Maximum Entropy Production Principle Research Articles

Maximization of entropy production during vibration in a suspension based on graphite and silicone oil.

The electrical conductivity of a suspension of graphite and silicone oil in the presence of a small electric potential difference and vibration (40÷50Hz) is considered. The concentration of the suspension was selected near the percolation threshold. It has been found that such a nonequilibrium system evolves to increase its dissipation power, and low-energy vibrations accelerate, and high-energy ones hinder this process. Since the dissipation power of the considered system is proportional to entropy production, the results obtained are consistent with the so-called maximum entropy production principle (MEPP). This is the first experimental confirmation of MEPP in the case of a nonequilibrium process with continuous transformations under conditions for the emergence of alternative variants for the development. The possibility of choice among alternatives in a complex system is a fundamental point in the experimental discussion of MEPP, and it was previously underestimated.

On the Occurrence of Domain Boundaries and Defects in Self-Organized Ordered Porous Anodic Alumina Systems.

The formation of domains and defects is a part of every self-organized structure without prepatterning which evolves from the electrochemical oxidation of valve metals like Ti, Al or Ta. Defects and domains, especially in highly ordered porous alumina films (PAOX), are one of the most studied phenomena in the current literature. The focus is on understanding their formation in order to find parameters to minimize their amount for applications that require the most highly organized structures. In this letter we give a solution to this problem by showing that the occurrence of defects and domains is an unavoidable consequence of the underlying self-organized process due to the simultaneous impact of the minimum (MINEP) and maximum (MAXEP) entropy production principle. As a consequence, experimental procedures to manufacture defect-free PAOX-films from a self-organization process face a fundamental limitation.

Planetary Energy Flow and Entropy Production Rate by Earth from 2002 to 2023.

In this work, satellite data from the Clouds and Earth's Radiant Energy System (CERES) and Moderate Resolution Imaging Spectroradiometer (MODIS) instruments are analyzed to determine how the global absorbed sunlight and global entropy production rates have changed from 2002 to 2023. The data is used to test hypotheses derived from the Maximum Power Principle (MPP) and Maximum Entropy Production Principle (MEP) about the evolution of Earth's surface and atmosphere. The results indicate that both the rate of absorbed sunlight and global entropy production have increased over the last 20 years, which is consistent with the predictions of both hypotheses. Given the acceptance of the MPP or MEP, some peripheral extensions and nuances are discussed.

A Theory of Maximum Entropy Production and Its Application to Microwave Remote Sensing—Simultaneous Retrieval of Soil Moisture and Vegetation Water Content

AbstractA theory of maximum entropy production (MEP) for electromagnetic wave propagation in dielectric materials is proposed and applied to simultaneously retrieving soil moisture (SM) and vegetation water content (VWC) from L‐band microwave brightness temperature (TB). One representation of the MEP principle states that a non‐equilibrium system corresponds to such a configuration of energy fluxes that minimizes a dissipation function under the constraint of energy conservation. The dissipation function for radiative transfer is formulated as an analogy of that for heat transfer. A new physical parameter, radiative inertia as an analogy of thermal inertia, is introduced to characterize radiative attenuation in dielectric media. The radiative inertia is parameterized in terms of the penetration depth of electromagnetic waves as a function of the complex dielectric constant. The MEP based retrieval algorithm predicts SM and VWC by minimizing the dissipation function under the constraint of the conservation of radiative energy. The retrievals of SM and VWC based on the MEP theory were validated against field observations in tropical and temperate forested regions of the Amazon and North America. The proof‐of‐concept analysis demonstrates the capability of the MEP algorithm for simultaneous retrievals of SM and VWC even for dense canopy (e.g., VWC > 5 kg m−2). The MEP method is a new theoretical framework for developing innovative remote sensing algorithms of the Earth system not limited to microwave observations.

Fractal interface of a spreading drop and maximum entropy production principle

The viscous spreading of a small liquid drop on a surface, where moving interface changes from circular to fractal, starting at a certain size, is considered. Based on the maximum entropy production principle, the analytical relation between the critical size of the morphological stability of a circular drop and the fractal dimension of the structure that appears during spreading is obtained for the first time. An experiment on the spreading of ink on a surface covered with acrylic paint quantitatively confirmed the validity of this relation.

Assessing the Complementary Role of Surface Flux Equilibrium (SFE) Theory and Maximum Entropy Production (MEP) Principle in the Estimation of Actual Evapotranspiration

AbstractAlthough evapotranspiration (ET) from the land is a key variable in Earth system models, the accurate estimation of ET based on physical principles remains challenging. Parameters used in current ET models are largely empirically based, which could be problematic under rapidly changing climatic conditions. Here, we propose a physically based ET model that estimates ET based on the surface flux equilibrium (SFE) theory and the maximum entropy production (MEP) principle. We derive an expression for aerodynamic resistance based on the MEP principle, then propose a novel ET model that integrates the SFE model and the MEP principle. The proposed model, which is referred to as the SFE‐MEP model, becomes equivalent to the MEP state in non‐equilibrium conditions when turbulent mixing is weak and the land surface is dry. Under conditions meeting land‐atmosphere equilibrium, the SFE‐MEP model is similar to ET estimation based on the SFE model. This blended nature of the SFE‐MEP ET model allows accurate ET estimation for most inland regions by overcoming the ET overestimation issue of the SFE model in dry conditions. As a result, the SFE‐MEP model significantly improves the performance of SFE ET estimation, particularly for arid regions. The proposed model and its high accuracy of ET estimation enable novel insight into various Earth system models as it does not require any empirical parameters and only uses readily obtainable meteorological variables including reference height air temperature, relative humidity, available energy, and radiometric surface temperature.

Self-Organization of Enzyme-Catalyzed Reactions Studied by the Maximum Entropy Production Principle.

The self-organization of open reaction systems is closely related to specific mechanisms that allow the export of internally generated entropy from systems to their environment. According to the second law of thermodynamics, systems with effective entropy export to the environment are better internally organized. Therefore, they are in thermodynamic states with low entropy. In this context, we study how self-organization in enzymatic reactions depends on their kinetic reaction mechanisms. Enzymatic reactions in an open system are considered to operate in a non-equilibrium steady state, which is achieved by satisfying the principle of maximum entropy production (MEPP). The latter is a general theoretical framework for our theoretical analysis. Detailed theoretical studies and comparisons of the linear irreversible kinetic schemes of an enzyme reaction in two and three states are performed. In both cases, in the optimal and statistically most probable thermodynamic steady state, a diffusion-limited flux is predicted by MEPP. Several thermodynamic quantities and enzymatic kinetic parameters, such as the entropy production rate, the Shannon information entropy, reaction stability, sensitivity, and specificity constants, are predicted. Our results show that the optimal enzyme performance may strongly depend on the number of reaction steps when linear reaction mechanisms are considered. Simple reaction mechanisms with a smaller number of intermediate reaction steps could be better organized internally and could allow fast and stable catalysis. These could be features of the evolutionary mechanisms of highly specialized enzymes.

Is the maximum entropy production just a heuristic principle? Metaphysics on natural determination

The Maximum Entropy Production Principle (MEPP) stands out as an overarching principle that rules life phenomena in Nature. However, its explanatory power beyond heuristics remains controversial. On the one hand, the MEPP has been successfully applied principally to non-living systems far from thermodynamic equilibrium. On the other hand, the underlying assumptions to lay the MEPP’s theoretical foundations and range of applicability increase the possibilities of conflicting interpretations. More interestingly, from a metaphysical stance, the MEPP’s philosophical status is hotly debated: does the MEPP passively translate physical information into macroscopic predictions or actively select the physical solution in multistable systems, granting the connection between scientific models and reality? This paper deals directly with this dilemma by discussing natural determination from three angles: (1) Heuristics help natural philosophers to build an ontology. (2) The MEPP’s ontological status may stem from its selection of new forms of causation beyond physicalism. (3) The MEPP’s ontology ultimately depends on the much-discussed question of the ontology of probabilities in an information-theoretic approach and the ontology of macrostates according to the Boltzmannian definition of entropy.

On the Theory of Shock Waves in Isotropic Hardening Plastic Media

Based on the thermomechanical model of plastic deformation of an elastically compressible isotropic hardening medium, the system of relations for describing plastic shock waves of finite amplitude is obtained, which satisfies the maximum entropy production principle at the front of strong discontinuity. A classification of admissible shock-wave transitions is performed within the framework of the model of isotropic hardening under the von Mises plasticity condition.

Dark matter fermions: from linear to non-linear structure formation

The transition from linear to non-linear structure formation in cosmology is here studied from the point of view of the thermodynamics of self-gravitating fermions. We start by reviewing the principle of maximum entropy production through which such a fermionic system can relax towards spherical equilibrium states able to explain the dark matter (DM) in galaxies. We then analyze the stability, lifetime and morphology of the above configurations, and show that the most general DM profile develops a compact core governed by degeneracy pressure, which is surrounded by an extended halo. For DM particles which are in the range of $\mathcal{O}$(10--100) keV, we apply this theory to the case of the Milky Way, and show that the compact DM-core explains the dynamics of all the best resolved S-cluster stars orbiting SgrA *, without the need of assuming a central black hole (BH). Further consequences of this theory regarding open issues in cosmology are outlined, including the problem of formation of supermassive BHs in the early Universe.

Foraging Dynamics and Entropy Production in a Simulated Proto-Cell.

All organisms depend on a supply of energetic resources to power behavior and the irreversible entropy-producing processes that sustain them. Dissipative structure theory has often been a source of inspiration for better understanding the thermodynamics of biology, yet real organisms are inordinately more complex than most laboratory systems. Here we report on a simulated chemical dissipative structure that operates as a proto cell. The simulated swimmer moves through a 1D environment collecting resources that drive a nonlinear reaction network interior to the swimmer. The model minimally represents properties of a simple organism including rudimentary foraging and chemotaxis and an analog of a metabolism in the nonlinear reaction network. We evaluated how dynamical stability of the foraging dynamics (i.e., swimming and chemotaxis) relates to the rate of entropy production. Results suggested a relationship between dynamical steady states and entropy production that was tuned by the relative coordination of foraging and metabolic processes. Results include evidence in support of and contradicting one formulation of a maximum entropy production principle. We discuss the status of this principle and its relevance to biology.

Kinetic theory of collisionless relaxation for systems with long-range interactions

We develop the kinetic theory of collisionless relaxation for systems with long-range interactions in relation to the statistical theory of Lynden-Bell. We treat the multi-level case. We make the connection between the kinetic equation obtained from the quasilinear theory of the Vlasov equation and the relaxation equation obtained from a maximum entropy production principle. We propose a method to close the infinite hierarchy of kinetic equations for the phase level moments and obtain a kinetic equation for the coarse-grained distribution function in the form of a generalized Landau, Lenard–Balescu or Kramers equation associated with a generalized form of entropy (Chavanis, 2004). This allows us to go beyond the two-level case associated with a Fermi–Dirac-type entropy. We discuss the numerous analogies with two-dimensional turbulence. We also mention possible applications of the present formalism to fermionic and bosonic dark matter halos.

Multi-Species Compressible Solver for Non-Continuum Flow Through a Micro-Channel

Compressible multi species flow solver, developed by the authors Kumar and Maheshwari [May 15, 2020. “Viscous Multi-Species Lattice Boltzmann Solver for Simulating Shock-Wave Structure.” Computers and Fluids 203. Article ID 104539], has been extended further to non-continuum flows. The approach uses the Onsager-BGK model, which ensures Onsager's maximum entropy production principle is followed, thus avoids unphysical solutions. Equations for velocity slip and temperature jump have been derived. The viscous slip, thermal slip and diffusion slip coefficients have been successfully validated with 13-moment solver's and experimental data. The departure from equilibrium in such flows has been approximated by a collision probability function (), instead of using the complicated second order perturbation over the Knudsen number (that leads to Burnett equations). This provided the necessary reduction in (viscous, thermal, mass) dissipation and the developed approximate solver is able to predict the thermal and viscous profiles in a non-continuum regime and validates against DSMC simulations. Test cases consisting of flow through micro-channels demonstrated the ability of solver to handle monoatomic, diatomic and poly atomic gases. The developed non-continuum solver is in a finite volume framework and is easily adaptable to legacy in-house Navier–Stokes solvers.

A heuristic wave equation parameterizing BEC dark matter halos with a quantum core and an isothermal atmosphere

The Gross–Pitaevskii–Poisson equations that govern the evolution of self-gravitating Bose–Einstein condensates, possibly representing dark matter halos, experience a process of gravitational cooling and violent relaxation. We propose a heuristic parametrization of this complicated process in the spirit of Lynden-Bell’s theory of violent relaxation for collisionless stellar systems. We derive a generalized wave equation that was introduced phenomenologically in Chavanis (Eur Phys J Plus 132:248, 2017) involving a logarithmic nonlinearity associated with an effective temperature $$T_\mathrm{eff}$$ and a damping term associated with a friction $$\xi $$ . These terms can be obtained from a maximum entropy production principle and are linked by a form of Einstein relation expressing the fluctuation-dissipation theorem. The wave equation satisfies an H-theorem for the Lynden-Bell entropy and relaxes towards a stable equilibrium state which is a maximum of entropy at fixed mass and energy. This equilibrium state represents the most probable state of a Bose–Einstein condensate dark matter halo. It generically has a core-halo structure. The quantum core prevents gravitational collapse and may solve the core-cusp problem. The isothermal halo leads to flat rotation curves in agreement with the observations. These results are consistent with the phenomenology of dark matter halos. Furthermore, as shown in a previous paper (Chavanis in Phys Rev D 100:123506, 2019), the maximization of entropy with respect to the core mass at fixed total mass and total energy determines a core mass–halo mass relation which agrees with the relation obtained in direct numerical simulations. We stress the importance of using a microcanonical description instead of a canonical one. We also explain how our formalism can be applied to the case of fermionic dark matter halos.

Probability entropy approach to the calculation of time before failure of seaport electrical systems

The paper substantiates the method of calculating the operating time to failure of the seaport electrical equipment under the influence of a set of destabilizing factors on the basis of the principle of the maximum entropy production. The interpretation of the results of applying the principles including the concept of entropy to the mathematical models of wear that are used in the theory of reliability is given. The paper considers the probability characteristics of the electrical contacts of mooring columns exposed to the influence of the marine airborne environment. A method for calculating the operating time to failure of marine equipment based on the principle of the maximum entropy production (Ziegler’s principle) was developed. The proposed method is based on the physical principle, which includes the fundamental physical law – the second principle of thermodynamics. In this paper, a new value of the working time corresponding to the maximum observed rate of entropy change is determined. The presented results on finding the operating time to failure of electrical contacts, when exposed to a marine multifactorial environment (as a system with a system-forming connection, in the form of entropy), confirm that the use of the maximum entropy production principle as a criterion for operating time corresponds to the real values of the operating time of devices, and the principle itself gives a physical representation of occurring processes. The paper uses an exponential representation of the probability function of the operational state with an approximated, non-stationary failure rate.

Progress in Entropy Principle, as Disclosed by Nine Schools of Thermodynamics, and Its Ecological Implication

The entropy principle has been commonly considered to be a selection principle. A history/philosophy-of-science analysis of development in thermodynamic thought was carried out based on a historical account of contributions to thermodynamics of nine Schools of thermodynamics plus that of Mayer/Joule (the Mayer-Joule principle), publication of A Treatise of Heat and Energy, development in maximum entropy production principle (MEPP), and process ecology formulated by Ulanowicz. The analysis discloses the dual nature in the entropy principle, as selection principle and causal principle, and that as well in thermodynamics: as equilibrium thermodynamics (Gibbsian thermodynamics) and as “engineering” thermodynamics in a general sense. Entropy-growth-potential (EGP) as the causal agent and the theory of engineering thermodynamics entail the concept of causal necessity, as suggested by Poincare. Recent development of the entropy principle into maximum entropy production principle (MEPP) is then critically analyzed. Special attention is paid to MEPP’s explanatory power of biological orders vs. that of process ecology: whereas MEPP asserts universal approach to physics and biology based on physical necessity and efficient causation, the case for “EGP as the causal agent and process ecology” allows biology to be different from physics by allowing the additional presupposition of causal necessity and efficacious causation.

Native Chemical Computation. A Generic Application of Oscillating Chemistry Illustrated With the Belousov-Zhabotinsky Reaction. A Review.

Computing with molecules is at the center of complex natural phenomena, where the information contained in ordered sequences of molecules is used to implement functionalities of synthesized materials or to interpret the environment, as in Biology. This uses large macromolecules and the hindsight of billions of years of natural evolution. But, can one implement computation with small molecules? If so, at what levels in the hierarchy of computing complexity? We review here recent work in this area establishing that all physically realizable computing automata, from Finite Automata (FA) (such as logic gates) to the Linearly Bound Automaton (LBA, a Turing Machine with a finite tape) can be represented/assembled/built in the laboratory using oscillatory chemical reactions. We examine and discuss in depth the fundamental issues involved in this form of computation exclusively done by molecules. We illustrate their implementation with the example of a programmable finite tape Turing machine which using the Belousov-Zhabotinsky oscillatory chemistry is capable of recognizing words in a Context Sensitive Language and rejecting words outside the language. We offer a new interpretation of the recognition of a sequence of chemicals representing words in the machine's language as an illustration of the “Maximum Entropy Production Principle” and concluding that word recognition by the Belousov-Zhabotinsky Turing machine is equivalent to extremal entropy production by the automaton. We end by offering some suggestions to apply the above to problems in computing, polymerization chemistry, and other fields of science.

Rheology of active emulsions with negative effective viscosity

ABSTRACT We numerically study by lattice Boltzmann simulations the rheological properties of an active emulsion made of a suspension of an active polar gel embedded in an isotropic passive background. We find that the hexatic equilibrium configuration of polar droplets is highly sensitive to both active injection and external forcing and may either lead to asymmetric unidirectional states which break top-bottom symmetry or symmetric ones. In this latter case, for large enough activity, the system develops a shear thickening regime at low shear rates. Importantly, for larger external forcing a regime with stable negative effective viscosity is found. Moreover, at intermediate activity a region of multistability is encountered and we show that a maximum entropy production principle holds in selecting the most favorable state.

Is the Evolution of Energy System Productive Structures Driven by a Physical Principle?

The aim of the paper is to identify the consequence of the Constructal Principle in the field of Thermoeconomics of (energy) production systems. This Principle has been recently formulated as an extension of the Maximum Entropy Production Principle and it has been used in literature to explain the shape and structure of all kind of flowing systems. First, the concept of Thermoeconomic Environment is defined consistently with the consumption of environmental resources and residual emissions, which inherently characterize every kind of production system. This approach allows to infer that the evolution of any energy system is strictly related to the exploitation of resources from the Thermoeconomic Environment. Moreover, the widely accepted assumption that energy systems have to be optimized by minimizing the specific resource (exergy) cost of products, has to be regarded as a consequence of a physical principle that tells us which energy systems can persist in time (to survive) and which others would be selected for extinction. The paper shows how the creation of a recycle may allow a reduction of the unit exergy cost of the product, obtaining a more sustainable behavior of the macro-system, made up by the production process together with its supply chains, consistently with the Constructal Principle. Finally, the definition of the Thermoeconomic Environment allows (at least in principle) to properly identify the resource (exergy) cost of disposing off residues and sub-products directly in the environment, without any kind of additional operation. As a consequence, residues and sub-products have to be generally converted into some kind of product by different (new) production processes, supporting the paradigm of the Circular Economy and highlighting the importance of recycling not only for system efficiency, but for system surviving. More generally, the results obtained may be regarded as the physical justifications of the evolutionary tendency toward the more and more complex and highly circular pathways that can be observed in both natural and artificial (energy) production systems.

An Evolution Based on Various Energy Strategies

The simplest model of the evolution of agents with different energy strategies is considered. The model is based on the most general thermodynamic ideas and includes the procedures for selection, inheritance, and variability. The problem of finding a universal strategy (principle) as a selection of possible competing strategies is solved. It is shown that when there is non-equilibrium between the medium and agents, a direction in the evolution of agents arises, but at the same time, depending on the conditions of the evolution, different strategies can be successful. However, for this case, the simulation results reveal that in the presence of significant competition of agents, the strategy that has the maximum total energy dissipation of agents arising as a result of evolution turns out to be successful. Thus, it is not the specific strategy that is universal, but the maximization of dissipation. This result discovers an interesting connection between the basic principles of Darwin–Wallace evolution and the maximum entropy production principle.