Supplementary Pages
Table of Supplements
In the original manuscript chapters are all called sections, because I wish to have continuous narrative of a more or less single line of the story. Therefore, here, I stick to the format.
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Preface & Study Guide Counting atoms and molecules
Minimizing metaphysics
Problem source books byR Kubo and his colleagues
0.1 Truth
Section 1
1.1 Lucretius/Epicurus
1.2 `Pure empiricism’ is not enough or What is the true empiricism?
1.2 Famous example of the consequence of uncritical fundamental principles: Thomson hated
evolution
1.3 Feynman lectures 1-3 says….
1.4 `Anthropic principle’
1.5 Cost of our brain
1.5 should critically review what the fundamental theory is
1.5 10^10 big?
Section 2 2.1 Archimedes
2.1 Archimedes’ rigorous calculation of the volume of the sphere
2.1 Descartes
2.1 Subject/object
2.4 1686
2.4 1738
2.4 Newton’s metaphysical atomism
2.5 French Revolution and thermodynamics
2.Q Air density and airplanes
Section 3 3.0 1933
3.1 What is volume? introduction to measures
3.2 Set theory
Lebesgue integral
3.4 Additivity and Cox’s theorem
3.4 Sigma additivity
3.10 1 + 1 = 3
Section 4 4.1 Ars Conjectandi
4.1 Law of large numbers Demo in R
4.1 Phylogenetic learning
4.2 Gambler’s fallacy
4.2 Chebyshev’s inequality and law of large numbers, illustrated
4.2 The strong law of large numbers---demonstration
4.2 Notable related theorems: 01 law and Regellosigkeit
4.3 Law of large numbers mathematical demonstration
4.7 CLT
4.7 Iterated logarithm
Section 5 5.1 Radon-Nikodym derivative
5.2 1860
5.2 Maxwell’s balance argument
5.2 Maxwell’s density distribution, a remark
5.5 Bochner’s theorem for characteristic functions
5.6 Sound speed
5.7 Equality of temperature
5.Q Beyond average and large deviation
Section 6 6.A Introduction to distribution theory
6.A Integral kernel
Section 7 7.1 Buys-Ballot
7.1 How to draw random walks using R
7.2 Fig 7.2 remark
7.3 RW without averaging
7.4 Bernoulli exchange model
7.4 Ideal gas collisions
Is gravity an entropic force?
8.2 LLN ext
8.6 Ball sequence independence of convergence
8.9 Laplacian and local averages: spherical mean value
9.1 Remark on LLN of Brownian motion
9.2 1829
9.2 Brown, Humboldt, Cook
9.2 Clarkia purchella in color 9.2 Lewis and Clark
9.3 1831
9.3 1857
9.3 1900
9.3 Brownian motion, historical
9.3 Brownian velocity correlation
9.7 Stokes’ law, demonstration
Section 10 10.6 Velocity of Brownian motion and fluctuation dissipation relation
10.8 LD Gaussian approximation
Section 11
11.1 Assumption about mechanical description
11.1 Internal energy identification
11.1 Moving coordinates
11.2 Volta, Seebeck, et al.
11.4 How realistic is the binary potential?
11.4 Energy additivity demonstration
11.4 Dipole-dipole interaction
11.4 Shielding
11.5 Additivity and extensivity
11.5 Particle number
11.7 1972
11.8 Recurrence
11.9 Boltzmann equation, introduction
11.9 Reliability of Boltzmann equation
11.11 How we feel time
Section 12
12.3 Kadanoff’s angels
12.10 Why is thermodynamics useful? 12.10 Quasistatic processes exist
Section 13 13.1 The domain of thermodynamic coordinates
13.6 1834
13.6 1848
13.6 1850
13.6 Jane Eyer quote
13.6 Saint German and Monet
13.14 Internal energy is C1
13.Q 13.3 Explanation
13.Q Magnetic potential energy
13.Q Newcomen note
14.6 Critical look at baths
14.7 Excess entropy
14.9 Landau-Lifshitz’s error
15.5 Ideal gas fundamental equation
15.6 Most irreversible process
15.7 How to realize reversible processes
15.8 Information-Entropy relation preview
15.Q Fridge general
15.Q Irreversible measure from the bath change
Section 16 On the differentiability of thermodynamic potentials
16.4 D A = 0
16.6 Gibbs free energy?
16.8 Convex analysis note
16.8 Inf and sup
16.9 Continuity proof illustrated
16.11 Outline of convex analysis
17.2 Gibbs’ statistical mechanics
17.5 Non-abelian case
17.8 Boundary condition
17.9 Direct or tensor product
17.10 Observation induced changes
17.Q 1884
17.Q Lagrange’s multiplier
17.Q Quantum version of Boltzmann equation
18.3 Stirling proof
18.5 I and II as E
18.5 math detail when phase transitions occur
18.9 Factorization?
18.12 ZQ equivalence---proof
18.Q A and Gibbs-Helmholtz confusion
18.Q Einstein Z?
19.7 Maxwell and equal probability
19.8 Initial condition, quantum cases
19.9 Green’s function
20.3 Colloidal particles
20.4 Wigner and semiclassical approximation
20.7 Modes detail
Information summary
21.Q Log sum lemma
22.1 No work detail
22.2 Sagawa Ueda detail
22.6 Information writing
23.10 Debye temperature is not constant
23.10 NaCl
24.1 Rubber volume
24.6 Differentiation
24.10 Elementary derivation of (24.35)
24.12 Maxwell History
24.14 Inaccessibility
24.16 Ideal magnet experiment
Section 25
26.14 Multivariate Gaussian
26.Q ATP experiments
27.2 Mass action detail
27.4 Homogeneous not linear
27.5 Thermodynamics and hydrodynamics
27.11 1878, 1884, 1803
27.14 Electric cell
27.Q Zone melting
28.5 Haag: spin-statistic relation
28.5 Stability, relativistic case
28.Q Quantum statistical mechanics equivalence demo
Section 29
30.2 Zero point energy shift
30.5 Planck prehistory
30.9 Nuclear spin: Ortho and para hydrogen
30.10 Rigid rotor
31.0 Phase transition relevant to biology
31.1 Bernal model
31.4 Gibbs genericity
31.5 Phase rule violation
31.7 Order-order transition
31.9 Generalized canonical ensemble
31.9 Ising Gossip
31.9 Protein nonequilibrium
31.11 Holomorphic vs analyticity
31.11 Thermodynamic limit
32.1 Landau theory
32.1 Order parameter examples
32.4 1D Ruelle theorem
32.4 Spin dimension
32.7 Kac model
32.7 Kac model Maxwell relation
32.9 Numerical methods
32.11 Ashton movies
32.11 Beyond 3D
32.Q Q32.1 Correspondence
32.Q Q32.3 footnote 9 XY
33.1 Gauss correlation
33.1 Simon’s proof
33.5 Ashton movie
33.7 Fetish
33.13 Flow projection
34.3 Bifurcation justification
34.5 Chase’s mean field theory work
34.8 Perron Frobenius theorem proof
34.9 Onsager proof
35.2 Group demonstration
36.4 C-infinity singularity
36.4 Super heating etc
36.8 No jump in T or P
A.23 Tensor product
A.28 Various uncertainty principles
A.33 Trotter formula and path integral
A.39 QM historical
Random systems
Polymers
XY
