well-defined biological nanoparticle, plant Photosystem I, is performed. This photosynthetic structure, which absorbs light and performs primary and secondary charge separation, operates with a quantum efficiency close to one. It is demonstrated that when monochromatic light is absorbed by the lowest lying electronic transition, the chlorophyll Qy transition, entropy production in the system bath plus entropy changes internal to the system are numerically less than the entropy decrease of the light field. A Second Law violation is therefore suggested for these experimental conditions. This conclusion, while at first sight is supportive of the famous and much discussed statement of Schroedinger, that “Life feeds on negentropy”, is analysed and the conditions in which this statement may be considered valid for a Plant Photosystem are defined and delimited.The remarkably high quantum efficiency, leading to minimal entropy production (energy wastage), seems to suggest that evolution of Photosystem I has gone down the road of maximal energy efficiency as distinct from maximal entropy production. Photosystem I cannot be considered a maximum entropy dissipation structure.

Energy conservation and maximal entropy production in enzyme reactions

A procedure for maximization of the density of entropy production in a single stationary two-step enzyme reaction is developed. Under the constraints of mass conservation, fixed equilibrium constant of a reaction and fixed products of forward and backward enzyme rate constants the existence of maximum in the density of entropy production is demonstrated. In the state with maximal density of entropy production the optimal enzyme rate constants, the stationary concentrations of the substrate and the product, the stationary product yield as well as the stationary reaction flux are calculated. The test, whether these calculated values of the reaction parameters are consistent with their corresponding measured values, is performed for the enzyme Glucose Isomerase. It is found that calculated and measured rate constants agree within an order of magnitude, whereas the calculated reaction flux and the product yield differ from their corresponding measured values for less than 20 % and 5 %, respectively. This indicates that the enzyme Glucose Isomerase, considered in a non-equilibrium stationary state, as found in experiments using the continuous stirred tank reactors, possibly operates close to the state with the maximum in the density of entropy production.

Is the catalytic activity of triosephosphate isomerase fully optimized? An investigation based on maximization of entropy production.

Triosephosphate isomerase (TIM) is often described as a fully evolved housekeeping enzyme with near-maximal possible reaction rate. The assumption that an enzyme is perfectly evolved has not been easy to confirm or refute. In this paper, we use maximization of entropy production within known constraints to examine this assumption by calculating steady-state cyclic flux, corresponding entropy production, and catalytic activity in a reversible four-state scheme of TIM functional states. The maximal entropy production (MaxEP) requirement for any of the first three transitions between TIM functional states leads to decreased total entropy production. Only the MaxEP requirement for the product (R-glyceraldehyde-3-phosphate) release step led to a 30% increase in enzyme activity, specificity constant kcat/KM, and overall entropy production. The product release step, due to the TIM molecular machine working in the physiological direction of glycolysis, has not been identified before as the rate-limiting step by using irreversible thermodynamics. Together with structural studies, our results open the possibility for finding amino acid substitutions leading to an increased frequency of loop six opening and product release.

A Generalization of Onsager’s Reciprocity Relations to Gradient Flows with Nonlinear Mobility

Abstract Onsager’s 1931 “reciprocity relations” result connects microscopic time reversibility with a symmetry property of corresponding macroscopic evolution equations. Among the many consequences is a variational characterization of the macroscopic evolution equation as a gradient-flow, steepest ascent, or maximal entropy production equation. Onsager’s original theorem is limited to close-to-equilibrium situations, with a Gaussian-invariant measure and a linear macroscopic evolution. In this paper, we generalize this result beyond these limitations and show how the microscopic time reversibility leads to natural generalized symmetry conditions, which take the form of generalized gradient flows.

Modeling the growth kinetics of a multi-component stoichiometric compound

The maximal entropy production principle was applied to model the growth kinetics of a multi-component stoichiometric compound. Compared with the solid-solution phase and the non-stoichiometric compound, the dissipation by the trans-interface diffusion makes the interface slow down by decreasing the effective interface mobility and does not result in solute trapping or disorder trapping. An application to the crystallization of a CuZr stoichiometric compound shows that the transition from the thermodynamic-controlled to the kinetic-controlled growth can be predicted.

Application of the maximal entropy production principle to rapid solidification: A multi-phase-field model

Because the Cahn–Hillard and Allen–Cahn equations cannot deal with the additional constraints in the multi-phase-field models, several approximate treatments, e.g. a specific partition relation and the condition of equal or unequal diffusion potentials, were proposed. In this paper, the problem is solved successfully by the maximal entropy production principle and a model is developed for rapid solidification of a binary alloy system. Due to the mixture law used to define the free energy density, solute concentration and chemical potential jumps happen at an “imaginary” sharp interface between solid and liquid. The solute diffusions in solid and liquid are described by two independent equations and additional non-linear equations do not need to be employed to fix the solute concentrations of solid and liquid. Application to solute trapping during rapid solidification of Si–9at.% As alloy shows that a good agreement between the model predictions and the experimental results is obtained. The interface and bulk contributions are decoupled at very low and very high interface velocities and in other cases the interaction between them depends weakly on the interface velocity.

Application of the maximal entropy production principle to rapid solidification: A sharp interface model

A maximal entropy production principle (MEPP) for chemical reactions was proposed to develop a sharp interface model for rapid solidification. In the modeling, the transport theorem was applied to distinguish the Gibbs energy dissipated by the interface and by the bulk phases from the total Gibbs energy. The bulk and the interface kinetics were described simultaneously and the effect of diffusion in the growing phase on the interface kinetics was incorporated. To obtain a general model, both the interface and the bulk phases were allowed to be under local non-equilibrium conditions. It was found that the model with solute drag is consistent with MEPP, in contrast with the model without solute drag. The model was applied to describe steady-state planar solidification of Si–9at.% As alloy, and a relatively good agreement between the model predictions and the experimental results was obtained. To show the solute drag effect, a partial solute drag model was proposed. Since an unreasonably large interface diffusion velocity results from negligible solute drag effect, the solute drag effect should be significant in solidification.

Wellness and the Thermodynamics of a Healthy Lifestyle

Wellness has recently emerged as an industry sector and a multidimensional academic discipline that includes psychological, physiological, social, demographic and ecological dimensions. Wellness enhances resilience and is therefore a survival imperative that is fundamental to life, yet current Western definitions of wellness do not refer to fundamental a priori principles. Eastern medicine on the other hand does refer to universal principles and suggests that bliss is a natural homeostatic set-point and that wellness can be achieved by living according to the Tao. Congruence between Eastern concepts and thermodynamics further suggests that Qi is related to information and flow, and that wellness arises from maximal flow and minimum entropy production. These principles, which can be represented by an Illness-Wellness Vortex, suggest that the healthiest lifestyle provides maximal enjoyment with minimal waste. Thus, conscious consumption and cultivation of psychological flow can provide the means for achieving wellness through aligning internal and external states.

Nonlinear quantum evolution equations to model irreversible adiabatic relaxation with maximal entropy production and other nonunitary processes

We first discuss the geometrical construction and the main mathematical features of the maximum-entropy-production/steepest-entropy-ascent nonlinear evolution equation proposed long ago by this author in the framework of a fully quantum theory of irreversibility and thermodynamics for a single isolated or adiabatic particle, qubit, or qudit, and recently rediscovered by other authors. The nonlinear equation generates a dynamical group, not just a semigroup, providing a deterministic description of irreversible conservative relaxation towards equilibrium from any non-equilibrium density operator. It satisfies a very restrictive stability requirement equivalent to the Hatsopoulos-Keenan statement of the second law of thermodynamics. We then examine the form of the evolution equation we proposed to describe multipartite isolated or adiabatic systems. This hinges on novel nonlinear projections defining local operators that we interpret as ``local perceptions'' of the overall system's energy and entropy. Each component particle contributes an independent local tendency along the direction of steepest increase of the locally perceived entropy at constant locally perceived energy. It conserves both the locally-perceived energies and the overall energy, and meets strong separability and non-signaling conditions, even though the local evolutions are not independent of existing correlations. We finally show how the geometrical construction can readily lead to other thermodynamically relevant models, such as of the nonunitary isoentropic evolution needed for full extraction of a system's adiabatic availability.

Linear dynamical entropy and free-independence for quantized linear maps on the torus

We study the relations between the averaged linear entropy production in periodically measured quantum systems and ergodic properties of their classical counterparts. Quantized linear automorphisms of the torus, both classically chaotic and regular ones, are used as examples. Numerical calculations show different entropy production regimes depending on the relation between the Kolmogorov–Sinai entropy and the measurement entropy. The hypothesis of free independence relations between the dynamics and measurement proposed to explain the initial constant and maximal entropy production is tested numerically for those models.

The abyssal stratification and circulation deduced from the principle of maximal entropy production

The abyssal stratification and circulation deduced from the principle of maximal entropy production

The abyssal stratification and circulation deduced from the principle of maximal entropy production

A theory for the abyssal stratification and circulation is derived from the principle of maximal production of information entropy used in non-equilibrium statistical dynamics. For an abyssal ocean of simple geometry and simple, though plausible, parameterization of the vertical diffusivity, stratification profiles together with their associated circulation are obtained. These profiles are characterized by an abyssal thermocline thickness scaling as kvH/ws0, where ws0 is the upwelling velocity at the top of an abyssal ocean of depth H, and κv is its vertical diffusivity. Remarkably, the associated circulation is barotropic and coincides with the classical theory of the abyssal circulation by Stommel and Arons.