Basic Statistical Mechanics: Temperature and entropy
, Ω, Ω , Ω, Ω EA A EB B
• Consider a system with total energy E consisting of 2 weakly interacting sub- systems A and B.
Weakly interacting = subsystems can exchange energy and E=E A+A B • The degeneracy Ω of E is astronomically large (10 23 ). These are the number of eigenstates Ω(E,V,N) of a system with energy E and N particles in a volume V.
Ω • For a given choice of E A, the number of degenerated states of the total Ω Ω system is A(E A). B(E B).
• It is convenient to have a measure of the degeneracy of the subsystems that is additive. [email protected] Atomic modeling of glass – LECTURE 4 MD BASICS-adds • It is convenient to have a measure of the degeneracy of the subsystems that is additive (log ! ).
Ω Ω Ω Ω (1) ln (E A,E B)=ln (E A,E-EA)=ln A (E A)+ln B (E-EA) • Subsystems A and B can exchange energy. Every energy state of the total system is equally likely.
Ω • The number of eigenstates A depends strongly on the value of E A. The most likely Ω value for E A is the one which maximizes ln (E A,E-EA), i.e. one has :