Cover -- Half-title -- Title -- Copyright -- Contents -- Preface -- 1 Thermostatics -- 1.1 Thermodynamic equilibrium -- 1.1.1 Microscopic and macroscopic descriptions -- 1.1.2 Walls -- 1.1.3 Work, heat, internal energy -- 1.1.4 Definition of thermal equilibrium -- 1.2 Postulate of maximum entropy -- 1.2.1 Internal constraints -- 1.2.2 Principle of maximum entropy -- 1.2.3 Intensive variables: temperature, pressure, chemical potential -- 1.2.4 Quasi-static and reversible processes -- 1.2.5 Maximum work and heat engines -- 1.3 Thermodynamic potentials -- 1.3.1 Thermodynamic potentials and Massieu functions -- 1.3.2 Specific heats -- 1.3.3 Gibbs-Duhem relation -- 1.4 Stability conditions -- 1.4.1 Concavity of entropy and convexity of energy -- 1.4.2 Stability conditions and their consequences -- 1.5 Third law of thermodynamics -- 1.5.1 Statement of the third law -- 1.5.2 Application to metastable states -- 1.5.3 Low temperature behaviour of specific heats -- 1.6 Exercises -- 1.6.1 Massieu functions -- 1.6.2 Internal variable in equilibrium -- 1.6.3 Relations between thermodynamic coefficients -- 1.6.4 Contact between two systems -- 1.6.5 Stability conditions -- 1.6.6 Equation of state for a fluid -- 1.7 Problems -- 1.7.1 Reversible and irreversible free expansions of an ideal gas -- 1.7.2 van der Waals equation of state -- 1.7.3 Equation of state for a solid -- 1.7.4 Specific heats of a rod -- 1.7.5 Surface tension of a soap film -- 1.7.6 Joule-Thomson process -- 1.7.7 Adiabatic demagnetization of a paramagnetic salt -- 1.8 Further reading -- 2 Statistical entropy and Boltzmann distribution -- 2.1 Quantum description -- 2.1.1 Time evolution in quantum mechanics -- 2.1.2 The density operators and their time evolution -- 2.1.3 Quantum phase space -- 2.1.4 (P, V, E) relation for a mono-atomic ideal gas -- 2.2 Classical description.

2.2.1 Liouville's theorem -- 2.2.2 Density in phase space -- 2.3 Statistical entropy -- 2.3.1 Entropy of a probability distribution -- 2.3.2 Statistical entropy of a mixed quantum state -- 2.3.3 Time evolution of the statistical entropy -- 2.4 Boltzmann distribution -- 2.4.1 Postulate of maximum of statistical entropy -- 2.4.2 Equilibrium distribution -- 2.4.3 Legendre transformation -- 2.4.4 Canonical and grand canonical ensembles -- 2.5 Thermodynamics revisited -- 2.5.1 Heat and work: first law -- 2.5.2 Entropy and temperature: second law -- 2.5.3 Entropy of mixing -- 2.5.4 Pressure and chemical potential -- 2.6 Irreversibility and the growth of entropy -- 2.6.1 Microscopic reversibility and macroscopic irreversibility -- 2.6.2 Physical basis of irreversibility -- 2.6.3 Loss of information and the growth of entropy -- 2.7 Exercises -- 2.7.1 Density operator for spin-1/2 -- 2.7.2 Density of states and the dimension of space -- 2.7.3 Liouville theorem and continuity equation -- 2.7.4 Loaded dice and statistical entropy -- 2.7.5 Entropy of a composite system -- 2.7.6 Heat exchanges between system and reservoir -- 2.7.7 Galilean transformation -- 2.7.8 Fluctuation-response theorem -- 2.7.9 Phase space volume for N free particles -- 2.7.10 Entropy of mixing and osmotic pressure -- 2.8 Further reading -- 3 Canonical and grand canonical ensembles: applications -- 3.1 Simple examples in the canonical ensemble -- 3.1.1 Mean values and fluctuations -- 3.1.2 Partition function and thermodynamics of an ideal gas -- 3.1.3 Paramagnetism -- 3.1.4 Ferromagnetism and the Ising model -- 3.1.5 Thermodynamic limit -- 3.2 Classical statistical mechanics -- 3.2.1 Classical limit -- 3.2.2 Maxwell distribution -- 3.2.3 Equipartition theorem -- 3.2.4 Specific heat of a diatomic ideal gas -- 3.3 Quantum oscillators and rotators -- 3.3.1 Qualitative discussion.

3.3.2 Partition function of a diatomic molecule -- 3.4 From ideal gases to liquids -- 3.4.1 Pair correlation function -- 3.4.2 Measurement of the pair correlation function -- 3.4.3 Pressure and energy -- 3.5 Chemical potential -- 3.5.1 Basic formulae -- 3.5.2 Coexistence of phases -- 3.5.3 Equilibrium condition at constant pressure -- 3.5.4 Equilibrium and stability conditions at constant -- 3.5.5 Chemical reactions -- 3.6 Grand canonical ensemble -- 3.6.1 Grand partition function -- 3.6.2 Mono-atomic ideal gas -- 3.6.3 Thermodynamics and fluctuations -- 3.7 Exercises -- 3.7.1 Density of states -- 3.7.2 Equation of state for the Einstein model of a solid -- 3.7.3 Specific heat of a ferromagnetic crystal -- 3.7.4 Nuclear specific heat of a metal -- 3.7.5 Solid and liquid vapour pressures -- 3.7.6 Electron trapping in a solid -- 3.8 Problems -- 3.8.1 One-dimensional Ising model -- 3.8.2 Negative temperatures -- 3.8.3 Diatomic molecules -- 3.8.4 Models of a boundary surface -- 3.8.5 Debye-Hückel approximation -- 3.8.6 Thin metallic film -- 3.8.7 Beyond the ideal gas: first term of virial expansion -- 3.8.8 Theory of nucleation -- 3.9 Further reading -- 4 Critical phenomena -- 4.1 Ising model revisited -- 4.1.1 Some exact results for the Ising model -- 4.1.2 Correlation functions -- 4.1.3 Broken symmetry -- 4.1.4 Critical exponents -- 4.2 Mean field theory -- 4.2.1 A convexity inequality -- 4.2.2 Fundamental equation of mean field theory -- 4.2.3 Broken symmetry and critical exponents -- 4.3 Landau's theory -- 4.3.1 Landau functional -- 4.3.2 Broken continuous symmetry -- 4.3.3 Ginzburg-Landau Hamiltonian -- 4.3.4 Beyond Landau's theory -- 4.3.5 Ginzburg criterion -- 4.4 Renormalization group: general theory -- 4.4.1 Spin blocks -- 4.4.2 Critical exponents and scaling transformations -- 4.4.3 Critical manifold and fixed points.

4.4.4 Limit distributions and correlation functions -- 4.4.5 Magnetization and free energy -- 4.5 Renormalization group: examples -- 4.5.1 Gaussian fixed point -- 4.5.2 Non-Gaussian fixed point -- 4.5.3 Critical exponents to order -- 4.5.4 anomalousScalingoperatorsand dimensions -- 4.6 Exercises -- 4.6.1 High temperature expansion and Kramers-Wannier duality -- 4.6.2 Energy-energy correlations in the Ising model -- 4.6.1 High temperature expansion and Kramers-Wannier duality -- 4.6.3 Mean field critical exponents for T Tc -- 4.6.4 Accuracy of the variational method -- 4.6.5 Shape and energy of an Ising wall -- 4.6.6 The Ginzburg-Landau theory of superconductivity -- 4.6.7 Mean field correlation function in r-space -- 4.6.8 Critical exponents for n 1 -- 4.6.9 Renormalization of the Gaussian model -- 4.6.10 fixedScalingfieldsattheGaussian point -- 4.6.11 Critical exponents to order for n = 1 -- 4.6.12 Irrelevant exponents -- 4.6.13 Energy-energy correlations -- 4.6.14 'Derivation' of the Ginzburg-Landau Hamiltonian from the Ising model -- 4.7 Further reading -- 5 Quantum statistics -- 5.1 Bose-Einstein and Fermi-Dirac distributions -- 5.1.1 Grand partition function -- 5.1.2 Classical limit: Maxwell-Boltzmann statistics -- 5.1.3 Chemical potential and relativity -- 5.2 Ideal Fermi gas -- 5.2.1 Ideal Fermi gas at zero temperature -- 5.2.2 Ideal Fermi gas at low temperature -- 5.2.3 Corrections to the ideal Fermi gas -- 5.3 Black body radiation -- 5.3.1 Electromagnetic radiation in thermal equilibrium -- 5.3.2 Black body radiation -- 5.4 Debye model -- 5.4.1 Simple model of vibrations in solids -- 5.4.2 Debye approximation -- 5.4.3 Calculation of thermodynamic functions -- 5.5 Ideal Bose gas with a fixed number of particles -- 5.5.1 Bose-Einstein condensation -- 5.5.2 Thermodynamics of the condensed phase.

5.5.3 Applications: atomic condensates and helium-4 -- 5.6 Exercises -- 5.6.1 The Maxwell-Boltzmann partition function -- 5.6.2 Equilibrium radius of a neutron star -- 5.6.3 Two-dimensional Fermi gas -- 5.6.4 Non-degenerate Fermi gas -- 5.6.5 Two-dimensional Bose gas -- 5.6.6 Phonons and magnons -- 5.6.7 Photon-electron-positron equilibrium in a star -- 5.7 Problems -- 5.7.1 Pauli paramagnetism -- 5.7.2 Landau diamagnetism -- 5.7.3 White dwarf stars -- 5.7.4 Quark-gluon plasma -- 5.7.5 Bose-Einstein condensates of atomic gases -- 5.7.6 Solid-liquid equilibrium for helium-3 -- 5.7.7 Superfluidity for hardcore bosons -- 5.8 Further reading -- 6 Irreversible processes: macroscopic theory -- 6.1 Flux, affinities, transport coefficients -- 6.1.1 Conservation laws -- 6.1.2 Local equation of state -- 6.1.3 Affinities and transport coefficients -- 6.1.4 Examples -- Heat diffusion in an insulating solid (or a simple .uid) -- Particle diffusion -- 6.1.5 Dissipation and entropy production -- 6.2 Examples -- 6.2.1 Coupling between thermal and particle diffusion -- 6.2.2 Electrodynamics -- 6.3 Hydrodynamics of simple fluids -- 6.3.1 Conservation laws in a simple fluid -- Mass conservation -- Conservation of momentum -- 6.3.2 Derivation of current densities -- 6.3.3 Transport coefficients and the Navier-Stokes equation -- 6.4 Exercises -- 6.4.1 Continuity equation for the density of particles -- 6.4.2 Diffusion equation and random walk -- 6.4.3 Relation between viscosity and diffusion -- 6.4.4 Derivation of the energy current -- 6.4.5 Lord Kelvin's model of Earth cooling -- 6.5 Problems -- 6.5.1 Entropy current in hydrodynamics -- 6.5.2 Hydrodynamics of the perfect fluid -- 6.5.3 Thermoelectric effects -- 6.5.4 Isomerization reactions -- 6.6 Further reading -- 7 Numerical simulations -- 7.1 Markov chains, convergence and detailed balance.

7.2 Classical Monte Carlo.