Syllabus
Methodical foundations. The relation of thermodynamics, statistical physics and mechanics, phase space, microstate and macrostate, statistical ensemble, time and ensemble averaging, fluctuations, homogeneous and heterogeneous systems, thermodynamic equilibrium, energy in thermodynamic systems, adiabatic processes, reversible and dissipative work, First law of thermodynamics, Second law of thermodynamics.
Statistical foundations. Probability description, distribution function, density of states, kinetic (master) equation, ergodic assumption, the principle of detailed balance.
Temperature, the meaning of temperature for large systems, thermal equilibrium, Boltzmann distribution, the meaning of temperature for small systems, partition function, negative temperature.
Entropy. Boltzmann-Gibbs definition, kanonical distribution, the law of increase of entropy, configurational entropy, the connection between equilibrium entropy and heat, Third law of thermodynamics.
Monatomic ideal gas. Quantisation of velocity and energy, velocity distribution, equation of state, heat capacities cV and cP, isothermal, adiabatic and Joule expansions, real gas.
Classical thermodynamics, extensive and intensive variables, heat engines, Carnot cycle, thermodynamic potentials, their properties and significance, thermodynamic relations, partial derivatives, Maxwell relations, relations involving cV and cP, electrical cell.
Classical statistical mechanics. Classical limit of quantum theory, Liouville theorem, density matrix, Liouville equation, equipartition theorem, fermions, bosons.
Statistical calculation of thermodynamic quantities. Energy, entropy, magnetic moment, pressure. Asymmetric diatomic gas, vacancies in solid, Gibbs paradox.
Systems with variable contents, Grand canonical (Gibbs) distribution, chemical potential, grand partition function (sum), Fermi-Dirac distribution, Bose-Einstein distribution, electron gas, Planck distribution, Debye theory of heat capacity.
Phase transitions and chemical equilibrium. Phase transitions classification, Clausius-Clapeyron equation, Ehrenfest equations, Landau theory of phase transition, the behavior near critical point. The equilibrion of the system of k-conponents and f-phases. Gibbs phase rule.
Computer simulation methods. Inter-molecular forces. Deterministic methods - molecular dynamics, stochastic methods - Monte Carlo.
Annotation
Obligatory course on thermodynamics and statistical physics for the bachelor degree plan Mathematical Modelling
(or master degree plan Mathematical Modelling in Physics and Technology). The course is suitable also for students (graduates) of non-physical specializations.