Maximum Entropy Production Principle Research Articles

Unifying catchment water balance models for different time scales through the maximum entropy production principle

AbstractThe paper presents a thermodynamic basis for water balance partitioning at the catchment scale, through formulation of flux‐force relationships for the constituent hydrological processes, leading to the derivation of optimality conditions that satisfy the principle of Maximum Entropy Production (MEP). Application of these optimality principles at three different time scales leads to the derivation of water balance equations that mimic widely used, empirical models, i.e., Budyko‐type model over long‐term scale, the “abcd” model at monthly scale, and the SCS model at the event scale. The applicability of MEP in each case helps to draw connections between the water balances at the three different time scales, and to demonstrate a common thermodynamic basis for the otherwise empirical water balance models. In particular, it is concluded that the long time scale Budyko‐type model and the event scale SCS model are both special cases of the monthly “abcd” model.

Life's arrow: the Epistemic Singularity.

For centuries people have been asking, “Why is there something rather than nothing?” Science has not been able to give us an answer so far. We still have to live with the basic statement that “Everything that is is, and it is as long as it keeps its identity, that is, its onticity”, which we may call the “Strong Ontic Principle”. Nonetheless, science can answer another ontological question, namely “Why does something happen; why there are events in the universe?” The answer is the second law of thermodynamics, which we may call the “Weak Ontic Principle”. It was discovered by Rudolf Clausius in 1865, and it has been applied successfully in technological practice. However, at the conceptual level, the law has been subject to an amazing misinterpretation for almost a century. Its recent reformulation may become one of the most remarkable chapters in the history of science. Energy is distributed unevenly in the universe, and it is those differences in energy densities—energy gradients—that drive all events. The universe has a “time arrow”: it is moving in one direction while a quantity called entropy always increases. Entropy has been interpreted incorrectly as being equal to disorder. However, the increase of entropy is in fact a measure of diminishing energy gradients, of energy dissipation and “homogenization”. Without energy gradients, the universe would be in thermodynamic equilibrium, and events would no longer be possible. The original version of the second law by Clausius—that entropy always increases—therefore defines the direction of the movement of the universe. During the second half of the 20th century, several scientists pondered over the rate of the movement and their reasoning culminated in a principle now called the “Maximum Entropy Production Principle” (MEPP): entropy not only tends to increase, but it tends to increase at the fasted rate …

Training Concept, Evolution Time, and the Maximum Entropy Production Principle

The maximum entropy production principle (MEPP) is a type of entropy optimization which demands that complex non-equilibrium systems should organize such that the rate of the entropy production is maximized. Our take on this principle is that to prove or disprove the validity of the MEPP and to test the scope of its applicability, it is necessary to conduct experiments in which the entropy produced per unit time is measured with a high precision. Thus we study electric-field-induced self-assembly in suspensions of carbon nanotubes and realize precise measurements of the entropy production rate (EPR). As a strong voltage is applied the suspended nanotubes merge together into a conducting cloud which produces Joule heat and, correspondingly, produces entropy. We introduce two types of EPR, which have qualitatively different significance: global EPR (g-EPR) and the entropy production rate of the dissipative cloud itself (DC-EPR). The following results are obtained: (1) As the system reaches the maximum of the DC-EPR, it becomes stable because the applied voltage acts as a stabilizing thermodynamic potential; (2) We discover metastable states characterized by high, near-maximum values of the DC-EPR. Under certain conditions, such efficient entropy-producing regimes can only be achieved if the system is allowed to initially evolve under mildly non-equilibrium conditions, namely at a reduced voltage; (3) Without such a “training” period the system typically is not able to reach the allowed maximum of the DC-EPR if the bias is high; (4) We observe that the DC-EPR maximum is achieved within a time, Te, the evolution time, which scales as a power-law function of the applied voltage; (5) Finally, we present a clear example in which the g-EPR theoretical maximum can never be achieved. Yet, under a wide range of conditions, the system can self-organize and achieve a dissipative regime in which the DC-EPR equals its theoretical maximum.

Steepest-entropy-ascent quantum thermodynamic modeling of the relaxation process of isolated chemically reactive systems using density of states and the concept of hypoequilibrium state.

This paper presents a study of the nonequilibrium relaxation process of chemically reactive systems using steepest-entropy-ascent quantum thermodynamics (SEAQT). The trajectory of the chemical reaction, i.e., the accessible intermediate states, is predicted and discussed. The prediction is made using a thermodynamic-ensemble approach, which does not require detailed information about the particle mechanics involved (e.g., the collision of particles). Instead, modeling the kinetics and dynamics of the relaxation process is based on the principle of steepest-entropy ascent (SEA) or maximum-entropy production, which suggests a constrained gradient dynamics in state space. The SEAQT framework is based on general definitions for energy and entropy and at least theoretically enables the prediction of the nonequilibrium relaxation of system state at all temporal and spatial scales. However, to make this not just theoretically but computationally possible, the concept of density of states is introduced to simplify the application of the relaxation model, which in effect extends the application of the SEAQT framework even to infinite energy eigenlevel systems. The energy eigenstructure of the reactive system considered here consists of an extremely large number of such levels (on the order of 10^{130}) and yields to the quasicontinuous assumption. The principle of SEA results in a unique trajectory of system thermodynamic state evolution in Hilbert space in the nonequilibrium realm, even far from equilibrium. To describe this trajectory, the concepts of subsystem hypoequilibrium state and temperature are introduced and used to characterize each system-level, nonequilibrium state. This definition of temperature is fundamental rather than phenomenological and is a generalization of the temperature defined at stable equilibrium. In addition, to deal with the large number of energy eigenlevels, the equation of motion is formulated on the basis of the density of states and a set of associated degeneracies. Their significance for the nonequilibrium evolution of system state is discussed. For the application presented, the numerical method used is described and is based on the density of states, which is specifically developed to solve the SEAQT equation of motion. Results for different kinds of initial nonequilibrium conditions, i.e., those for gamma and Maxwellian distributions, are studied. The advantage of the concept of hypoequilibrium state in studying nonequilibrium trajectories is discussed.

How the Second Law of Thermodynamics Has Informed Ecosystem Ecology through Its History

Many attempts have been made to develop a general principle governing how systems develop and organize in ecology. We reviewed the historical developments that led to the conceptualization of several goal-oriented principles in ecosystem ecology. We focused on two prominent principles—the maximum power principle (MPP) and the maximum entropy production principle (MEPP)—and the literature that applies to both. Although these principles have conceptual overlap, we found considerable differences in their historical development, the disciplines that apply these principles, and their adoption in the literature. These principles were more similar than dissimilar, and the maximization of power in ecosystems occurs with maximum entropy production. These principles have great potential to explain how systems develop, organize, and function, but there are no widely agreed-on theoretical derivations for the MEPP and MPP, hindering their broader use in ecological research. We end with recommendations for how ecosystems-level studies may better use these principles.

Electrohydrodynamics of a Cone–Jet Flow at a High Relative Permittivity

We have proposed a new solution of the electrohydrodynamic equations describing a novel cone–jet flow structure formed at a conductive liquid meniscus in an electric field. Focusing on the liquids characterized by a high relative permittivity and using the slender body approximation, the cone–jet transition profiles and their characteristic radii are predicted in relation to the material parameters. The stable value of the cone angle is obtained using the Onsager’s principle of maximum entropy production. Three different regimes of the cone–jet flow behavior are identified depending on the relative importance of capillary, viscous and inertial stress contributions. The presented complete analytical solutions for the cone–jet transition zone and the far jet region yield several different laws of algebraic decrease for the radius, surface charge, and electric field of the jet.

O14] Application of maximum entropy production principle to rapid solidification

O14] Application of maximum entropy production principle to rapid solidification

The Thermodynamics of Marine Biogeochemical Cycles: Lotka Revisited.

Nearly 100 years ago, Alfred Lotka published two short but insightful papers describing how ecosystems may organize. Principally, Lotka argued that ecosystems will grow in size and that their cycles will spin faster via predation and nutrient recycling so as to capture all available energy, and that evolution and natural selection are the mechanisms by which this occurs and progresses. Lotka's ideas have often been associated with the maximum power principle, but they are more consistent with recent developments in nonequilibrium thermodynamics, which assert that complex systems will organize toward maximum entropy production (MEP). In this review, we explore Lotka's hypothesis within the context of the MEP principle, as well as how this principle can be used to improve marine biogeochemistry models. We need to develop the equivalent of a climate model, as opposed to a weather model, to understand marine biogeochemistry on longer timescales, and adoption of the MEP principle can help create such models.

Electrohydrodynamics of stationary cone-jet streaming

We discover novel types of stationary cone-jet steams emitting from a nozzle of a syringe loaded with a conductive liquid. The predicted cone-jet-flow geometries are based on the analysis of the electrohydrodynamic equations including the surface current. The electric field and the flow velocity field inside the cone are calculated. It is shown that the electric current along the conical stream depends on the cone angle. The stable values of this angle are obtained based on the Onsager’s principle of maximum entropy production. The characteristics of the jet that emits from the conical tip are also studied. The obtained results are relevant both for the electrospraying and electrospinning processes.

Life’s a Gas: A Thermodynamic Theory of Biological Evolution

This paper outlines a thermodynamic theory of biological evolution. Beginning with a brief summary of the parallel histories of the modern evolutionary synthesis and thermodynamics, we use four physical laws and processes (the first and second laws of thermodynamics, diffusion and the maximum entropy production principle) to frame the theory. Given that open systems such as ecosystems will move towards maximizing dispersal of energy, we expect biological diversity to increase towards a level, Dmax, representing maximum entropic production (Smax). Based on this theory, we develop a mathematical model to predict diversity over the last 500 million years. This model combines diversification, post-extinction recovery and likelihood of discovery of the fossil record. We compare the output of this model with that of the observed fossil record. The model predicts that life diffuses into available energetic space (ecospace) towards a dynamic equilibrium, driven by increasing entropy within the genetic material. This dynamic equilibrium is punctured by extinction events, which are followed by restoration of Dmax through diffusion into available ecospace. Finally we compare and contrast our thermodynamic theory with the MES in relation to a number of important characteristics of evolution (progress, evolutionary tempo, form versus function, biosphere architecture, competition and fitness).

Invariance of specific mass increment in the case of non-equilibrium growth

The invariance of specific mass increments of crystalline structures that co-exist in the case of non-equilibrium growth is grounded for the first time by using the maximum entropy production principle. Based on the hypothesis of the existence of a universal growth equation, and through the dimensional analysis, an explicit form of the time-dependent specific mass increment is proposed. The applicability of the obtained results for describing growth in animate nature is discussed.

Multiscale Analysis of the Predictability of Stock Returns

Due to the strong complexity of financial markets, economics does not have a unified theory of price formation in financial markets. The most common assumption is the Efficient-Market Hypothesis, which has been attacked by a number of researchers, using different tools. There were varying degrees to which these tools complied with the formal definitions of efficiency and predictability. In our earlier work, we analysed the predictability of stock returns at two time scales using the entropy rate, which can be directly linked to the mathematical definition of predictability. Nonetheless, none of the above-mentioned studies allow any general understanding of how the financial markets work, beyond disproving the Efficient-Market Hypothesis. In our previous study, we proposed the Maximum Entropy Production Principle, which uses the entropy rate to create a general principle underlying the price formation processes. Both of these studies show that the predictability of price changes is higher at the transaction level intraday scale than the scale of daily returns, but ignore all scales in between. In this study we extend these ideas using the multiscale entropy analysis framework to enhance our understanding of the predictability of price formation processes at various time scales.

A thermodynamic interpretation of Budyko and L'vovich formulations of annual water balance: Proportionality Hypothesis and maximum entropy production

AbstractThe paper forms part of the search for a thermodynamic explanation for the empirical Budyko Curve, addressing a long‐standing research question in hydrology. Here this issue is pursued by invoking the Proportionality Hypothesis underpinning the Soil Conservation Service (SCS) curve number method widely used for estimating direct runoff at the event scale. In this case, the Proportionality Hypothesis posits that the ratio of continuing abstraction to its potential value is equal to the ratio of direct runoff to its potential value. Recently, the validity of the Proportionality Hypothesis has been extended to the partitioning of precipitation into runoff and evaporation at the annual time scale as well. In this case, the Proportionality Hypothesis dictates that the ratio of continuing evaporation to its potential value is equal to the ratio of runoff to its potential value. The Budyko Curve could then be seen as the straightforward outcome of the application of the Proportionality Hypothesis to estimate mean annual water balance. In this paper, we go further and demonstrate that the Proportionality Hypothesis itself can be seen as a result of the application of the thermodynamic principle of Maximum Entropy Production (MEP). In this way, we demonstrate a possible thermodynamic basis for the Proportionality Hypothesis, and consequently for the Budyko Curve. As a further extension, the L'vovich formulation for the two‐stage partitioning of annual precipitation is also demonstrated to be a result of MEP: one for the competition between soil wetting and fast flow during the first stage; another for the competition between evaporation and base flow during the second stage.

Statistical optimization for passive scalar transport: maximum entropy production versus maximum Kolmogorov–Sinai entropy

Abstract. We derive rigorous results on the link between the principle of maximum entropy production and the principle of maximum Kolmogorov–Sinai entropy for a Markov model of the passive scalar diffusion called the Zero Range Process. We show analytically that both the entropy production and the Kolmogorov–Sinai entropy, seen as functions of a parameter f connected to the jump probability, admit a unique maximum denoted fmaxEP and fmaxKS. The behaviour of these two maxima is explored as a function of the system disequilibrium and the system resolution N. The main result of this paper is that fmaxEP and fmaxKS have the same Taylor expansion at first order in the deviation from equilibrium. We find that fmaxEP hardly depends on N whereas fmaxKS depends strongly on N. In particular, for a fixed difference of potential between the reservoirs, fmaxEP(N) tends towards a non-zero value, while fmaxKS(N) tends to 0 when N goes to infinity. For values of N typical of those adopted by Paltridge and climatologists working on maximum entropy production (N ≈ 10–100), we show that fmaxEP and fmaxKS coincide even far from equilibrium. Finally, we show that one can find an optimal resolution N* such that fmaxEP and fmaxKS coincide, at least up to a second-order parameter proportional to the non-equilibrium fluxes imposed to the boundaries. We find that the optimal resolution N* depends on the non-equilibrium fluxes, so that deeper convection should be represented on finer grids. This result points to the inadequacy of using a single grid for representing convection in climate and weather models. Moreover, the application of this principle to passive scalar transport parametrization is therefore expected to provide both the value of the optimal flux, and of the optimal number of degrees of freedom (resolution) to describe the system.

Energy, growth, and evolution: Towards a naturalistic ontology of economics

In recent years new approaches to the integration of economics and thermodynamics have been developed which build on the physics of open non-equilibrium systems, the so-called ‘Maximum Entropy Production Principle’. I review these contributions in the light of the implications for economic ontology, i.e. the question what the fundamental constituents of real world economic phenomena are. I argue in favor of the ‘naturalization’ of economic ontology, using the phenomenon of economic growth as my workhorse, and I explore the implications for the cross-disciplinary foundations of ecological economics. The paper shows how economic growth can be conceived as a ‘natural’ process that is driven by fundamental physical forces. The argument proceeds in three steps. After a short review of recent research on the linkage between energy and growth, I establish the connection with bioeconomic theories about evolution that allow restating the role of Lotka's Maximum Power Principle (MPP) as a property of open non-equilibrium flow systems with sufficient degrees of freedom of structural adaptation. The MPP is then related to the recent literature on Maximum Entropy Production (MEP), especially as deployed in the Earth Sciences. Economic growth can be seen as resulting from evolutionary adaptations of flow gradients in economic systems that increase throughputs of exergy and generation of work, and which thereby enhance the capacity of the Earth System to maximize entropy production. This framework offers fresh perspectives on a number of issues in research and policy, which I discuss in the conclusion.

Self-assembled wiggling nano-structures and the principle of maximum entropy production.

While behavior of equilibrium systems is well understood, evolution of nonequilibrium ones is much less clear. Yet, many researches have suggested that the principle of the maximum entropy production is of key importance in complex systems away from equilibrium. Here, we present a quantitative study of large ensembles of carbon nanotubes suspended in a non-conducting non-polar fluid subject to a strong electric field. Being driven out of equilibrium, the suspension spontaneously organizes into an electrically conducting state under a wide range of parameters. Such self-assembly allows the Joule heating and, therefore, the entropy production in the fluid, to be maximized. Curiously, we find that emerging self-assembled structures can start to wiggle. The wiggling takes place only until the entropy production in the suspension reaches its maximum, at which time the wiggling stops and the structure becomes quasi-stable. Thus, we provide strong evidence that maximum entropy production principle plays an essential role in the evolution of self-organizing systems far from equilibrium.

Hillock formation by surface drift-diffusion driven by the gradient of elastic dipole interaction energy under compressive stresses in bi-crystalline thin films

We investigated surface drift diffusion induced grain boundary (GB) grooving and ridge (hillock) formation and growth, under the combined actions of the capillary forces and applied uniaxial compressive stresses, in bi-crystal thin films with dynamical computer simulations. In the present theory, the generalized driving force for the stress induced surface drift diffusion includes not only the usual gradient of the elastic strain energy density, but also the elastic dipole tensor interaction energy. During the morphological evolution of GB ridge formation and growth, triple junction (TJ) displacement and its velocity are continuously tracked down in order to resolve precisely the crossover time and depth at which velocity sign inversion takes place. An incubation time for the onset of the ridge growth stage coupled to the GB-TJ displacement velocity inversion is defined and its dependence on the stress is investigated. This analysis implies that the ridge growth stage is not controlled by Ziegler’s ‘maximum entropy production principle’ but rather Prigogine’s ‘minimum entropy production hypothesis’ for the stationary non-equilibrium states in complex systems, which are exposed to external applied body forces and surface tractions. Keywords: Surfaces and interfaces; Grain boundary grooving; Non-equilibrium thermodynamics; Surface/grain boundary diffusion; Compressive stresses; Thin films DOI: 10.17350/HJSE19030000010 Full Text:

干旱半干旱区灌丛斑块与降水量响应关系的熵模型模拟

PDF HTML阅读 XML下载 导出引用 引用提醒 干旱半干旱区灌丛斑块与降水量响应关系的熵模型模拟 DOI: 10.5846/stxb201405080909 作者: 作者单位: 1.北京师范大学资源学院,1.北京师范大学资源学院,1.北京师范大学资源学院,云南财经大学国土资源与持续发展研究所,1.北京师范大学资源学院 作者简介: 通讯作者: 中图分类号: 基金项目: 国家自然科学基金(41025001,91425301) Relationship and response of shrub patches to precipitation using the entropy model in arid and semiarid regions of China Author: Affiliation: College of resource science and technology，Beijing Normal University,College of resource science and technology，Beijing Normal University,,, Fund Project: 摘要 | 图/表 | 访问统计 | 参考文献 | 相似文献 | 引证文献 | 资源附件 | 文章评论 摘要:灌丛斑块分布格局是灌木在干旱缺水条件下对生存环境的自我调节和适应的具体表现。应用熵理论和Klausmier模型,解释了灌丛斑块水分聚集原理并模拟了不同年降水条件下灌丛斑块的最佳面积比值(即最佳灌丛盖度)。研究结果表明:灌丛斑块生物量与其土壤含水量呈反比例函数关系,当生态系统处于稳定状态时(即熵最大状况下),年降水量与灌丛斑块面积比值符合一定的线性关系。研究采用内蒙古草原地区的野外调查数据,获得模型所需参数,进而模拟了不同年降水量条件下灌丛斑块最佳面积比值,研究结果可为半干旱地区植被保护与恢复提供参考。 Abstract:In arid and semiarid regions, shrubs are often spatially distributed in patchy patterns, allowing shrubs to self-regulate and adapt to dry conditions. Shrub encroachment (also known as shrub invasion) is a typical pattern of patchy shrub distribution. This phenomenon represents one of the major environmental problems faced by the world's grassland ecosystems, and widely occurs in Africa, the USA, Australia, Asia, Europe. Shrub encroachment is exacerbated by overgrazing, prairie fires, climate change, atmospheric carbon dioxide concentrations, and biotic and abiotic environmental factors. Precipitation is considered to be an influential factor of patchy shrub distribution in arid and semiarid regions, which may regulate shrub coverage and the patch size. Theoretically, a steady shrub ecosystem would have a balance between water supply and demand, while certain levels of precipitation should correspond with optimal shrub coverage, i.e., the optimal ratio of shrub patch size to the total area in the steady patchy shrub ecosystem. The maximum entropy production principle (MEP) to living systems may be used to quantitatively explain optimization in the non-equilibrium process, such as the evolution of biological macromolecules and the plant optimization theory at different scales. Shrub patches and interspace may be considered as a water gathering system, in which entropy production is mainly caused by two processes: (1) soil water mixing in shrub patches and (2) either rainfall or outside runoff. For entropy flow, the main contributing factors are precipitation, evaporation, and transpiration processes in shrub patches. In this study, a modified model for a shrub patch ecosystem was built. It was applied to explain the moisture gathering in shrub patches. The model was based on the entropy change theory and Klausmier moisture gathering model, consisting of a pair of partial differential equations on soil moisture and plant biomass in the two-dimension plane. Based on the principle of maximum entropy production (MEP), the optimal ratio of shrub patches responding to different annual precipitation may be simulated. The simulation results showed a negative correlation between biomass and soil water content, which was verified by field experiments. When the ecosystem was steady (and the MEP principle was satisfied), the annual precipitation and the optimal ratio of shrub patches had a certain linear relationship. The existing data for Inner Mongolia was used to set up the model parameters, from which the optimal ratio of shrub patches responding to different annual precipitation values varying from 50 mm to 450 mm was simulated. Then the optimal shrub area ratios for practical application were determined in arid and semiarid regions. For example a region with 300 mm precipitation produced a shrub patch ratio of around 30%. This result provided theoretical support and practical guidance for ecosystem protection and plant recovery in arid and semiarid regions. The simulated values varied considerably, which may be because the effects of surface runoff were simplified to a linear relationship with precipitation in the modified model. Therefore, surface runoff sensitivity to patchy shrub distribution patterns requires further research. 参考文献 相似文献 引证文献

The maximum entropy production principle in the evolution of the macrosystems: some new results

Closed non-equilibrium macrosystems, which are in the process of evolution to the equilibrium state, subject to the maximum entropy production principle are considered in the paper. A procedure for direct calculation of entropy production in an arbitrary step of evolution is developed. In accordance with the maximum entropy production principle, the nonlinear equations of the distribution dynamics in the non-equilibrium closed system are obtained. It is shown that the development trajectory of such system is entirely determined by the nature of the initial distribution and distribution in the equilibrium state. Far from the equilibrium state, a decisive role in the evolution equation is played not by the difference between these values, but the difference of their logarithms. The definition of internal system time is given. A theorem, which states that distribution of elements by the phase space cells, which keeps a sum of the logarithms of their number constant is implemented at each time point for the closed non-equilibrium system, developed in accordance with the maximum entropy production principle is proved. Its formulation for the case of continuous distributions is given. The connection with the Liouville's theorem is shown. Dynamic invariant of the evolution of closed systems, evolving in accordance with the maximum entropy production principle is defined.

Steepest entropy ascent model for far-nonequilibrium thermodynamics: unified implementation of the maximum entropy production principle.

By suitable reformulations, we cast the mathematical frameworks of several well-known different approaches to the description of nonequilibrium dynamics into a unified formulation valid in all these contexts, which extends to such frameworks the concept of steepest entropy ascent (SEA) dynamics introduced by the present author in previous works on quantum thermodynamics. Actually, the present formulation constitutes a generalization also for the quantum thermodynamics framework. The analysis emphasizes that in the SEA modeling principle a key role is played by the geometrical metric with respect to which to measure the length of a trajectory in state space. In the near-thermodynamic-equilibrium limit, the metric tensor is directly related to the Onsager's generalized resistivity tensor. Therefore, through the identification of a suitable metric field which generalizes the Onsager generalized resistance to the arbitrarily far-nonequilibrium domain, most of the existing theories of nonequilibrium thermodynamics can be cast in such a way that the state exhibits the spontaneous tendency to evolve in state space along the path of SEA compatible with the conservation constraints and the boundary conditions. The resulting unified family of SEA dynamical models is intrinsically and strongly consistent with the second law of thermodynamics. The non-negativity of the entropy production is a general and readily proved feature of SEA dynamics. In several of the different approaches to nonequilibrium description we consider here, the SEA concept has not been investigated before. We believe it defines the precise meaning and the domain of general validity of the so-called maximum entropy production principle. Therefore, it is hoped that the present unifying approach may prove useful in providing a fresh basis for effective, thermodynamically consistent, numerical models and theoretical treatments of irreversible conservative relaxation towards equilibrium from far nonequilibrium states. The mathematical frameworks we consider are the following: (A) statistical or information-theoretic models of relaxation; (B) small-scale and rarefied gas dynamics (i.e., kinetic models for the Boltzmann equation); (C) rational extended thermodynamics, macroscopic nonequilibrium thermodynamics, and chemical kinetics; (D) mesoscopic nonequilibrium thermodynamics, continuum mechanics with fluctuations; and (E) quantum statistical mechanics, quantum thermodynamics, mesoscopic nonequilibrium quantum thermodynamics, and intrinsic quantum thermodynamics.