- Thermodynamic system and thermodynamic state
- State variables
- Equations of state
- Thermodynamic equation of state for a classical gas
- Encoding thermodynamic information
- Thermodynamic contacts
- Zeroth law of thermodynamics
- First law of thermodynamics
- Second law of thermodynamics
- Third law of thermodynamics
- Thermodynamic processes
- Differentials

Exercises:

- Exact and inexact differentials I [tex5]
- Fast heat [tex143]

- Expansion and compression of nitrogen gas [tex144]
- Bathtub icebreaker [tex145]

- Exact and inexact differentials II [tex146]

- Exact and inexact differentials III [tex168]

Additional materials:

- Thermodynamics overview [tln2]

- Equations of state for ideal gas and real fluid [tsl12]
- Physical constants [tsl47]

- Relevant textbooks [tln90]

- Carnot engine
- Efficiency of Carnot engine
- Maximum efficiency of heat engine
- Absolute temperature
- Entropy
- Internal energy
- Reversible processes in fluid systems
- Gasoline engine (Otto cycle)
- Diesel engine
- Escher-Wyss gas turbine
- Stirling engine

Exercises:

- Entropy change caused by
expanding ideal gas [tex1]

- Heating the air in a room [tex2]

- Carnot engine of a classical
ideal gas [tex3]

- Carnot engine for an ideal
paramagnet [tex4]

- Adiabates of the classical ideal gas [tex7]

- Idealized Otto cycle [tex8]

- Work extracted from finite
heat reservoir in infinite environment [tex9]

- Work extracted from finite
heat reservoir in finite environment [tex10]

- Room heater: electric radiator
versus heat pump [tex13]

- Idealized Diesel cycle [tex16]

- Roads from 1 to 2: isothermal,
isentropic, isochoric, isobaric [tex25]

- Ideal-gas engine with two-step
cycle I [tex106]

- Ideal-gas engine with two-step
cycle II [tex107]

- Joule cycle [tex108]

- Idealized Stirling cycle [tex131]
- Absolute temperature from
measurements [tex134]

- Circular heat engine I [tex147]

- Circular heat engine II [tex148]

- Square heat engine for
classical ideal gas [tex149]

- Work performance and heat transfer [tex155]
- Ideal-gas engine with
three-step cycle I [tex196]

- Ideal-gas engine with three-step cycle II [tex198]

- Ideal-gas engine with three-step cycle I [tex200]

- Fundamental equation of thermodynamics

- Analogy with mechanical equilibrium
- Free energy in a mechanical system
- Free energy in a thermodynamic system
- Thermodynamic potentials for a fluid system
- Differentials of thermodynamic potentials
- Facts about thermodynamic potentials
- Thermodynamic functions for fluid system
- Substitutions for magnetic system
- Maxwell's relations
- Free energy stored and retrieved
- Response functions
- Thermal response functions
- Mechanical response functions
- Magnetic response functions
- Isothermal and adiabatic processes
- Conditions for thermal equilibrium
- Stability of thermal equilibrium

Exercises:

- Retrievable and irretrievable energy put in
heat reservoir [tex6]

- Mayer's relation for heat capacities of the classical ideal gas [tex12]
- Entropy and internal energy of the classical ideal gas [tex14]
- Thermodynamic potentials of the classical ideal gas [tex15]
- Chemical potential of the classical ideal gas [tex17]
- Positive and negative heat capacities [tex26]
- Some fluid system [tex158]

Additional materials:

- Legendre transform [tln77]

- Alternative set of thermodynamic potentials [tln9]
- Useful relations between partial derivatives [tln6]
- Jacobi transformations [tln21]

- Classical ideal gas
- Van der Waals gas
- Cooling a gas by free expansion (Joule effect)
- Cooling a gas by throttling (Joule-Thomson effect)
- Entropy of mixing in classical ideal gas
- Ideal paramagnet
- Adiabatic demagnetization
- Ideal paramagnetic gas
- Photon gas
- Rubber band elasticity
- Inhomogeneous systems

Exercises:

- How not to modify the ideal gas equation of state [tex11]
- Sound velocity in the classical ideal gas I [tex18]

- Thermodynamics of an ideal paramagnet I [tex19]

- Thermodynamics of an ideal paramagnet II [tex20]

- Thermodynamics of an ideal paramagnet III [tex21]

- Thermodynamics of a classical ideal
paramagnetic gas I [tex22]

- Thermodynamics of black-body radiation [tex23]

- Carnot cycle of thermal radiation [tex24]

- Heat capacities of the van der Waals gas [tex27]

- Determining C
_{V}of condensed matter [tex28]

- Assembling thermodyamic information [tex29]

- Joule coefficient of van der Waals gas [tex31]

- Joule-Thomson coefficient of van der Waals gas
[tex32]

- Effects of first virial correction on ideal
gas properties [tex33]

- Ideal gas heat capacity by design [tex35]

- Thermodynamics of a real paramagnet [tex36]

- Internal energy and entropy of van der Waals
gas [tex38]

- Rubber band heat engine [tex39]

- Equation of state and adiabate of an elastic
band [tex40]

- Reconstructing the equation of state of a
fluid system [tex42]

- Reconstructing the equation of state of a gas
[tex43]

- Sound velocity in the classical ideal gas II [tex99]

- Hydrostatic pressure [tex132]

- Thermodynamics of a classical ideal
paramagnetic gas II [tex133]

- Polytropic process of classical ideal gas [tex138]

- Heavy piston I [tex141]

- Isothermal atmosphere [tex150]

- Adiabatic atmosphere [tex151]

- Homogeneous atmosphere [tex152]
- Heavy piston II [tex170]

- Effect of mixing on chemical potential [tex173]
- Square heat engine with photon gas [tex205]

Additional materials:

- Joule-Thomson inversion curves [tsl1]

- Osmotic pressure [tln26]

- Entropy landscape of paramagnetic salt [tsl2]

- Mechanocaloric and thermomechanical effects [tln34]

- Typical solid-liquid-gas phase diagram
- Additional and alternative phases
- Classification of phase transitions
- Discontinuous transition
- Continuous transition
- Order parameter
- Phase coexistence: Gibbs' phase rule
- Clausius-Clapeyron equation
- Effects of a uniform gravitational field

Exercises:

- Entropy of supercooled liquid [tex30]

- Coexistence line of continuous phase
transition [tex37]

- Heat capacity of vapor in equilibrium with
liquid phase [tex41]

- Melting or freezing? [tex51]

- Triple-point phase changes I [tex52]

- Abnormal phase behavior [tex54]

- Phase coexistence of ammonia [tex55]
- Discontinuous transition: change in internal
energy [tex123]

- Latent heat and response functions [tex124]

- Dry ice [tex125]

- Cooling down? Heating up? [tex153]

- Triple-point phase changes II [tex156]

- Effects of heat input [tex159]
- Triple-point phase changes III [tex204]

- Destabilization of triple-point equilibrium I
[tex206]

- Destabilization of
triple-point equilibrium II [tex207]

Additional materials:

- Phase diagram of H
_{2}O [tsl4] - Liquid crystal phases [tsl51]

- Ferrimagnetic phases [tsl49]

- Ordering of surfactant molecules [tsl50]

- Law of corresponding states (using van der
Waals equation of state)

- Maxwell construction (using Gibbs potential or
Helmholtz potential)

- Nucleation of droplets or bubbles (coexistence
line, spinodal line)

Exercises:

- Dieterici equation of state [tex34]

- Latent heat and heat capacies at
superconducting transition [tex44]

- Mean-field ferromagnet I
[tex45]

- Mean-field ferromagnet II [tex46]

- Structural transition of iron [tex53]
- Joule coefficient of Dieterici gas [tex197]

- Heat capacity of Dieterici gas [tex202]

Additional materials:

- Helium liquids and superfluidity [tln33]

- Superconducting transition [tln35]

- Thermodynamics of a ferromagnet [tsl5]
- Mean-field ferromagnet [tln84]

- Statistical concept of uncertainty
- Statistical concept of information
- Statistical uncertainty and entropy
- Kinetics of classical ideal gas
- Maxwell velocity distribution
- Boltzmann equation

- H-function
- H-theorem
- H-theorem and irreversibility

Exercises:

- Statistical uncertainty: verification of
criteria [tex47]

- Information regarding a census of birds [tex48]

- Pressure and mean-square velocity in classical
ideal gas [tex49]

- Maxwell velocity distribution (Maxwell's
derivation) [tex50]

- Maxwell distribution in D dimensions [tex56]

- Energy distribution for N ideal gas atoms [tex57]

- Maxwell velocity distribution (Boltzmann's
derivation) [tex58]

- Ideal-gas entropy and Boltzmann's H-function [tex59]

- Maxwell distribution from variational principle [tex60]
- Information of sequenced messages [tex61]
- Doppler broadening of atomic spectral lines [tex63]

- Gas container with tiny hole
- Leakage from container with heat conducting walls
- Leakage from container with insulating walls
- Particle flow and energy flow between containers
- Kinematic pressure and interaction pressure
- Kinetic forces and mobility
- Collision rate and mean free path

Exercises

- Ideal gas atoms escaping from a container I [tex62]
- Toward thermal equilibrium via particle transfer [tex64]
- Isotope separation via diffusion [tex65]

- Interaction pressure produced by Gaussian interparticle potential [tex66]
- Rate of chemical reaction in gas phase [tex67]
- Average force of particle beam on heavy hard
sphere [tex68]

- Mobility of a hard sphere in a dilute gas [tex69]

- Collision rate in a classical ideal gas [tex70]

- Mean free path of particle in classical ideal
gas [tex71]

- Effect of escaping particles on temperature of 1D ideal gas [tex72]
- Ideal gas atoms escaping from a container II [tex176]
- Ideal gas atoms escaping from a container III [tex177]

- Classical Hamiltonian systems
- Points and trajectories in phase space
- Probability density in phase space
- Probability flow in phase space
- Classical Liouville operator
- Stationarity condition for phase-space probability density
- Density operator
- Quantum time evolution
- Stationarity condition for density operator
- Gibbs entropy
- Phase-space volume allocated per quantum state
- Microcanonical ensemble
- Aspects of significance
- Simple applictions
- Entropy of mixing revisited
- Negative temperatures

Exercises:

- Classical ideal gas [tex73]

- Array of classical harmonic oscillators [tex74]

- Array of quantum harmonic oscillators I [tex75]

- Array of quantum harmonic oscillators II [tex126]

- Quantum paramagnet [tex127]

- Extremum principle
- Canonical partition function
- Systems of noninteracting particles
- From phase-space density to Maxwell velocity distribution
- Ensemble averages
- Energy fluctuations and heat capacity
- Classical ideal gas (relativistic)
- Inhomogeneous systems
- Partition function and density of states

Exercises:

- Nonrelativistic ideal gas [tex76]

- Ultrarelativistic ideal gas [tex77]
- Array of classical harmonic oscillators [tex78]
- Relative momentum of two
ideal-gas particles [tex80]

- Ideal gas partition function and density of states [tex81]
- Relativistic ideal gas I: canonical partition
function [tex91]

- Relativistic ideal gas II: entropy and
internal energy [tex92]

- Relativistic ideal gas III: heat capacity [tex93]
- Gas pressure and density inside centrifuge [tex135]

- Irreversible decompression [tex136]

- Irreversible heat exchange [tex137]
- Reversible decompression [tex139]

- Reversible heat exchange [tex140]

- Heavy piston I [tex141]
- Ultrarelativistic ideal gas in two dimensions [tex154]

- Vibrational heat capacities of solids
- Theory of Dulong and Petit
- Theory of Einstein
- Atoms interacting via harmonic forces
- Theory of Debye
- Paramagnetism of localized magnetic dipoles
- Langevin paramagnetism
- Two-level system
- Brillouin paramagnetism
- Fluctuations in a magnetic system
- Gases with internal degrees of freedom
- Translational motion (classical)
- Rotational motion (classical)
- Rotational motion (quantum)
- Vibrational motion (quantum)
- Fine structure
- Orthohydrogen and parahydrogen

Exercises:

- Classical ideal gas in a uniform gravitational
field [tex79]

- Array of quantum harmonic oscillators [tex82]

- Vibrational heat capacity of a solid [tex83]

- Classical paramagnet [tex84]

- Quantum paramagnet (two-level system) [tex85]

- Quantum paramagnet (Brillouin function) [tex86]
- Classical rotational free
energies of NH
_{3}gas [tex87] - Classical rotational entropies of HCl and N
_{2}gases [tex88]

- Quantum rotational heat capacity of a gas at
low temperature [tex89]

- Quantum rotational heat capacity of a gas at high temperature [tex90]
- Anharmonic oscillator and
thermodynamic perturbation [tex104]

- Fluctuation in a magnetic system [tex109]
- Ising trimer [tex142]
- Quantum paramagnet (three-level system) [tex157]
- Heat capacity of gas due to internal degree of
freedom [tex199]

- Canonical partition functions [tex208]

Additional materials:

- Vibrational heat capacities of solids [tsl29]

- Paramagnetic salts [tsl30]

- Thermodynamic perturbation expansion [tln80]

- Extremum principle
- Grandcanonical partition function
- Density fluctuations and compressibility
- Gentle introduction to quantum statistics
- Permutation symmetry
- Occupation number representation
- Canonical partition function (for quantum
gases)

- Grandcanonical partition function (for quantum gases)
- Grand potential
- Average number of particles and state occupancies
- Entropy and state occupancies

- Internal energy and state occupancies
- Fluctuations of state occupanices

- Density of states
- Occupancy of 1-particle states

Exercises:

- Classical ideal gas [tex94]

- Density fluctuations [tex95]

- Density fluctuations and compressibility [tex96]

- Energy fluctuations and thermal response
functions [tex103]

- Occupation number fluctuations [tex110]

- Density of 1-particle states [tex111]

- Maxwell-Boltzmann gas in
*D*dimensions [tex112] - MB gas with ultrarelativistic energy-momentum
relation [tex160]

- Ultrarelativistic ideal gas [tex169]
- Some fantasy gas [tex171]

- Entropy and internal energy from state
occupancies [tex178]

- Equation of state
- Reference values
- Isochores
- Coexistence of gas and condensate
- Isotherms
- Isobars
- Phase diagrams
- Entropy
- Internal energy
- Heat capacity

Exercises:

- Heat capacity at high temperature [tex97]
- Ultrarelativistic Bose-Einstein gas [tex98]
- Statistical mechanics of blackbody radiation [tex105]
- Fundamental relations [tex113]

- Isochores [tex114]

- Isotherms and isobars [tex115]

- Heat capacity at low temperature [tex116]

- Isothermal compressibility [tex128]

- Isobaric expansivity [tex129]

- Speed of sound [tex130]
- Entropy and internal energy [tex179]

Additional materials:

- Equation of state
- Chemical potential
- Level occupancies
- Isochores
- Phase transition
- Isotherms
- Entropy
- Internal energy
- Heat capacity

Exercises:

- Heat capacity at high temperature [tex100]
- Heat capacity at low temperature [tex101]
- Ground-state energy [tex102]
- Chemical potential I [tex117]

- Chemical potential II [tex118]

- Statistical interaction pressure [tex119]

- Isotherm and adiabate [tex120]

- Stable white dwarf star [tex121]

- Unstable white dwarf star [tex122]

Additional materials:

- Fermi-Dirac functions [tsl42]

- Thermionic emission (Richardson effect)
- Schottky effect
- Photoelectric emission (Hallwachs effect)
- Pauli paramagnetism (PPM)
- PPM analyzed in canonical ensemble
- PPM thermodynamic potentials and functions
- PPM response functions
- PPM magnetization curves (numerical analysis)
- PPM magnetization curves at T = 0 (exact results)
- PPM magnetization curves in D = 2 (exact analysis)
- PPM isothermal susceptibility at H = 0
- PPM correction to Langevin-Brillouin result at high T

Exercises:

- Paramagnetic FD gas I: pressure and entropy [tex161]

- Paramagnetic FD gas II: internal energy [tex162]

- Paramagnetic FD gas III: heat capacity C
_{VM}[tex163]

- Paramagnetic FD gas IV: heat capacity C
_{VH}[tex164]

- Paramagnetic FD gas V: isothermal
susceptibility [tex165]

- Paramagnetic FD gas VI: isothermal
compressibilities [tex166]

- Paramagnetic FD gas VII: isobaric expansivity
[tex167]

- Paramagnetic FD gas VIII: magnetization curves
at T > 0 [tex180]

- Paramagnetic FD gas IX: magnetization curves
at T = 0 [tex181]

- Paramagnetic FD gas X: exact magnetization
curve for D = 2 [tex182]

- Paramagnetic FD gas XI: isothermal
susceptibility at H = 0 [tex183]

- Paramagnetic FD gas XII: Langevin-Brillouin
limit at high T [tex184]

- Ginzburg-Landau theory for secon-order phase transition
- Ginzburg-Landau theory for first-order phase transition
- Ornstein-Zernike theory for correlations
- Critical-point exponents
- Critical singularities of magnetic system
- Critical singularities of fluid system
- Inequalities of critical-point exponents
- Test of scaling laws
- Marginal dimensionality

Exercises:

- Order parameter of first-order Ginzburg-Landau
transition [tex174]

- Critical singularities of van der Waals gas [tex175]

- Nearly ideal classical gas

- Ising magnet

- Ising lattice gas
- Mapping between magnet and lattice gas
- Transfer matrix solution of 1D Ising magnet
- Expectation values via transfer matrix
- Correlation functions via transfer matrix
- Ising lattice gas in D=1
- Ideal lattice gas limit
- Ising lattice gas equation of state in D=1
- Ising lattice gas entropy in D=1
- Ising lattice gas internal energy in D=1

Exercises:

- Ideal lattice gas [tex172]

- Ising chain: transfer matrix solution I [tex185]

- Ising chain: transfer matrix solution II [tex189]

- Ising lattice gas in D=1: equation of state [tex194]

- Ising lattice gas in D=1: entropy I [tex195]

- Ising lattice gas in D=1: entropy II [tex201]
- Ising model in Bethe approximation [tex203]

- ...

Additional materials:

- Ising model and descendents [tln93]

- Exchange interaction [tln94]

- Metallic alloys [tln95]

- T=0 phase diagrams of Ising chains [tln96]
- Approximating the Ising model [tln97]

- Equivalent-neighbor Ising model [tln98]

- ...

- NLS model
- Free bosons
- Impenetrable bosons and free fermions
- Two bosons with finite contact repulsion
- Three bosons subject to finite two-body contact repulsion
- General Bethe ansatz equations of the NLS
model

- Trigonometric Bethe ansatz equations
- Iterative solutions
- Particles and holes
- Densities of particle momenta and hole momenta
- Ground state of the NLS model from
Lieb-Liniger equation

- ...

Exercises:

- Wave function of impenetrable bosons for
*N*=2 and*N*=3 [tex190] - Two-boson Bethe wave functions [tex191]
- Three-boson Bethe ansatz equations [tex192]
- Trigonometric Bethe ansatz equations for the NLS model [tex193]
- ...

- Fermions
- BosonsC
- Size L and XL particles
- Semions
- Particles with internal degrees of freedom
- Distinguishable species of particles in shared orbitals
- Hosts and caps
- Hosts, hybrids, and caps
- Hosts, hybrids, and tags
- Configurational entropy
- Examples with one species
- Example with two species
- Semions versus hosts and caps

Exercises:

- Configurational entropy of statistically
interacting particles [tex186]

- Hosts and tags at level 1 [tex187]

- Hosts and tags at level 2 [tex188]

Additional materials

- Conversion of dynamical interactions into statistical interactions
- Partition function, average occupancies, and
entropy

- ...

- ...