Ongoing translation from Russian: Осмысление энтропии в свете свечи. No link – a chapter has not been translated yet.
Introduction: Einstein on phenomenological and fundamental theories of physics. The problem of coordination and experimental science. Theory of physics. Continuum mechanics. Statistical mechanics. Outline of the book.
Part 1. Classical Thermodynamics: A burning candle as an example to discuss thermodynamic phases. A description of the drawing from Sadi Carnot’s book – it will be used in this part. Outline of this part.
Chapter 1. Temperature and Thermal Equation of State: Maxwell on temperature. Thermal equation of state. From the history of thermometry. Ideal gas and absolute temperature scale. Mathematics of the thermal equation of state. From temperature to temperature field.
Chapter 2. From Caloric Theory to Thermodynamics: Steam engines. Heat and calorimetry. Main stages in the development of thermodynamics – Carnot cycle, Mechanical equivalent of heat. First and second laws of thermodynamics. Equilibrium and reversible processes.
Chapter 3. Thermodynamic Properties of Substances: Calorimeter and Functions of State. The Basic Equation of Thermodynamics. The Legendre Transformation and New Functions of State—Enthalpy, Helmholtz Energy, Gibbs Energy. Thermodynamic Tables.
Chapter 4. Clausius Inequality as an Equilibrium Criterion: Clausius Inequality for an Isolated System. A Simple Example of Heat Death. The Fundamental Inequality of Thermodynamics. Local and Global Equilibrium. The Construction of Thermodynamics.
Chapter 5. Adiabatic Flame Temperature: General Problem Statement. Calculating Flame Temperature for a Complete Reaction. Calculating Equilibrium Composition at Given Temperature and Pressure. From the Carnot Cycle to Chemical Thermodynamics.
Chapter 6. Entropy of Nonequilibrium States: Entropy in Classical Thermodynamics. Nonequilibrium States in Discontinuous Systems. From the Temperature Field to Nonequilibrium Thermodynamics. Limits of Applicability of Classical Thermodynamics.
Part 2. Statistical Mechanics: Outline of the second part of the book. Semiclassical approximation. Clausius inequality and the arrow of time. Information entropy.
Chapter 1. Conceptual Models of Statistical Mechanics: Classical Statistical Mechanics. Quantum Statistical Mechanics. The Born-Oppenheimer Approximation. Molecular Mechanics and Molecular Dynamics. Quantum Effects in the Semiclassical Approximation.
Chapter 2. Equilibrium Statistical Mechanics: Key events in the development of statistical mechanics. Probability distribution and phase space. Microcanonical and canonical distributions. Partition function of an ideal polyatomic gas.
Chapter 3. The Arrow of Time in Statistical Mechanics: The Evolution of Ludwig Boltzmann’s Views. Loschmidt’s Paradox. Boltzmann’s Suicide. Statistical Interpretation of the Second Law. Gibbs’s Statistical Entropy. Mixing in Phase Space.
Chapter 4. Entropy, Knowledge, and Information: Maxwell and Gibbs on the Role of Perception. Shannon’s Information Theory. Extension of Information to Statistical Mechanics. Edwin Jaynes’s Maximum Entropy Principle. Carnap for the Objectivity of Entropy.
Chapter 5. Maxwell’s Demon and Information: Maxwell’s Demon. Brownian Motion and the Second Law. Smoluchowski: Naturalizing Maxwell’s Demon. Szilard’s Demon. Brillouin: The Negentropic Information Principle. Landauer and the Thermodynamics of Computation.
Chapter 6. Nonequilibrium States in Statistical Mechanics: Back to Boltzmann! Macrostate Entropy. Nonequilibrium Macrostates and Microstates. Entropy of Nonequilibrium States and Kinetics. Nonequilibrium Statistical Mechanics in Practice.
Part 3. What does physics say? The use of mathematics in physics — a metaphor of mathematical glasses. Contrasting tables of thermodynamic properties with the statement “mathematics is just a language”. Outline of the part.
Chapter 1. Physics, Mathematics, and the World: Everyday life and the physical world. Theory and experiment in physics. Experimental science in physics. Extrapolationism as a research program. Radical extrapolationism.
Chapter 2. Mathematics and the World in Continuum Mechanics: Qualitative explanation of candle combustion. Quantitative characteristics of the properties of matter. Entropy and experiment. Entropy and time: Clausius’s inequality. Entropy and time: entropy production.
Chapter 3. Mathematics and the world in statistical mechanics: Ludwig Boltzmann’s philosophy of physics. A conceptual model of molecular-kinetic theory. Spectroscopy. Fundamental constants. Quantum mechanics. Oscillatory motion. The Gibbs ensemble and probabilities.
Chapter 4. Burning of a Candle and Levels of Organization: Arthur Eddington’s Two Tables. Calculating the Properties of Matter from Molecular Constants. Burning of a Candle at the Level of Statistical Mechanics. Deriving the Equations of Continuum Mechanics from Statistical Mechanics. Explanatory Arrows and Emergence.
Chapter 5. Critique of the Thermodynamics of Information: What does Szilard’s Demon prove? Landauer’s principle, reversible computation, and fluctuations. The inadequacy of Szilard’s thought experiment. Information and the physical as levels of organization.
Chapter 6. Objectivity in Physics: Two meanings of objectivity. Objectivity as impartiality. Experience as sensory perception. Reality itself and mathematical glasses.
Conclusion. What is entropy? Entropy as a property of matter. Entropy of a nonequilibrium state of a system. An isolated system. Entropy as an equilibrium criterion. Entropy as an arrow of time.