Theoretical arguments on exergy method and non-equilibrium in nuclear processes

The present Ph.D. thesis aims at discussing theoretical aspects and arguments concerning thermodynamic methods and applications to fission and fusion nuclear plants. All parts of the thesis are rooted in the ground of the scientific literature, and all outcomes and conclusions corroborate the conceptual building with no disprove of any foundations constituting the framework accepted and shared by the whole scientific community. Though, clarifications, extensions, generalizations and applications of concepts and definitions represent primary outcomes deemed by the author beneficial for a rational and systematic perspective of Physics and Thermodynamics in the research and applications to technological and industrial developments. This abstract attempt to summarize state-of-the-art and references, methods, achievements, original results, future perspectives and is followed by an index breaking down all sections to enable an overview on the way the thesis is organized. The mechanical aspect of the entropy-exergy relationship, together with the thermal aspect usually considered, represents the outset of the research and one of the central topics. This very aspect leads to a formulation of physical exergy and chemical exergy based on both useful work and useful heat, or useful work and useful mass, representing first outcomes based on the concept of available energy of a thermodynamic system interacting with a reservoir. By virtue of the entropy-exergy relationship, this approach suggests that a mechanical entropy contribution can be defined, in addition to the already used thermal entropy contribution, for work interaction due to pressure and volume variations. The mechanical entropy is related to energy transfer through work interaction, and it is complementary to the thermal entropy that accounts energy transfer by means of heat interaction. Then, the logical sequence to get mechanical exergy expression to evaluate useful work withdrawn from available energy is demonstrated. Based on mechanical exergy expression, the mechanical entropy set forth is deduced in a general form valid for any process. Finally, the formulation of physical exergy is proposed that summarizes the contribution of either heat or work interactions and related thermal exergy as well as mechanical exergy that both result as the outcome from the available energy of the composite of the system interacting with a reservoir. This formulation contains an additional term that takes into account the volume and, consequently, the pressure that allow to evaluate exergy with respect to the reservoir characterized by constant pressure other than constant temperature. The basis and related conclusions of this paper are not in contrast with principles and theoretical framework of thermodynamics and highlight a more extended approach to exergy definitions already reported in literature that remain the reference ground of present analysis. The literature reports that equality of temperature, equality of potential and equality of pressure between a system and a reservoir are necessary conditions for the stable equilibrium of the system-reservoir composite or, in the opposite and equivalent logical inference, that stable equilibrium is a sufficient condition for equality. A novelty of the present study is to prove that equality of temperature, potential and pressure is also a sufficient condition for stable equilibrium, in addition to necessity, implying that stable equilibrium is a condition also necessary, in addition to sufficiency, for equality. A subsequent implication is that the proof of the sufficiency of equality (or the necessity of stable equilibrium) is attained by means of the generalization of the entropy property, derived from the generalization of exergy property, which is used to demonstrate that stable equilibrium is a logical consequence of equality of generalized potential. This proof is underpinned by the Second Law statement and the Maximum-Entropy Principle based on the generalized entropy which depends on temperature, potential and pressure of the reservoir. The conclusion, based on these two novel concepts, consists of the theorem of necessity and sufficiency of stable equilibrium for equality of generalized potentials within a composite constituted by a system and a reservoir. Among all statements of Second Law, the existence and uniqueness of stable equilibrium, for each given value of energy content and composition of constituents of any system, has been adopted to define thermodynamic entropy by means of the impossibility of Perpetual Motion Machine of the Second Kind (PMM2) which is a consequence of the Second Law. Equality of temperature, chemical potential and pressure in many-particle systems are proved to be necessary conditions for the stable equilibrium. The proofs assume the stable equilibrium and derive, through the Highest-Entropy Principle, equality of temperature, chemical potential and pressure as a consequence. In this regard, a first novelty of the present research is to demonstrate that equality is also a sufficient condition, in addition to necessity, for stable equilibrium implying that stable equilibrium is a condition also necessary, in addition to sufficiency, for equality of temperature potential and pressure addressed to as generalized potential. The second novelty is that the proof of sufficiency of equality, or necessity of stable equilibrium, is achieved by means of a generalization of entropy property, derived from a generalized definition of exergy, both being state and additive properties accounting for heat, mass and work interactions of the system underpinning the definition of Highest-Generalized-Entropy Principle adopted in the proof. To complement the physical meaning and the reasons behind the need of a generalized definition of thermodynamic entropy, it is proposed a logical relation of its formulation on the base of Gibbs equation expressing the First Law. Moreover, a step forward is the extension of the canonical Equation of State in the perspective of thermal and chemical aspect of microscopic configurations of a system related to inter-particle kinetic energy and inter-particle potential energy determining macroscopic parameters. As a consequence, a generalized State Equation is formulated accounting for thermal, chemical and mechanical thermodynamic potentials characterizing any system in any state. As far as the Non-Equilibrium Thermodynamic is concerned, the present research aims at discussing the hierarchical structure of so-called mesoscopic systems configuration. In this regard, thermodynamic and informational aspects of entropy concept are highlighted to propose a unitary perspective of its definitions as an inherent property of any system in any state, both physical and informational. The dualism and the relation between physical nature of information and the informational content of physical states of matter and phenomena play a fundamental role in the description of multi-scale systems characterized by hierarchical configurations. A method is proposed to generalize thermodynamic and informational entropy property and characterize the hierarchical structure of its canonical definition at macroscopic and microscopic levels of a system described in the domain of classical and quantum physics. The conceptual schema is based on dualisms and symmetries inherent to the geometric and kinematic configurations and interactions occurring in many-particle and few-particle thermodynamic systems. The hierarchical configuration of particles and sub-particles, representing the constitutive elements of physical systems, breaks down into levels characterized by particle masses subdivision, implying positions and velocities degrees of freedom multiplication. This hierarchy accommodates the allocation of phenomena and processes from higher to lower levels in the respect of the equipartition theorem of energy. However, the opposite and reversible process, from lower to higher level, is impossible by virtue of the Second Law, expressed as impossibility of Perpetual Motion Machine of the Second Kind (PMM2) remaining valid at all hierarchical levels, and the non-existence of Maxwell’s demon. Based on the generalized definition of entropy property, the hierarchical structure of entropy contribution and production balance, determined by degrees of freedom and constraints of systems configuration, is established. Moreover, as a consequence of the Second Law, the non-equipartition theorem of entropy is enunciated, which would be complementary to the equipartition theorem of energy derived from the First Law. A section is specifically dedicated to specialize Second Law analyses to characterize balances of properties, and efficiencies of processes, occurring in elemental fission and fusion nuclear reactions. The conceptual schema is underpinned by the paradigm of microscopic few-particle systems and the inter-particle kinetic energy and binding potential energy determined by interactions among atomic nuclei and subatomic particles in non-equilibrium states along irreversible phenomena. The definition here proposed for thermodynamic entropy calculation is based on energy and exergy both being measurable properties by means of those values calculated from particles mass defect and used to directly derive entropy balances along nuclear processes occurring in operating industrial plants. Finally, it is proposed a preliminary exergy analysis of EU DEMO pulsed fusion power plant considering the Primary Heat Transfer Systems, the Intermediate Heat Transfer System (IHTS) including the Energy Storage System (ESS) as a first option to ensure the continuity of electric power released to the grid. A second option here considered is a methane fired auxiliary boiler replacing the ESS. The Power Conversion System (PCS) performance is evaluated as well in the overall balance. The performance analysis is based on the exergy method to correctly assess the amount of exergy destruction determined by irreversible phenomena along the whole cyclic process. The pulse and dwell phases of the reactor operation are evaluated considering the state of the art of the ESS adopting molten salts alternate heating and storage in a hot tank followed by a cooling and recovery of molten salt in a cold tank to ensure the continuity of power release to the electrical grid. An alternative plant configuration is evaluated on the basis of an auxiliary boiler replacing the ESS with a 10% of the power produced by the reactor during pulse mode. The conclusive summary of main achievements and original outcomes is followed by proposals of future developments in different fields of theoretical and applied research and technology. These themes represent an outlook on the opportunities and initiatives originating from the passionate dedication effort spent along the here ended Doctorate

Combinatorial Information Theory: I. Philosophical Basis of Cross-Entropy and Entropy

This study critically analyses the information-theoretic, axiomatic and combinatorial philosophical bases of the entropy and cross-entropy concepts. The combinatorial basis is shown to be the most fundamental (most primitive) of these three bases, since it gives (i) a derivation for the Kullback-Leibler cross-entropy and Shannon entropy functions, as simplified forms of the multinomial distribution subject to the Stirling approximation; (ii) an explanation for the need to maximize entropy (or minimize cross-entropy) to find the most probable realization; and (iii) new, generalized definitions of entropy and cross-entropy - supersets of the Boltzmann principle - applicable to non-multinomial systems. The combinatorial basis is therefore of much broader scope, with far greater power of application, than the information-theoretic and axiomatic bases. The generalized definitions underpin a new discipline of ``{\it combinatorial information theory}'', for the analysis of probabilistic systems of any type. Jaynes' generic formulation of statistical mechanics for multinomial systems is re-examined in light of the combinatorial approach. (abbreviated abstract)Comment: 45 pp; 1 figure; REVTex; updated version 5 (incremental changes

Projection operator formalism and entropy

The entropy definition is deduced by means of (re)deriving the generalized non-linear Langevin equation using Zwanzig projector operator formalism. It is shown to be necessarily related to an invariant measure which, in classical mechanics, can always be taken to be the Liouville measure. It is not true that one is free to choose a ``relevant'' probability density independently as is done in other flavors of projection operator formalism. This observation induces an entropy expression which is valid also outside the thermodynamic limit and in far from equilibrium situations. The Zwanzig projection operator formalism therefore gives a deductive derivation of non-equilibrium, and equilibrium, thermodynamics. The entropy definition found is closely related to the (generalized) microcanonical Boltzmann-Planck definition but with some subtle differences. No ``shell thickness'' arguments are needed, nor desirable, for a rigorous definition. The entropy expression depends on the choice of macroscopic variables and does not exactly transform as a scalar quantity. The relation with expressions used in the GENERIC formalism are discussed

Carnot Cycle and Heat Engine Fundamentals and Applications II

This second Special Issue connects both the fundamental and application aspects of thermomechanical machines and processes. Among them, engines have the largest place (Diesel, Lenoir, Brayton, Stirling), even if their environmental aspects are questionable for the future. Mechanical and chemical processes as well as quantum processes that could be important in the near future are considered from a thermodynamical point of view as well as for applications and their relevance to quantum thermodynamics. New insights are reported regarding more classical approaches: Finite Time Thermodynamics F.T.T.; Finite Speed thermodynamics F.S.T.; Finite Dimensions Optimal Thermodynamics F.D.O.T. The evolution of the research resulting from this second Special Issue ranges from basic cycles to complex systems and the development of various new branches of thermodynamics

Generalized formulation of theoretical maximum energy efficiency of light-powered systems based on photon entropy analysis

Certain questions regarding the analysis of theoretical maximum energy efficiency $\eta_{max}$ of light-powered systems by the radiant temperature and its use for the Boltzmann coefficient remain unanswered. A potential reason for this could be the confusion about equilibrium and reversibility. Therefore, this study performed a quantum statistical entropy analysis of a light-powered system based on reversibility as the solely essential condition and without recourse to the concept of radiation temperature. Several quantitative analyses that cannot be performed with radiation temperature can be performed using the generalized formula. As examples, this study presents the formulation of $\eta_{max}$ considering the entropy change caused by photochemical reactions, such as that in photosynthesis and photosynthetically active radiation (PAR), and the formulations of several quantities under radiation with arbitrary $\Omega$ and P. Furthermore, analysis from this study found that $\eta_{max}$ decreases as the light absorption rate increases, which had not previously been considered. This general formula is presented, which fills the gap between the Jeter efficiency (Carnot efficiency) $\eta_{C}=1-T_{out}/T_{in}$ and the Spanner efficiency $\eta_{S}$=1-(4/3)$T_{out}$/$T_{in}$ (where $T_{out}$ is ambient temperature and $T_{in}$ is the temperature in the system) for black-body radiation. The analyses generally formulated in this study allow practical analyses of systems such as photosynthesis and photovoltaics, under various conditions relating to sunlight scattered through the atmosphere. Finally, it is proved with elementary geometry that the total entropy of the solar radiation from the Sun to the upper atmosphere of the Earth remains at a constant value. This means that the use of solar energy on satellites in space is expected to be more efficient than on the earth's surface.Comment: 59 Pages, 7 Figures, 5 Appendices, The displayed abstract is shorter than one in the main body due to character limi

Entropy and its application to urban systems

Since its conception over 150 years ago, entropy has enlightened and confused scholars and students alike, from its origins in physics and beyond. More recently, it has been considered within the urban context in a rather eclectic range of applications. The entropy maximization approach, as applied by AlanWilson and others from the 1960s, contrasts with considerations from the 1990s of the city as a thermodynamic dissipative system, in the tradition of Ilya Prigogine. By reviewing the relevant mathematical theory, we draw the distinction among three interrelated definitions of entropy, the thermodynamic, the figurative, and the information statistical. The applications of these definitions to urban systems within the literature are explored, and the conflation of the thermodynamic and figurative interpretations are disentangled. We close this paper with an outlook on future uses of entropy in urban systems analysis