- Equilibrium thermodynamics overview [nln6]
- Thermal equilibrium and nonequilibrium [nln1]
- Levels of description in statistical physics [nln2]
- Contraction - memory - time scales [nln15]
- Markov process: map of specifications [nln16]

- Brownian motion: panoramic view [nln23]

- Linear response and equilibrium dynamics [nln24]

- Two bus companies: regular versus random schedules
- Pick the winning die [nex2]
- Educated guess [nex4]
- Coincident birthdays [nex82]
- Win the new car or take the goat! [nex11]
- Three-cornered duel [nex13]
- Bad luck: waiting for the worst [nex74]
- Bertrand's paradox

- Random quadratic equations [nex12]
- Crossing a river [nex84]

- Combinatorics of poker hands [nex124]

- Know your odds [nex125]

- Elements of set theory [nln4]

- Set identities [nex88]
- Sample space and events
- Probability axioms and simple theorems [nex94]

- Joint probability and conditional probability
[nex90]

- Symmetry and elementary events
- Bayes' theorem
- Statistical independence
- Statistical uncertainty and information [nln5], [tex47]

- Event or complement? That is the question [nex9]
- Successive random picks [nex91]
- Heads or tails [nex93]

- Quantity and quality [nex76]
- Diagnosis of a rare disease [nex77]

- Subtlety of statistical independence [nex1]
- Random train connections [nex92]
- Random inkjet printer [nex10]
- Information and the reduction of ignorance [tex48]
- Information of sequenced messages [tex61]

- Probability distributions
- Moments, variance, standard deviation
- Moment expansion and characteristic function
- Cumulant expansion
- Factorial moments and cumulants, generating function
- Multivariate distributions [nln7]

- Transformation of random variables
- Propagation of statistical uncertainty [nex24]

- Chebyshev's inequality [nex6]

- Law of large numbers [nex7]

- Binomial, Poisson, and Gaussian distribution [nln8]

- Binomial to Poisson distribution [nex15]
- De
Moivre
- Laplace limit theorem [nex21]

- Central limit theorem [nln9]

- Multivariate Gaussian distribution

- Robust probability distributions [nex19]

- Stable probability distributions [nex81]

- Exponential distribution [nln10]

- Waiting time problem [nln11]

- Pascal distribution [nex22]

- Reconstructing probability distributions [nex14]
- Probability distribution with no mean value [nex95]

- Variances and covariances [nex20]
- Statistically independent or merely uncorrelated? [nex23]
- Sum and product of uniform distribution [nex96]

- Exponential integral distribution [nex79]
- Generating exponential and Lorentzian random numbers [nex80]
- Random chords (Bertrand's paradox) [nex5]
- From Gaussian to exponential distribution [nex8]
- Transforming a pair of random variables [nex78]
- Gaussian shootist versus Lorentzian shootist [nex3]
- Moments and cumulants of the Poisson distribution [nex16]
- Maxwell velocity distribution [nex17]

- Random bus schedules [nex18]
- Life expectancy of the young and the old [nex106]

- Life expectancy of the ever young [nex38]

- Random frequency oscillator [nex35]

- Time-dependent probability distributions

- Correlation functions and characteristic functions

- Equilibrium - nonequilibrium - stationarity

- Classification of processes (factorizing/Markov/non-Markov)
- Deterministic versus stochastic time evolution
- Contraction - memory - time scales [nln15]

- General specification of Markov process

- Chapman-Kolmogorov equation
- Diffusion process and Cauchy process
- Stationarity, normalization, consistency, Markovian
nature [nex26]

- Computer generated sample paths [nsl1]

- Continuous versus discontinuous processes
(Lindeberg
condition) [nex97]

- Differential Chapman-Kolmogorov equation
- Fokker-Planck equation (drift and diffusion processes)
- Drift equation (deterministic processes) [nex29]

- Master equation (jump processes) [nex28]

- Non-differentiability of sample paths [nex99]

- Master
equation with finite jump moments [nex32]

- Equations of motion for mean and variance [nex30]

- Markov process: map of specifications [nln16]
- Approach to a stationary state (detailed
balance) [nex85]

- Markov chains (discrete variables, discrete time)
- Transition matrix, left and right eigenvectors,
stationary
states

- Regularity, ergodicity, detailed balance, absorbing
states

- Master equation with detailed balance
(discrete
variables, continuous time) [nln12]

- Regression theorem for autocorrelation functions [nex39]
- Birth death processes (specifications, models, levels of description) [nln18]
- Birth and death of single species [nln19]

- Birth-death master equation: stationary state [nln17]
- Nonlinear birth-death process

- Diffusion process [nex27]

- Cauchy process [nex98]

- Random walk in one dimension: unit steps at
unit
times [nex34]

- Random walk in one dimension: unit steps at random times [nex33]
- Random walk in one dimension: tiny steps at
frequent times [nex100]

- Random walk in Las Vegas: chance and necessity [nex40]
- Poisson process [nex25]
- Free particle with uncertain position and
velocity [nex36]

- Fokker-Planck equation with constant
coefficients [nex101]

- House of the mouse: two-way doors only [nex102]

- House of the mouse: some one-way doors [nex103]

- House of the mouse: one-way doors only [nex104]
- House of the mouse: mouse with inertia [nex105]
- House of the mouse: mouse with memory [nex43]

- Mixing marbles red and white [nex42]
- Random traffic around city block [nex86]

- Modeling a Markov chain [nex87]

- Ornstein-Uhlenbeck process [nex31] [nex41]
- Predator-prey system: deterministic, stochastic, observational [nsl3]
- Populations with linear birth and death rates I [nex44]
- Populations with linear birth and death rates
II [nex112]

- Catalyst-driven chemical reaction: stationary
state [nex46]

- Catalyst driven chemical reaction: dynamics [nex107]

- Catalyst driven chemical reaction: total rate
of
reactions [nex108]

- Air in leaky tank I: generating function [nex48]

- Air in leaky tank II: probability distribution
[nex109]

- Air in leaky tank III: detailed balance [nex49]
- Air in leaky tank IV: evolution of mean and
variance [nex110]

- Pascal distribution and Planck radiation law [nex50]

- Effects of nonlinear death rate I:
Malthus-Verhulst equation [nex111]

- Effects of nonlinear death rate II:
stationarity
and fluctuations [nex51]

- Modified linear birth rate I: stationarity [nex113]

- Modified linear birth rate II: evolution of
mean
and variance [nex114]

- Modified linear birth rate III: generating
function [nex115]

- Modified linear birth rate IV: probability
distribution [nex116]

- Bistable chemical system [nex52]
- Ultracold neutrons in an ideal Steyerl bottle
[nex47]

- Random light switch [nex45]

- Relevant time scales (collisions, relaxation,
observations)

- Einstein's theory
- Smoluchovski equation with link to
Fokker-Planck
equation

- Einstein relation (example of fluctuation-dissipation relation)
- Fick's law for particle current
- Fourier's law for heat current

- Thermal diffusivity [nex117]

- Shot noise (e.g. electric current in vacuum tube)
- Campbell's theorem [nex37]

- Critically damped ballistic galvanometer [nex70]

- Langevin's theory (on most contracted level of description)
- White noise

- Brownian motion and Gaussian white noise [nln20]

- Wiener process [nsl4]
- Autocorrelation function of Wiener process [nex54]

- Ballistic and diffusive regimes of Langevin solution
- Langevin's equation: attenuation without
memory [nln21]

- Formal solution of Langevin equation [nex53]

- Velocity correlation function of Brownian
particle I [nex55]

- Mean-square displacement of Brownian particle
[nex56], [nex57],
[nex118]

- Ergodicity [nln13]

- Intensity spectrum and spectral density
(Wiener-Khintchine
theorem) [nln14]

- Fourier analysis of Langevin equation
- Velocity correlation function of Bownian
particle
II [nex119]

- Generalized Langevin equation: attenuation
with
memory [nln22]

- Fluctuation-dissipation theorem
- Velocity correlation function of Brownian
particle III [nex120]

- Brownian harmonic oscillator I: Fourier
analysis [nex121]

- Brownian harmonic oscillator II: position
correlation function [nex122]

- Brownian harmonic oscillator III: contour
integrals [nex123]

- Brownian harmonic oscillator IV: velocity correlations [nex58]
- Brownian harmonic oscillator V: formal
solution
for velocity [nex59]

- Brownian harmonic oscillator VI:
nonequilibrium
correlations [nex60]

- Generalized Langevin equation inferred from microscopic dynamics
- Brownian motion: levels of contraction and modes of description [nln23]

- Overview [nln24]
- Many-body system perturbed by radiation field [nln25]

- Response function and generalized
susceptibility [nln26]

- Kubo formula for response function [nln27]

- Symmetry properties [nln30]

- Kramers-Kronig dispersion relations [nln37]

- Causality property of response function [nex63]

- Energy transfer between system and radiation
field [nln38]

- Reactive and absorptive part of response
function [nex64]

- Fluctuation-dissipation theorem (quantum and
classical) [nln39] (2)

- Spectral representations [nex65]

- Linear response of classical realxator [nex66]

- Linear response of classical oscillator [nex67]

- Introdution [nln28]

- Time-dependence of expectation values (quantum and classical)
- Zwanzig's kinetic equation: generalized master
equation [nln29] [nex68]

- Projection operator method (Mori formalism) [nln31]

- Kubo inner product [nln32]

- Projection operators [nln33]
- First and second projections [nln34] [nln35]

- Continued-fraction representation of
relaxation
function [nln36]

- Recursion method (algorithmic implementation of Mori formalism)
- Relaxation function with uniform
continued-fraction
coefficients [nex69]

- Continued-fraction expansion and moment expansion
- Generalized Langevin equation
- n-pole approximation
- Green's function formalism
- Structure function of harmonic oscillator [nex71], [nex72],
[nex73]

- Scattering process and dynamic structure factor
- Electron scattering, neutron scattering, light scattering
- Scattering from a free atom
- Scattering from an atom bound in a harmonic potential
- Scattering from a harmonic crystal

Some Relevant Textbooks
and
Monographs:

- L. E. Reichl:
*A modern course in statisitical physics.*Wiley-Interscience, New York 1998. - R. E. Wilde and S. Singh:
*Statistical mechanics. Fundamentals and modern applications.*Wiley, New York 1998. - C. W. Gardiner:
*Handbook of stochastic methods for physics, chemistry, and the natural sciences.*Springer-Verlag, New York 1985. - W. Brenig:
*Statistical theory of heat. Nonequilibrium phenomena.*Springer-Verlag, New York 1989. - R. Kubo, M. Toda, and N. Hashitsume:
*Statistical physics II. Nonequilibrium statistical mechanics.*Springer-Verlag, New York 1985. - E. Fick and G. Sauermann:
*The quantum statistics of dynamic processes.*Springer-Verlag, New York 1990. - J. McLennan:
*Introduction to nonequilibrium statistical mechanics.*Prentice Hall 1989. - S. W. Lovesey:
*Condensed matter physics. Dynamic correlations.*Benjamin/ Cummings, Reading 1980. - J. Honerkamp:
*Statistical physics. An advanced approach with applications.*Springer-Verlag, New York 1998. - A. Papoulis:
*Probability, random variables, and stochastic processes.*McGraw-Hill, New York 1991. - R. F. Streater:
*Statistical dynamics. A stochastic approach to nonequilibrium thermodynamics.*Imperial College Press, London 1995. - R. Balescu:
*Statistical dynamics. Matter out of equilibrium.*Imperial College Press, London 1997. - Gerd Röpke:
*Nonequilibrium statistical physics*. Wiley-VCH, 2013. - R. Mahnke, J. Kaupuzs, and I. Lubashevsky:
*Physics of stochastic processes*.

Wiley-VCH, 2009.

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[nex]?

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Last updated 01/27/14