Lecture 46 Statistical interpretation of entropy Microstates Dominance

Lecture 46 Statistical interpretation of entropy • Microstates • Dominance of certain macrostates • Boltzmann connection • Statistical meaning of Entropy

Statistical Interpretation of Entropy and the Second Law • The microstate of a system would be specified in giving the position and velocity of every particle (or molecule). • The macrostate of a system is specified by giving the macroscopic properties of the system-the temperature, pressure, number of moles, and so on. • In reality, we can know only the macrostate of a system. 2

三 正 Flipping coins 二 正 一 反 • A basic assumption behind the statistical approach is that each microstate is equally probable. • Some microstates are the same, we can not distinguish these states. • The distribution of microstates is not uniform. 一 正 二 反 三 反 3

Probabilities of Various Macrostates for 100 Coin Tosses 4

When there are more coins • 5

Free expansion • 6

The most probable state • 7

Boltzmann's entropy formula • 8

Deriving the Boltzmann formula • 9

Statistical interpretation of entropy • The entropy of a system is the logarithm of the total number of possible microstate, giving the total volume, temp, pressure, etc. 10

Gibbs Entropy Formula • 11

Entropy in information theory • 12