Chapter 10 - Distribution of independent particles

Abstract

Constituents of independent systems can be distinguishable or indistinguishable particles. Maxwell–Boltzmann method is used to examine the number of microstates per macrostate in isolated system of distinguishable independent particles with no limitations on the number of particles per energy level. Attention is also paid to restrictions and constraints, relative population over the individual states, and mathematical modification required by degeneracy. Fermi-Dirac statistics are used to present the distribution of independent indistinguishable particles with a limit of one particle per energy state (fermions). However, the distribution of independent indistinguishable particles with no limit on the number of particles (bosons) per energy state are investigated according to Bose-Einstein statistics. In these studies, most probable particle distribution, Lagrange multipliers, equilibrium particle distribution of bosons or fermions, and when total number of particles is not conserved are explored. Then, we investigate the relationship between the reversible work and energy change while population remains constant, examine the correlation between entropy and the distribution of energy, justified the Boltzmann definition of entropy, and justify the relation between entropy and probability.