Main concepts of Statistical Physics: separation of
microscopic and macroscopic description of a system; microstates vs.
configurations; sharpness of the distribution of microstates over
configuration space; basic idea of statistical ensembles and of
concepts of Statistical Physics as applied to a simple modelsystem of
two-state spins: numbering of microscopic states; multiplicity
function; continuous approximation of the multiplicity function;
probabilities of micro- and macro- states; characteristics of
probability function, mean, variance and standard deviation; sharpness
of the probability distribution of a macroscopic variable; correlation
of two random variables.
Microcanonical ensemble: probabilities of microscopic states in
an isolated system at equilibrium; example of equilibration in the
system of spins; thermal equilibrium of two arbitrary systems;
definition of temperature; entropy in microcanonical ensemble;
additivity of entropy; the postulate of entropy increase in an isolated
system (second Law of Thermodynamics); the direction of heat flow.
Canonical ensemble: Boltzmann Distribution; partition function;
microscopic state probabilities; average energy of a system in thermal
equilibrium; fluctuations in energy and their relation to heat
capacity; Helmoholtz Free energy and its relation to the partition
Applications of the canonical ensemble: the system of spins;
Schottky anomaly; partition function, energy and free energy of a
ideal monoatomic gas.
Thermodynamic equilibrium and thermodynamic processes;
characteristic time scales; reversible and irreversible processes;
quasi-stationary process; examples of quasi-stationary heat transfer
and of work.
and Work in thermodynamics; First Law of Thermodynamics; differential
relations between thermodynamic quantities; Maxwell relations;
enthalpy; heat capacity; intensive and extensive quantities; entropy,
pressure and heat capacity of a classical ideal monoatomic gas.
More applications of Canonical ensemble: classical
oscillators, single and coupled; normal modes in the linear
beads-springs system; Equipartition Theorem.
Heat capacity of solids: Dulong-Petit law; classical treatment of
the problem; deviations from Dulong-Petit law; Einstein theory of
heat capacity; Einstein temperature; Debye theory; Debye temperature;
phonons; heat capacity of diatomic gas.
Grand Canonical ensemble: chemical potential; Gibbs
Distribution; grand partition function; grand thermodynamic potential
and its relation to grand partition function; average number of
molecules and fluctuations in the number of molecules in the system at
thermal and diffusive equilibrium; Maxwell relations for chemical
Applications of Grand Canonical ensemble: external chemical
potential; distribution of molecules in atmosphere; equilibrium between
adsorbed molecules and gas.
Engines: perpetuum mobile of first and second type; Kelvin-Planck and
Clausius formulations of second law of Termodynamics; PV-diagram of
processes in a heat engine; efficiency of a heat engine; isothermal,
isobaric, isochoric and adiabatic processes; Carnot
Summary of Statistical Mechanics and Thermodynamics I; centrality
of the Second Law of Thermodynamics in physics and other disciplines;
C. Kittel and H. Kroemer, Thermal Physics
F. Reif F, Fundamentals of Statistical and Thermal Physics,
McGraw-Hill, NY 1965, QC 175.R43