Maximum Entropy Production Principle Research Articles

Maximum entropy production as a necessary admissibility condition for the fluid Navier–Stokes and Euler equations

In a particle physics dynamics, we assume a uniform distribution as the physical measure and a measure-theoretic definition of entropy on the velocity configuration space. This distribution is labeled as the physical solution in the remainder of the article. The dynamics is governed by an assumption of a Lagrangian formulation, with the velocity time derivatives as the momenta conjugate to the velocity configurations. From these definitions and assumptions, we show mathematically that a maximum entropy production principle selects the physical measure from among alternate solutions of the Navier-Stokes and Euler equations, but its transformation to an Eulerian frame is not established here, a topic that will be considered separately.

Optimizing Our Patients' Entropy Production as Therapy? Hypotheses Originating from the Physics of Physiology.

Understanding how nature drives entropy production offers novel insights regarding patient care. Whilst energy is always preserved and energy gradients irreversibly dissipate (thus producing entropy), increasing evidence suggests that they do so in the most optimal means possible. For living complex non-equilibrium systems to create a healthy internal emergent order, they must continuously produce entropy over time. The Maximum Entropy Production Principle (MEPP) highlights nature’s drive for non-equilibrium systems to augment their entropy production if possible. This physical drive is hypothesized to be responsible for the spontaneous formation of fractal structures in space (e.g., multi-scale self-similar tree-like vascular structures that optimize delivery to and clearance from an organ system) and time (e.g., complex heart and respiratory rate variability); both are ubiquitous and essential for physiology and health. Second, human entropy production, measured by heat production divided by temperature, is hypothesized to relate to both metabolism and consciousness, dissipating oxidative energy gradients and reducing information into meaning and memory, respectively. Third, both MEPP and natural selection are hypothesized to drive enhanced functioning and adaptability, selecting states with robust basilar entropy production, as well as the capacity to enhance entropy production in response to exercise, heat stress, and illness. Finally, a targeted focus on optimizing our patients’ entropy production has the potential to improve health and clinical outcomes. With the implications of developing a novel understanding of health, illness, and treatment strategies, further exploration of this uncharted ground will offer value.

A thermodynamic analytical model based on entropy production for predicting the grain size and yield strength of the joint formed by continuous drive friction welding

A self-consistent analytical model for predicting qualities of a joint welded by continuous drive friction welding (CDFW) was developed based on the Onsager-Ziegler maximum entropy production principle (OZ-MEPP), dislocation kinetics, and the CDFW analytical model developed in our previous work. The microstructure and mechanical properties of the friction-welded joint can be predicted by the model requiring only the geometric, thermal, and physical parameters of the specimens without any assumed or premeasured response parameters. The accuracy of the model was verified by the microstructure and properties of the joints fabricated by CDFW of 304 stainless steel. The results indicated that the model is feasible and effective for forecasting the grain size and yield strength of the joints, which means it is possible to use a single thermodynamic state function, i.e., entropy production, for predicting the qualities of a CDFW joint, especially when the joined alloy has a simple phase composition.

Viscous multi-species lattice Boltzmann solver for simulating shock-wave structure

The Onsager Bhatnagar Gross Krook kinetic model proposed by Mahendra et al. [32, 33] has been extended to arrive at the viscous compressible flow equations for a multi-species diffusion problem. The multi-species model ensures (i) correct exchange coefficients, (ii) positivity, (iii) that it follows indifferentiability principle and (iv) that correct amount of entropy get added as per the Onsager’s maximum entropy production principle (MEPP). A Lattice Boltzmann method (LBM) has been developed using the derived methodology within the framework of finite volume method (FVM). This solver incorporates the physics of polyatomic gases with internal degrees of freedom with flexible Prandl number. This solver can simulate the problem with species having different specific heat ratio and molecular weights. Although the equations are derived for multi-species, only binary test cases have been considered in this paper. The solver has been validated against binary shock-wave structure problems using experimental and theoretical data. Two dimensional Richtmyer Meshkov instability test case has been compared with and without viscous effects. The diffusive (viscous and mass diffusion) effects are manifested in the reduction in amplitude and increment in width of the mushroom structure. In the framework of FVM, the proposed scheme of LBM is efficient with good resolution of solutions and is easily adaptable.

In pursuit of the framework behind the biosphere: S-curves, self-assembly and the genetic entropy paradox

The origins, evolution and functioning of the Biosphere have occupied humankind for as long as recorded history has existed. In this paper we examine the claims of thermodynamics to be the framework within which we can understand the evolution, functioning and development of the Biosphere, exploring the evidence from ecology, molecular science and evolutionary biology, and particularly focussing upon the maximum entropy production principle (MEPP), and its explanatory potential in terms of many of the logistic relationships found within the Biosphere. We introduce the genetic entropy paradox, where the DNA increases in terms of internal information entropy, as the genetic code is continuously randomized through mutation, and yet this leads to increasing external entropy production, as increasingly more complicated structures and functions are produced in the form of new protein morphologies and metabolic pathways (again determined by the bioenergetic context). We suggest that the central dogma acts as a form of entropy exchange mechanism, but at the core of this is change in information entropy, which increases within the genetic code, and decreases within the organism. This would appear to be a truly unique event, and highlights a key interaction between two levels of organization within the Biosphere, the genome and the proteome, in terms of entropy production. The Biosphere is seen as being composed of a series of self-organizing sub-groups, each maximizing entropy production within the constraints of time, feedback and system constraints. The entropic production of the Biosphere is thus an emergent property.

Evolution of Agricultural Technologies: from “Gray” to “Green”

The evolution of agricultural technologies in the development of human civilization is considered. Based on this example, it is shown that a new stage in soil cultivation technology began in the 20th century. It is associated with the transition from extensive “gray” technologies for the management of natural resources, which are strictly oriented only by momentary economic feasibility, to nontraditional (“nature-based”) “green” farming technologies. A natural transition has taken place from the strategy of its development based on Ziegler’s principle of maximum entropy production to Prigogine’s strategy of minimum entropy production, which is based on the rationalization of the use of available resources for a dissipative structure on the planet, such as the human population. The foundation for the rationalization is nature-based technology for human use of natural resources. The theoretical justification of the inevitability of “green farming” is confirmed by the example of a long-term biosphere experiment on the development of agricultural technologies. This type of farming is characterized by a more economical method of tillage: partial or complete rejection of soil-turn plowing, the absence of vertical mixing of the arable layer, minimal disturbance of the soil cover by agricultural machines, and mandatory soil mulching (“no-till” or “mulch tillage”) in order to preserve the soil moisture and reduce soil erosion. The no-till soil processing system, i.e., the absence of interference in the natural processes of soil formation, is a modern farming system in which the soil is not processed and its surface is covered with specially crushed plant residues (mulch). It is illustrated that the no-till technology of direct sowing and mulching is currently being introduced in various regions of the planet with shallow, surface loosening or even complete rejecting tillage. It is shown that the application of the green farming technologies leads to rationalization of the use of not only energy and soil resources but also water resources, for which the situation is becoming increasingly tense for human civilization.

Identification of active pathways of Chlorella protothecoides by elementary mode analysis integrated with fluxomic data

Microalgae are bio-factories for CO2 fixation, biofuel production, and high-value added product biosynthesis and wastewater treatment. Deep understandings of the intracellular pathways, metabolic regulations and physiological responses of microalgae are critical for process optimization and strain modification. In this study, a metabolic network in small scale was reconstructed for the green microalgae, Chlorella protothecoides. The reliability of this metabolic network model was confirmed by metabolic phenotype prediction. The pathway length distribution of all the elementary modes was calculated. These elementary modes were divided into 5 groups based on their macroreactions of elementary modes. The group with a short pathway length was that of lactate production. The group with a long pathway length included biomass formation. In addition, the active pathways were identified by decomposition of the determined metabolic fluxes under three conditions from references onto elementary modes with six objective functions, maximum biomass formation, minimum norm, maximum entropy production principle, maximum activity of the shortest pathway length by linear programming, maximum activity of the shortest pathway length by quadratic programming and maximum activity of the longest pathway length by linear programming. The identified active pathways were consistent with the physiological states of microalgae. These results were helpful for exploring metabolic regulatory mechanism in microalgae.

Intercomparison of the Surface Energy Partitioning in CMIP5 Simulations

The warming climate significantly modifies the global water cycle. Global evapotranspiration has increased over the past decades, yet climate models agree on the drying trend of land surface. In this study, we conducted an intercomparison analysis of the surface energy partitioning across Coupled Model Intercomparison Phase 5 (CMIP5) simulations and evaluated its behaviour with surface temperature and soil moisture anomalies, against the theoretically derived thermodynamic formula. Different responses over land and sea surfaces to elevated greenhouse gas emissions were found. Under the Representative Concentration Pathway of +8.5 W m−2 (RCP8.5) warming scenario, the multi-model mean relative efficiency anomaly from CMIP5 simulations is 3.83 and −0.12 over global sea and land, respectively. The significant anomaly over sea was captured by the thermodynamic solution based on the principle of maximum entropy production, with a mean relative error of 14.6%. The declining trend over land was also reproduced, but an accurate prediction of its small anomaly will require the inclusions of complex physical processes in future work. Despite increased potential evapotranspiration under rising temperatures, both CMIP5 simulations and thermodynamic principles suggest that the soil moisture-temperature feedback cannot support long-term enhanced evapotranspiration at the global scale. The dissipation of radiative forcing eventually shifts towards sensible heat flux and accelerates the warming over land, especially over South America and Europe.

Thermodynamic analysis of thermal convection based on entropy production

Flow patterns have a tendency to break the symmetry of an initial state of a system and form another spatiotemporal pattern when the system is driven far from equilibrium by temperature difference. For an annular channel, the axially symmetric flow becomes unstable beyond a given temperature difference threshold imposed in the system, leading to rotational oscillating waves. Many researchers have investigated this transition via linear stability analysis using the fundamental conservation equations and the generic model amplitude equation, i.e., the complex Ginzburg-Landau equation. Here, we present a quantitative study conducted of the thermal convection transition using thermodynamic analysis based on the maximum entropy production principle. Our analysis results reveal that the fluid system under nonequilibrium maximizes the entropy production induced by the thermodynamic flux in a direction perpendicular to the temperature difference. Further, we show that the thermodynamic flux as well as the entropy production can uniquely specify the thermodynamic states of the entire fluid system and propose an entropy production selection rule that can be used to specify the thermodynamic state of a nonequilibrium system.

Inevitability and Prospects of the Use of the “Green Farming” Strategy by Humanity

The article presents the physical substantiation of the basic laws of ecology of B. Commoner. It is shown that the evolution of dissipative structures on the Earth, which include, amongst other things, living organisms and superorganismal systems, obeys a fundamental principle–Ziegler’s principle of maximum entropy production. However, when a system approaches its stationary state due to the exhaustion of the free energy available to the dissipative structures of the planet, evolutionary changes are replaced by the relatively slow processes of the optimization of the homeostasis of the emergent structures. At this stage, Prigogine’s principle of minimum entropy production becomes the main principle. It is shown that humanity found itself in this situation at the present stage of the Holocene, facing the inevitable need for rational use of the resources available to us. A similar rationalization was already implemented by Nature at the end of the previous stage of evolution (in the absence of man) based on the ability of biota (which developed over billions of years) to regulate and stabilize the biosphere of the planet. Therefore, at the present stage of evolution, B. Commoner’s law of ecology is manifested: nature knows better. It has been demonstrated that humanity is already in the situation of the operation of this law. Over the past two decades, the so-called “green economy” has emerged—a direction in economics in which it is believed that the economy is a dependent component of its natural environment and is a part of it. In particular, it is shown that the use of “green farming” is expanding in the field of agriculture and the associated water sector (especially in the arid and semiarid regions of the planet). It is largely compensating for the growing challenges to the food and water security of the population.

Integrability-Protected Adiabatic Reversibility in Quantum Spin Chains.

We consider the out-of-equilibrium dynamics of the Heisenberg anisotropic quantum spin-1/2 chain threaded by a time-dependent magnetic flux. In the spirit of the recently developed generalized hydrodynamics (GHD), we exploit the integrability of the model for any flux values to derive an exact description of the dynamics in the limit of slowly varying flux: the state of the system is described at any time by a time-dependent generalized Gibbs ensemble. Two dynamical regimes emerge according to the value of the anisotropy Δ. For |Δ|>1, reversibility is preserved: the initial state is always recovered whenever the flux is brought back to zero. On the contrary, for |Δ|<1, instabilities of quasiparticles produce irreversible dynamics as confirmed by the dramatic growth of entanglement entropy. In this regime, the standard GHD description becomes incomplete and we complement it via a maximum entropy production principle. We test our predictions against numerical simulations finding excellent agreement.

Thermodynamic Merger of Fluctuation Theorem and Principle of Least Action: Case of Rayleigh–Taylor Instability

Abstract Entropy fluctuations with time occur in finite-sized time-evolving dissipative systems. There is a need to comprehend the role of these fluctuations on the fluctuations-averaged entropy generation rate, over a large enough observation time interval. In this non-equilibrium thermodynamic investigation, the Fluctuation Theorem (FT) and Principle of Least Action are re-visited to articulate their implications for dissipative systems. The Principle of Maximum Entropy Production (MaxEP: the entropy generation rate of a dissipative system is maximized by paths of least action) is conceptually identified as the Principle of Least Action for dissipative systems. A Thermodynamic Fusion Theorem that merges the FT and the MaxEP is introduced for addressing the role of fluctuations in entropy production. It identifies “entropy fluctuations” as the “least-action path” for maximizing the time-averaged entropy production in a dissipative system. The validity of this introduced theorem is demonstrated for the case of entropy fluctuations in Rayleigh–Taylor flow instability.

The thermodynamic analytical models for steady-state of continuous drive friction welding based on the maximum entropy production principle

An analytical model was developed based on the thermodynamic theory of Onsager-Ziegler maximum entropy production principle (OZ-MEPP) and the relevant dynamic laws, and used for characterizing the steady-state system of the severe plastic deformation (SPD) produced by continuous drive friction welding (CDFW) without any pre-assumed or measured response parameters. The accuracy and universality of the model were verified by the CDFW experiments of eight kinds of alloys, the results of which indicated that the model could precisely predict the temperature, axial shortening rate, welding power. Moreover, the coefficient of friction, traditionally regarded as an empirical parameter, could be forecasted too.

Oscillatory dynamics of an electrically driven dissipative structure.

Physical systems open to a flow of energy can exhibit spontaneous symmetry breaking and self-organization. These nonequilibrium self-organized systems are known as dissipative structures. We study the oscillatory mode of an electrically driven dissipative structure. Our system consists of aluminum beads in shallow oil, which, when subjected to a high voltage, self-organize into connected ‘tree’ structures. The tree structures serve as pathways for the conduction of charge to ground. This system shows a variety of spatio-temporal behaviors, such as oscillating movement of the tree structures. Utilizing a dynamical systems model of the electromagnetic phenomena, we explore a potential mechanism underlying the system’s behavior and use the model to make additional empirical predictions. The model reproduces the oscillatory behavior observed in the real system, and the behavior of the real system is consistent with predictions from the model under various constraints. From the empirical results and the mathematical model, we observe a tendency for the system to select modes of behavior with increased dissipation, or higher rates of entropy production, in accord with the proposed Maximum Entropy Production (MEP) Principle.

Entropy production and luminosity–effective temperature relation for main-sequence stars

Based on the maximum entropy production principle, a relation between luminosity and effective temperature for main-sequence stars is obtained. Simplicity of the derivation and absence of any empirical parameters in the result is a fundamental difference of the present method from the classic ones where equations of stellar structure are analyzed. Using available photometric data (Webda, ESPG) for more than 7.5 thousand stars, it is shown that the obtained luminosity–temperature relation is better than previously used ones.

Study on the friction interface evolution during rotary friction welding of tube

In this study, evolution characteristics of the friction interface during rotary friction welding of tube were investigated. The friction interface that obtained at different welding stage were observed by confocal laser scanning microscopy. The results show that the friction interface transforms from sliding friction state to visco-plastic deformation state when the welding torque reaches the peak value. In addition, based on the thermodynamic framework extracted from the maximum entropy production principle, an analytical model for transition criterion from sliding friction to visco-plastic deformation was established. The model was verified by the corresponding experimental results of eight alloys, which indicated that the accuracy and generality of the model is satisfactory.

Study on eco-compensation standard for adjacent administrative districts based on the maximum entropy production

The upper and lower limits of eco-compensation standards are theoretically determined respectively by ecosystem service value and opportunity cost. However, there are some unresolved problems in the study of the upper limit. The relationship between ecological service values and compensation standard is vague and there exists a huge gap in capital amount in practical applications. This paper proposes a solution of ecological service value analysis based eco-compensation standard in a real case between three administrative districts in E'zhou City, China. This research analysed the relationship of eco-compensation based on the principle of maximum entropy production and designed the calculation method of eco-compensation standard for adjacent administrative districts. It explored the research gap in the field of eco-compensation standard. As a result, Liangzi Lake district received 235.03 and 41.17 million CNY respectively from E'cheng and Huarong district in 2016. This study provides a novel and objective system solution of eco-compensation standard, which would facilitate the governments' financial transfer decision.

Minimal time, Weibull distribution and maximum entropy production principle: Comment on “Redundancy principle and the role of extreme statistics in molecular and cellular biology” by Z. Schuss et al.

Minimal time, Weibull distribution and maximum entropy production principle: Comment on “Redundancy principle and the role of extreme statistics in molecular and cellular biology” by Z. Schuss et al.

Использование кластерных моделей для разработки композиционных материалов систем Ni-Al и Ti-Al

&nbsp; This work is devoted to obtaining samples of composite materials of Ni-Al, Al-Ti systems using mechanochemical processes. The Ni-Al multilayer powder composite is obtained by the 13MPA pressure welding method of a multilayer plate pack. The results of phase analysis demonstrate that the pressure welding method allows to obtain the Ni3Al phase having unique physical properties. The Ti-Al composite is an excellent structural material obtained by explosion welding. Titanium has an HCP lattice that is stable up to a temperature of 882°С; it passes into a stable BCC lattice at a higher temperature. The sample has been subjected to heat treatment - two-stage annealing. The Ti2Al and Ti3Al phases with BCC lattices are detected after the annealing so that this material can work in a wide range of temperatures. TiAl2 - has good properties at low temperatures, TiAl3 - has good properties at high temperatures. All processes of phase transitions follow the principle of maximum entropy production. As a result, the entropy of the obtained structures may be negative. This is possible due to the switching of chemical bonds in the process of mechanochemical reactions. The product volume of the mechanochemical reaction is always less than the initial volume. In this paper, we propose cluster models of powder sintering areas. Cluster models describe well the sequence of reactions in the area of mechanical sintering of powders. According to the obtained results, the conditions for developing a technology for producing powder and multilayer composites to create a Ni3Al superalloy, as well as to obtain strong and ductile multilayer Ti-Al composites, are defined.

Modeling of rotary friction welding process based on maximum entropy production principle

The interfacial transition point isolated by maximum entropy production principle (MEPP) was used to construct a two-dimensional (2D) finite element (FE) model of continuous-drive rotary friction welding (RFW) with GH4169 superalloy. The transition point from sliding friction to shear friction was calculated based on the equal entropy of these two kinds of heat liberation mechanisms at this point. The FE model was shown valid by the consistency of comparison between simulation and experiment. The simulation issued an interfacial distribution of non-uniform heat intensity that determined the corona bond, which corresponded to higher temperature zone over the transition temperature. The influences of linear speed and friction pressure on welding time were examined, which showed that a shorter welding time could be acquired when the linear speed was about 1.96 m/s and the friction pressure is larger.