Principle Of Minimum Entropy Production Research Articles

Soluble Model of a Nonequilibrium Steady State: The Van Kampen Objection and Other Lessons.

A simple model of charge transport is provided by a classical particle in a random potential and a dissipative coupling to the environment. The corresponding nonequilibrium steady state (NESS) can be determined analytically when both the disorder and dissipation are weak. We use it to illuminate some foundational issues in nonequilibrium statistical mechanics. We show that at nonlinear level dissipative response sensitively depends on the system-environment coupling, and the range of validity of the linear response theory is set by this coupling. This validates the Van Kampen objection. We also show that the principle of minimum entropy production does not determine the NESS beyond linear order in the electric field, while entropy maximization fails to produce the correct NESS already at linear order.

Exergy Flow as a Unifying Physical Quantity in Applying Dissipative Lagrangian Fluid Mechanics to Integrated Energy Systems.

Highly integrated energy systems are on the rise due to increasing global demand. To capture the underlying physics of such interdisciplinary systems, we need a modern framework that unifies all forms of energy. Here, we apply modified Lagrangian mechanics to the description of multi-energy systems. Based on the minimum entropy production principle, we revisit fluid mechanics in the presence of both mechanical and thermal dissipations and propose using exergy flow as the unifying Lagrangian across different forms of energy. We illustrate our theoretical framework by modeling a one-dimensional system with coupled electricity and heat. We map the exergy loss rate in real space and obtain the total exergy changes. Under steady-state conditions, our theory agrees with the traditional formula but incorporates more physical considerations such as viscous dissipation. The integral form of our theory also allows us to go beyond steady-state calculations and visualize the local, time-dependent exergy flow density everywhere in the system. Expandable to a wide range of applications, our theoretical framework provides the basis for developing versatile models in integrated energy systems.

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.

EXPERIMENTAL AND THEORETICAL CHARACTERIZATION OF TWO-PHASE FLOW DISTRIBUTION IN UNBALANCED FLOW NETWORKS

This study investigates the two-phase flow distribution of R-1234yf into two-branched channels. The effect of unbalanced pressure drop and tube diameter on the flow distribution was especially characterized and modeled. The experiments were conducted for a mass flux ranging from 393 kg/m<sup>2</sup>s to 1179 kg/ m<sup>2</sup>s, and the inlet quality was fixed at 0.2. The flow distribution was mainly governed by the pressure drop ratio between two branched channels. The mal-distribution under the unbalanced pressure drop condition was mitigated by increasing mass flux, whereas sustained mal-distribution was observed under unbalanced tube diameter conditions. Correspondingly, a theoretical representation of the phenomenon based on the principle of minimum entropy production was developed and adopted to predict two-phase flow distribution in an unbalanced flow network. The characteristics of the experimental data were clearly and quantitatively reflected in the prediction results. Under the unbalanced pressure drop condition, the predictions agreed well with the experimental data, maintaining the maximum deviation within ± 30%, whereas it exceeded ± 30% under the unbalanced tube diameter condition. The analysis of such theoretical formulation suggests the necessity of appropriate pressure drop models of flow impact, contraction, and merging at the outlet channel, which are compatible with the extremization of entropy production for further improving the prediction accuracy without compromising its generality.

Energy-Saving Analysis of Epichlorohydrin Plant Based on Entransy

To improve energy efficiency and to recover energy, various mathematical models, such as pinch analysis, entropy analysis, exergy analysis, and entransy analysis, have been established to analyze heat transfer networks. In this study, these methods were applied to analyze the energy-saving effect of the epichlorohydrin unit in a certain enterprise. The results showed that when the minimum heat transfer temperature difference (ΔTmin) was 10K, 15K, and 20K, the efficiencies of the second law of thermodynamics calculated by entropy analysis were 88.02%, 93.52%, and 99.49%, respectively. The analytical method calculated an efficiency of 61.01%, 59.28%, and 57.27%, respectively, with public works’ savings of 16.59%, 14.86%, and 12.02%. The pinch analysis method achieved public works’ savings of 22.80%, 21.50%, and 19.35%. The entransy analysis method calculated an entransy transfer efficiency of 42.81%, 42.13%, and 41.00%, respectively, with public works’ savings of 19.41%, 18.01%, and 15.70%. Based on the results, entropy analysis was found to be contrary to the principle of minimum entropy production. Exergy analysis was not able to establish a heat transfer network. The pinch analysis method was not suitable for determining the thermal efficiency of a heat transfer network as the criterion for evaluating energy saving. On the other hand, the entransy analysis method was able to establish a heat transfer network and evaluate the heat utilization of the network by entransy transfer efficiency. Overall, the data analysis was reasonable.

SIMULATION OF AGGREGATION PROCESS IN CERIUM AND ZIRCONIUM DIOXIDE NANOPARTICLES

A study of the aggregative stability of the CeO2-ZrO2 system was carried out in various pH ranges of the medium. To create a mathematical model of the stability of aggregates, the generalized DLVO theory was taken. The parameters of the structural component of the potential energy of particle interaction are determined using the principle of minimum entropy production. The limiting particle sizes of an an aggregatively stable system are determined.

Validity of Prigogine’ s minimum entropy production principle for a rigid heat-conducting solid beyond the Fourier heat transport regime

Validity of Prigogine’ s minimum entropy production principle for a rigid heat-conducting solid beyond the Fourier heat transport regime

A systematic approach as a methodological basis for the knowledge of the reception of law

The study analyzed the principles of interaction between the national legal system such as the reception of law. The reception of law, being a cultural phenomenon of social progress, occurs in a specific social environment backed up by the growing political, economic, social, and legal integration. It serves as a significant factor of mutual enrichment with universal human values. The process is governed by certain methodological prerequisites, such as principles validated by the objective evolution of nature and society.
 The research is based on the systemic approach to legal phenomena and the dialectical method, which calls for their study in being, functioning, and development. The meaning and significance of the widely used categories of the legal discourse of social phenomena, such as methodology, interaction, and movement, have been analyzed. Among the variety of movement interpretations, the most fruitful one in the legal science is the extended interpretation by Hegel and its identification with sublation in the dialectical method, emphasizing the unity of movement and legal matter. Such understanding of movement necessitates permanent improvement of the legal system and search for conditions and ways of its stable functioning in the existing external environment.
 The author notes the possible applications of natural sciences principles, such as Le Chateliers principle and Prigogines principle of minimum entropy production, reflecting the facts of stability and directionality of the establishment of a new stability in the reviewed system and other open system interactions.
 A set of methodological principles of interaction between national legal systems have been formulated based on the systemic approach and the natural sciences achievements that allow to understand the stability factors of a legal system and the internal reaction of a legal system and its external environment during the reception of law.

Semitheoretical formulation of annular flow void fraction using the principle of minimum entropy production

The two-phase flow void fraction is a critical parameter for characterising the pressure drop as well as heat and mass transfer capability of the working fluid within thermal systems, the accurate estimation of which drives heat exchanger design and control optimisation. A semitheoretical expression for the void fraction of two-phase flows, also applicable to small-sized channels, is obtained from an analytical study based on the principle of minimum entropy production and the introduction of empirical coefficients to be fitted to experimental data available in the open literature. These coefficients embody the importance of the simplified physical terms of this formulation while recovering the accuracy loss owing to nonlinear phenomena, heat and mass transfer, and three-dimensional effects. By accounting for surface tension, this model generalises previous theories and describes the influence of smaller-sized channels in terms of the stable void fraction. This mathematical framework can be used to summarise data covering different refrigerants, channel diameters, and operating conditions.

Theoretical study on regular reflection of shock wave–boundary layer interactions

Abstract

Errata: Formulation of steady-state void fraction through the principle of minimum entropy production [Journal of Thermal Science and Technology (2020jtst0025)

Errata: Formulation of steady-state void fraction through the principle of minimum entropy production [Journal of Thermal Science and Technology (2020jtst0025)

Formulation of steady-state void fraction through the principle of minimum entropy production

Formulation of steady-state void fraction through the principle of minimum entropy production

A general thermodynamic law for multi-phase systems without turbulences in the non-linear regime and its application to separation processes

Prigogine's principle of minimum entropy production is valid only for single-phase thermodynamic systems with non-equilibrium stationary states in the linear regime. We will show that it can be generalized to a more general law in the non-linear regime for multi-phase thermodynamic systems without turbulences in the flow quantities. We take the example of fluid-mixture separation of the binary fluid mixture benzene-trichloroethylene in a distillation column, which is driven always with constant power in the various rectification processes. We will demonstrate that there are lots of stationary states depending on the additional free parameter of the return ratio of the liquid and vapor flow. We will show further that there is always one stationary state with minimum entropy production. This state corresponds to the optimum separation condition of the column and it is the one, which has the longest setting time. Although engineers use well-known, empirically found relations and equations for their calculations to optimize rectification processes, this new fundamental law of non-equilibrium thermodynamics for non-linear multi-phase systems with laminar flow quantities rationalizes the engineers' empirical knowledge. We will demonstrate that optimizing non-linear non-equilibrium multi-phase thermodynamic processes is based on maximization of entropy flow and minimization of entropy production, which corresponds to maximum reversible separation work for all kinds of separation processes. All performed calculations are based on rigorous thermodynamics. In following papers, we will show that this new discovery is valid for a broad range of non-linear open thermodynamic multi-phase processes and can be beneficially used, e.g. for optimizing chemical and biochemical processes.

New look at an old principle: an alternative formulation of the theorem of minimum entropy production

We formulate a direct generalization of the Prigogine’s principle of minimum entropy production, according to a new isoperimetric variation principle by classical non-equilibrium thermodynamics. We focus our attention on the possible mathematical forms of constitutive equations. Our results show that the Onsager’s reciprocity relations are consequences of the suggested variation principle. Furthermore, we show by the example of the thermo-diffusion such reciprocity relations for diffusion tensor, which are missing in Onsager’s theory. Our theorem applied to the non-linear constitutive equations indicates the existence of dissipation potential. We study the forms of general reciprocity with the dissipation potential. This consideration results in a weaker condition than Li-Gyarmati-Rysselberhe reciprocity has. Furthermore, in the case of electric conductivity in the magnetic field, our theorem shows the correct dependence of the Onsager’s kinetic coefficient by the axial vector of magnetic induction. We show in general that the evolution criterion of the global entropy production is a Lyapunov-function, and so the final stationer state is independent of the initial, time-independent boundary conditions.

On the Efficiency of Electrochemical Devices from the Perspective of Endoreversible Thermodynamics

Abstract The current work presents a concept that deals with the production of entropy generated by non-equilibrium processes in consequence of mass and energy transfer. The often used concept of endoreversible thermodynamics is based on the non-realistic conjecture that the entire entropy production is realized at the system boundary. In this contribution, an open system in a thermodynamically non-equilibrium state is assumed. Production of entropy is generated due to non-equilibrium processes accompanied by energy conversion. The steady state of the system is maintained by a negative entropy flux. The conclusions for expansion energy conversion, i. e., thermal machines, confirm the general outcomes of the endoreversible thermodynamics. However, the presented conclusions related to non-expansion energy conversion offer a new perspective on the principle of minimum entropy production and the corresponding stability conditions at steady state. The analysis of the energy conversion in closed cycles is presented for fuel cells, i. e., non-expansion energy conversion. The efficiency of the energy conversion is maximal at zero power output. Moreover, the efficiency of the fuel cells, and consequently the efficiency of all non-expansion energy conversion processes, depends on the load and then the maximal possible efficiency can be determined.

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.

On using the minimum energy dissipation to estimate the steady-state of a flow network and discussion about the resulting power-law:application to tree-shaped networks in HVAC systems

The paper analyses how to compute the steady-state flow distribution through a given network by using the Minimum Entropy Production (MinEP) principle. For isothermal and incompressible flows, this is equivalent to the minimal dissipation of energy. The conditions that make this method equivalent to the conventional one are studied. There must exist a power-law for the energy dissipation (entropy generation) where the exponent must be the same for the whole network. To our knowledge, Niven was the first to get to this result. However he applied MinEP only to parallel pipes and unfortunately discarded it as a general method.The paper shows why it cannot be discarded yet. We discuss the role of the chosen exponent m and its link to the underlying physical phenomena.Moreover it is shown that there is a “hidden” fixed point value problem that must be studied further. The method introduced in this paper is developed specially for tree-shaped duct-networks which are frequently encountered in HVAC (Heating Ventilation and Air Conditioning) systems. The paper explains briefly what triggered this research; specifically, difficulties related with branched junctions, mainly in return-type networks.Finally, we illustrate the method with some examples.

Application of the minimum entropy production principle to shock reflection induced by separation

In this paper separation-induced shock reflection is studied theoretically and experimentally. An analytical model is proposed to establish the connections among upstream conditions, downstream conditions and shock configurations. Furthermore, the minimum entropy production principle is employed to determine the incident shock angles as well as the criterion for the transition from regular reflection to Mach reflection, which agrees well with experimental results. Additionally, a solution path for a reflected shock that fulfills the minimum entropy production principle is found in the overall regular reflection domain, based on which the steadiest shock configuration may be determined according to upstream and downstream conditions.

On the Interaction of the Deformation and Photonic Self-Organizations in Condensed Media: Overview

The experimental data on the mass transfer in condensed media under the action of mechanical stress and light pressure are presented. In both cases, the observed formation of periodic structures is interpreted from the point of view of the dynamical principle of minimum entropy production. The prospects of using the discovered self-organizing processes for the formation of photonic crystals and optical metamaterials are discussed.

Filament Dynamics in Resistive Switching

The hallmark of nonequilibrium phase transitions is the strong spatial inhomogeneity associated with bi-stability of macroscopic phases. We consider the resistive switching in transition metal oxides as a prototypical nonequilibrium phase transition associated with an equilibrium phase transition. We analyze the behavior of the hysteretic behavior of I-V relations in the resistive switching, especially the negative differential resistance regime during the reverse sweep of applied voltage. We show that the peculiar I-V behavior is closely related to the bi-stability of the metallic and insulating phases and the dynamics of the metallic filament, and investigate the filament dynamics in terms of the minimum entropy production principle in the nonequilibrium theormodynamics.