c
O
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The Boltzman Distribution (01:00 ............................................................................................................ 2
The Two Lagrangange Multiplier Conditions......................................................................................... 2
How many distinct configurations (10:00 ............................................................................................. 2
Approximation when N becomes large (24:00 ...................................................................................... 3
Maximize using Lagrange Multipliers (36:00......................................................................................... 3
Giving the Boltzmann distribution P(i)=e
-(1+ɲ)
e
-ɴEi
.................................................................................. 4
Set the Lagrange Multipliers (ɲ ɴ) to Satisfy Constraints ...................................................................... 4
Why is T = 1/ɴ ? Susskind note 2.3 ....................................................................................................... 4
(ɲ ) is The Partition Function
................................................................................... 5
(ɴ temperature) is a function of the average energy......................................................................... 5
Solving for the Lagrange Multipliers Susskind notes 2.1 ....................................................................... 5
The Two Basic Formulas (59:00 ................................................................................................................ 6
The Partition Function Z(ɴ)=ɇ e
-ɴEi
........................................................................................................ 6
Temperature ʹEnergy RelaƟonship E = эlog Z(ɴ)/эɴ .......................................................................... 6
Defintion of Helmholtz Free Energy ( A = -T log Z = -log Z / ɴ ) .................................................................. 6
Helmholtz Free Energy Susskind notes 2.2 ........................................................................................... 6
Relationship between Helmholtz Free Energy and Entropy .................................................................. 7
Entropy in terms of log Z (71:00 ........................................................................................................... 7
Brief Theory of Flucuations (72:00 ........................................................................................................... 8
Variance in Energy ............................................................................................................................... 8
The variance in energy is the 2
nd
derivative of logX wrt ɴ (84:00 ....................................................... 9
Fluctuations Susskind notes 3 .............................................................................................................. 9
Standard Definitions using Boltzman Constants (95:00 .......................................................................... 10
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