Elementary Principles in Statistical Mechanics

Principles of Statistical Mechanics

These lectures comprise an introductory course in statistical mechanics. The Gibbs formulation of the canonical ensemble is introduced and illustrated by application to simple models of magnets and fluids, specifically the ideal gas and the magnetic Ising spin chain. In addition, the classical mean field theories of fluids and ferromagnets, namely the van der Waals theory of fluids and the Curi...

Principles of statistical mechanics of random networks

We develop a statistical mechanics approach for random networks with uncorrelated vertices. We construct equilibrium statistical ensembles of such networks and obtain their partition functions and main characteristics. We find simple dynamical construction procedures that produce equilibrium uncorrelated random graphs with an arbitrary degree distribution. In particular, we show that in equilib...

Non-extensive statistical mechanics and particle spectra in elementary interactions

We generalize Hagedorn’s statistical theory of momentum spectra of particles produced in high-energy collisions using Tsallis’ formalism of non-extensive statistical mechanics. Suitable non-extensive grand canonical partition functions are introduced for both fermions and bosons. Average occupation numbers and moments of transverse momenta are evaluated in an analytic way. We analyse the energy...

First-principles statistical mechanics approach to step decoration at surfaces

Using a first-principles parameterized lattice-gas Hamiltonian we study the adsorbate ordering behavior at atomic steps of a Pd(100) surface exposed to an oxygen environment. We identify a wide range of gas-phase conditions comprising near atmospheric pressures and elevated temperatures around 900 K, in which the step is decorated by a characteristic O zigzag arrangement. For catalytic processe...

Time-Dependent Statistical Mechanics 1C. The basic postulate of equilibrium statistical mechanics and elementary properties of time correlation functions