- Table of contents [ntc]

- 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]

- Stage for recursion method [nln79]

- Modules of recursion method [nln80]

- Regular versus random schedules [nln40]

- 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 [nln41]

- 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]
- Elementary probabilities [nln42]

- Probability axioms and simple theorems [nex94]

- Joint probability and conditional probability
[nln44] [nex90]

- Elements of probability theory [nln43]

- Statistical independence [nln45]

- 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 [nln46]

- Characteristic function, moments, and
cumulants [nln47]

- Cumulants expressed in terms of moments [nex126]

- Generating function and factorial moments [nln48]

- Multivariate distributions [nln7]

- Transformation of random variables [nln49]

- Sums of independent exponentials [nex127]

- 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 [nln50]

- Correlation functions and characteristic functions
- Degrees of memory [nln51]

- Markovian or non-Markovian I [nln52]

- Markovian or non-Markovian II [nln53]

- Contraction - memory - time scales [nln15]

- Markov process: general attributes [nln54]

- Diffusion process and Cauchy process [nln55]

- Stationarity, normalization, consistency, Markovian
nature [nex26]

- Computer generated sample paths [nsl1]

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

- Differential Chapman-Kolmogorov equation [nln56]

- Fokker-Planck equation (drift and diffusion
processes) [nln57]

- Drift equation (deterministic processes) [nex29]

- Master equation (jump processes) [nex28]

- Non-differentiability of sample paths [nex99]
- Predominantly small jumps [nln58]

- Time evolution of mean and variance [nln59]

- 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 [nln61]

- 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 [nln60]

- 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 [nln62] [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]

- Populations with linear birth and death rates
III [nex130]

- 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]

- Early Landmarks [nln63]

- Relevant time scales (collisions, relaxation,
observations) [nln64]

- Einstein's theory [nln65]

- Diffusion equation analyzed [nln73]

- Release of Brownian particle from box
confinement [nex128]

- Smoluchowski equation [nln66]

- Einstein's fluctuation-dissipation relation [nln67]

- Smoluchowski vs Fokker-Planck [nln68]

- Fourier's law for heat conduction [nln69]

- Thermal diffusivity [nex117]

- Shot noise [nln70]

- Campbell's theorem [nex37]

- Critically damped ballistic galvanometer [nex70]

- Langevin's theory [nln71]

- White noise

- Brownian motion and Gaussian white noise [nln20]

- Wiener process [nsl4]
- Autocorrelation function of Wiener process [nex54]
- 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 [nln72]

- Attenuation with memory [nln22]

- Velocity correlation function of Brownian
particle III [nex120]

- Brownian harmonic oscillator [nln75]

- Brownian harmonic oscillator VII: equivalent
specifications [nex129]

- 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]

- Langevin dynamics from microscopic model [nln74]

- 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)

- Moment expansion [nln78]

- Spectral representations [nex65]
*

- Linear response of classical relaxator [nex66]

- Dielectric relaxation in liquid water [nln76]

- Linear response of classical oscillator [nex67]

- Scattering process and dynamic structure
factor [nln89]

- Scattering from free atoms [nln93] *

- Scattering from atoms bound to lattice [nln94]

- Scattering from a harmonic crystal [nln95]

- Magnetic resonance or scattering [nln97]

- Introduction [nln28]

- Time-dependence of expectation values (quantum
and classical) [nln77] *

- 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]

- n-pole approximation [nln87] *

- Relaxation function with uniform
continued-fraction coefficients [nex69]

- Link to Green's function formalism [nln88]

- Structure function of harmonic oscillator [nex71], * [nex72],
[nex73]

- Stage for recursion method [nln79]

- Modules of recursion method [nln80]

- Representations of recursion method [nln81]

- Orthogonal expansion of dynamical variables [nln82]

- Gram-Schmidt orthogonalization I [nln83]
*

- Relaxation function and spectral density [nln84]

- Moment expansion vs continued fraction I [nln85]

- Link to generalized Langevin equation [nln86]

- Orthogonal expansion of wave functions [nln90]

- Gram-Schmidt orthogonalization II [nln91]

- Structure function [nln92]

- Moment expansion vs continued fraction II [nln96]

- Genetic code of spectral densities [nln98]

- Spectral Lines from finite sequences of
continued-fraction coefficients [nln99]

- Spectral densities with bounded support [nln100]

- Bandwidth and gap in spectral density [nln101]

- Spectral densities with unbounded support [nln102]

- Unbounded support and gap [nln103]

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. - V. S. Viswanath and G. Müller:
*The recursion method. Application**to**many-body dynamics.*Springer-Verlag, New York 1994.

Do you have a question about any of the problems [nex]?

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Last updated 04/26/18