krainaksiazek physical significance of entropy or of the second law 20120253
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Excerpt From Physical Significance Of Entropy Or Of The Second Law This Article Is Intended For Those Students Of Engineering Who Already Have Some Elementary Knowledge Of Thermodynamics. It Is Intended To Clear Up A Difficulty That Has Beset Every
Książki Obcojęzyczne>Angielskie>Mathematics & science>Physics>Thermodynamics & heatKsiążki Obcojęzyczne>Angielskie>Mathematics & sci...
Geometric Entropy LAP Lambert Academic Publishing
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The laws of mechanics of stationary black holes bear a close resemblance with the laws of thermodynamics. This is not only a mathematical analogy but also a physical one that helps us answer deep questions related to the thermodynamic properties of the black holes. It turns out that we can define an entropy which is purely geometrical for black holes. In this thesis we explain Wald's formulation which identifies black hole entropy for an arbitrary covariant theory of gravity. We would like to know precisely what inputs go into arriving at Wald's formalism. This expression for the entropy clearly depends on the precise form of the action. The secondary theme of this thesis is to distinguish thermodynamic laws which are kinematic from those which are dynamical. We would like to see explicitly in the derivation of these laws, where exactly the form of action plays a role. In the beginning we motivate the definition of entropy using the Einstein-Hilbert Lagrangian. We encounter the Zeroth law, the Hawking radiation, the second law, and then Wald's formulation.
The Second Law of Economics Springer, Berlin
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Nothing happens in the world without energy conversion and entropy production. These fundamental natural laws are familiar to most of us when applied to the evolution of stars and life or the working of an internal combustion engine, but what about industrial economies and wealth production, or their constant companion, pollution? Does economics conform to the First and Second Laws of Thermodynamics? In this important book, Reiner Kümmel takes us on a fascinating tour of these laws and their influence on natural, technological, and social evolution. Analyzing economic growth in Germany, Japan and the USA and its associated technological constraints, he upends conventional economic wisdom by showing that the productive power of energy far outweighs its small share of costs, while for labor just the opposite is true. Wealth creation by energy conversion is accompanied and limited by polluting emissions that are coupled to entropy production. These facts constitute the Second Law of Economics. They take on unprecedented importance in a world that is facing peak oil, debt-driven economic turmoil, and global threats from pollution and climate change. The Second Law complements the First Law of Economics: Wealth is allocated on markets, and the legal framework determines the outcome. By applying the First and Second Laws we understand the true origins of wealth production, the issues that imperil the goal of sustainable development, and the technological options that are compatible both with this goal and with natural laws. The critical role of energy and entropy in the productive sectors of the economy must be understood if we are to create a road map that avoids a Dark Age of shrinking natural resources, environmental degradation, and increasing social tensions.Nothing happens in the world without energy conversion and entropy production. This message of the first two laws of thermodynamics reflects the pivotal role of energy conversion in the evolution of stars, life, and industrial economies. In this engaging and insightful book, Professor Kümmel summarizes the facts behind these fundamental physical laws and shows why "The Constitution of the Universe" must govern economic thinking if we are to come to grips with the challenges of sustainable development. From the point of view of a physicist, the author shows why energy must be taken into account, together with labor and capital, as a factor in production and economic growth, and describes how entropy production, the ugly twin sister of energy conversion,devalues energy, increases disorder, generates emissions and pollution, and establishes limits to growth in a finite world. Since profit and overall welfare optimization are subject to technological constraints on capital, labor and energy, fundamental assumptions of mainstream economics are called into question. New econometric analyses using the capital-labor-energy triad accurately reproduce economic growth in Germany, Japan and the USA, and show that, for energy, productive power far outweighs its small share of costs while for labor just the opposite is true. Reconsidering economics from the perspective of thermodynamics can help us to create a road map for the future that avoids a Dark Age of shrinking natural resources and increasing social tensions.
Probability, Statistics and Truth Dover Publications
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PREFACE PREFACE TO THE THIRD GERMAN EDITION FIRST LECTURE The Definition of Probability Amendment of Popular Terminology Explanation of Words Synthetic Definitions Terminology The Concept of Work in Mechanics An Historical Interlude The Purpose of Rational Concepts The Inadequacy of Theories Limitation of Scope Unlimited Repetition The Collective The First Step towards a Definition Two Different Pairs of Dice Limiting Value of Relative Frequency The Experimental Basis of the Theory of Games The Probability of Death First the Collective-then the Probability Probability in the Gas Theory An Historical Remark Randomness Definition of Randomness: Place Selection The Principle of the Impossibility of a Gambling System Example of Randomness Summary of the Definition SECOND LECTURE The Elements of the Theory of Probability The Theory of Probability is a Science Similar to Others The Purpose of the Theory of Probability The Beginning and the End of Each Problem must be Probabilities Distribution in a Collective Probability of a Hit; Continuous Distribution Probability Density The Four Fundamental Operations First Fundamental Operation: Selection Second Fundamental Operation: Mixing Inexact Statement of the Addition Rule Uniform Distribution Summary of the Mixing Rule Third Fundamental Operation: Partition Probabilities after Partition Initial and Final Probability of an Attribute The So-called Probability of Causes Formulation of the rule of Partition Fourth Fundamental Operation: Combination A New Method of Forming Partial Sequences: Correlated Sampling Mutually Independent Collectives Derivation of the Multiplication Rule Test of Independence Combination of Dependent Collectives Example of Noncombinable Collectives Summary of the Four Fundamental Operations A Problem of Chevalier de Méré Solution of the Problem of Chevalier de Méré Discussion of the Solution Some Final Conclusions Short Review THIRD LECTURE Critical Discussion of the Foundations of Probability The Classical Definition of Probability Equally Likely Cases ... ... Do Not Always Exist A Geometrical Analogy How to Recognize Equally Likely Cases Are Equally Likely Cases of Exceptional Significance? The Subjective Conception of Probability Bertrand's Paradox The Suggested Link between the Classical and the New Definitions of Probability Summary of Objections to the Classical Definition Objections to My Theory Finite Collectives Testing Probability Statements An Objection to the First Postulate Objections to the Condition of Randomness Restricted Randomness Meaning of the Condition of Randomness Consistency of the Randomness Axiom A Problem of Terminology Objections to the Frequency Concept Theory of the Plausibility of Statements The Nihilists Restriction to One Single Initial Collective Probability as Part of the Theory of Sets Development of the Frequency Theory Summary and Conclusion FOURTH LECTURE The Laws of Large Numbers Poisson's Two Different Propositions Equally Likely Events Arithmetical Explanation Subsequent Frequency Definition The Content of Poisson's Theorem Example of a Sequence to which Poisson's Theorem does not Apply Bernoulli and non-Bernoulli Sequences Derivation of the Bernoulli-Poison Theorem Summary Inference Bayes's Problem Initial and Inferred Probability Longer Sequences of Trials Independence of the Initial Distribution The Relation of Bayes's Theorem to Poisson's Theorem The Three Propositions Generalization of the Laws of Large Numbers The Strong Law of Large Numbers The Statistical Functions The First Law of Large Numbers for Statistical Functions The Second Law of Large Numbers for Statistical Functions Closing Remarks FIFTH LECTURE Application Statistics and the Theory of Errors What is Statistics? Games of Chance and Games of Skill Marbe's Uniformity in the World' Answer to Marbe's Problem Theory of Accumulation and the Law of Series Linked Events The General Purpose of Statistics Lexis' Theory of Dispersion The Mean and the Dispersion Comparison between the Observed and the Expected Variance Lexis' Theory and the Laws of Large Numbers Normal and Nonnormal Dispersion Sex Distribution of Infants Statistics of Deaths with Supernormal Dispersion Solidarity of Cases Testing Hypotheses R. A. Fisher's Likelihood' Small Sample Theory Social and Biological Statistics Mendel's Theory of Heredity Industrial and Technological Statistics An Example of Faulty Statistics Correction Some Results Summarized Descriptive Statistics Foundations of the Theory of Errors Galton's Board Normal Curve Laplace's Law The Application of the Theory of Errors SIXTH LECTURE Statistical Problems in Physics The Second Law of Thermodynamics Determinism and Probability Chance Mechanisms Random Fluctuations Small Causes and Large Effects Kinetic Theory of Gases Order of Magnitude of 'Improbability' Criticism of the Gas Theory Brownian Motion Evolution of Phenomena in Time Probability 'After Effects' Residence Time and Its Prediction Entropy Theorem and Markoff Chains Svedberg's Experiments Radioactivity Prediction of Time Intervals Marsden's and Barratt's Experiments Recent Development in the Theory of Gases Degeneration of Gases: Electron Theory of Metals Quantum Theory Statistics and Causality Causal Explanation Newton's Sense Limitations of Newtonian Mechanics Simplicity as a Criterion of Causality Giving up the Concept of Causality The Law of Causality New Quantum Statistics Are Exact Measurements Possible? Position and Velocity of a Material Particle Heisenberg's Uncertainty Principle Consequences for our Physical Concept of the World Final Considerations SUMMARY OF THE SIX LECTURES IN SIXTEEN PROPOSITIONS NOTES AND ADDENDA SUBJECT INDEX NAME INDEX
The Variational Principles of Mechanics Dover Publications
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Introduction 1. The variational approach to mechanics 2. The procedure of Euler and Lagrange 3. Hamilton's procedure 4. The calculus of variations 5. Comparison between the vectorial and the variational treatments of mechanics 6. Mathematical evaluation of the variational principles 7. Philosophical evaluation of the variational approach to mechanics I. The Basic Concepts of Analytical Mechanics 1. The Principal viewpoints of analytical mechanics 2. Generalized coordinates 3. The configuration space 4. Mapping of the space on itself 5. Kinetic energy and Riemannian geometry 6. Holonomic and non-holonomic mechanical systems 7. Work function and generalized force 8. Scleronomic and rheonomic systems. The law of the conservation of energy II. The Calculus of Variations 1. The general nature of extremum problems 2. The stationary value of a function 3. The second variation 4. Stationary value versus extremum value 5. Auxiliary conditions. The Lagrangian lambda-method 6. Non-holonomic auxiliary conditions 7. The stationary value of a definite integral 8. The fundamental processes of the calculus of variations 9. The commutative properties of the delta-process 10. The stationary value of a definite integral treated by the calculus of variations 11. The Euler-Lagrange differential equations for n degrees of freedom 12. Variation with auxiliary conditions 13. Non-holonomic conditions 14. Isoperimetric conditions 15. The calculus of variations and boundary conditions. The problem of the elastic bar III. The principle of virtual work 1. The principle of virtual work for reversible displacements 2. The equilibrium of a rigid body 3. Equivalence of two systems of forces 4. Equilibrium problems with auxiliary conditions 5. Physical interpretation of the Lagrangian multiplier method 6. Fourier's inequality IV. D'Alembert's principle 1. The force of inertia 2. The place of d'Alembert's principle in mechanics 3. The conservation of energy as a consequence of d'Alembert's principle 4. Apparent forces in an accelerated reference system. Einstein's equivalence hypothesis 5. Apparent forces in a rotating reference system 6. Dynamics of a rigid body. The motion of the centre of mass 7. Dynamics of a rigid body. Euler's equations 8. Gauss' principle of least restraint V. The Lagrangian equations of motion 1. Hamilton's principle 2. The Lagrangian equations of motion and their invariance relative to point transformations 3. The energy theorem as a consequence of Hamilton's principle 4. Kinosthenic or ignorable variables and their elimination 5. The forceless mechanics of Hertz 6. The time as kinosthenic variable; Jacobi's principle; the principle of least action 7. Jacobi's principle and Riemannian geometry 8. Auxiliary conditions; the physical significance of the Lagrangian lambda-factor 9. Non-holonomic auxiliary conditions and polygenic forces 10. Small vibrations about a state of equilibrium VI. The Canonical Equations of motion 1. Legendre's dual transformation 2. Legendre's transformation applied to the Lagrangian function 3. Transformation of the Lagrangian equations of motion 4. The canonical integral 5. The phase space and the space fluid 6. The energy theorem as a consequence of the canonical equations 7. Liouville's theorem 8. Integral invariants, Helmholtz' circulation theorem 9. The elimination of ignorable variables 10. The parametric form of the canonical equations VII. Canonical Transformations 1. Coordinate transformations as a method of solving mechanical problems 2. The Lagrangian point transformations 3. Mathieu's and Lie's transformations 4. The general canonical transformation 5. The bilinear differential form 6. The bracket expressions of Lagrange and Poisson 7. Infinitesimal canonical transformations 8. The motion of the phase fluid as a continuous succession of canonical transformations 9. Hamilton's principal function and the motion of the phase fluid VIII. The Partial differential equation of Hamilton-Jacobi 1. The importance of the generating function for the problem of motion 2. Jacobi's transformation theory 3. Solution of the partial differential equation by separation 4. Delaunay's treatment of separable periodic systems 5. The role of the partial differential equation in the theories of Hamilton and Jacobi 6. Construction of Hamilton's principal function with the help of Jacobi's complete solution 7. Geometrical solution of the partial differential equation. Hamilton's optico-mechanical analogy 8. The significance of Hamilton's partial differential equation in the theory of wave motion 9. The geometrization of dynamics. Non-Riemannian geometrics. The metrical significance of Hamilton's partial differential equation IX. Relativistic Mechanics 1. Historical Introduction 2. Relativistic kinematics 3. Minkowski's four-dimensional world 4. The Lorentz transformations 5. Mechanics of a particle 6. The Hamiltonian formulation of particle dynamics 7. The potential energy V 8. Relativistic formulation of Newton's scalar theory of gravitation 9. Motion of a charged particle 10. Geodesics of a four-dimensional world 11. The planetary orbits in Einstein's gravitational theory 12. The gravitational bending of light rays 13. The gravitational red-shirt of the spectral lines Bibliography X. Historical Survey XI. Mechanics of the Continua 1. The variation of volume integrals 2. Vector-analytic tools 3. Integral theorems 4. The conservation of mass 5. Hydrodynamics of ideal fluids 6. The hydrodynamic equations in Lagrangian formulation 7. Hydrostatics 8. The circulation theorem 9. Euler's form of the hydrodynamic equations 10. The conservation of energy 11. Elasticity. Mathematical tools 12. The strain tensor 13. The stress tensor 14. Small elastic vibrations 15. The Hamiltonization of variational problems 16. Young's modulus. Poisson's ratio 17. Elastic stability 18. Electromagnetism. Mathematical tools 19. The Maxwell equations 20. Noether's principle 21. Transformation of the coordinates 22. The symmetric energy-momentum tensor 23. The ten conservation laws 24. The dynamic law in field theoretical derivation Appendix I; Appendix II; Bibliography; Index
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t1=0.023, t2=0, t3=0, t4=0, t=0.023