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lec13 - MIT OpenCourseWare http/ocw.mit.edu 8.044...

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MIT OpenCourseWare http://ocw.mit.edu 8.044 Statistical Physics I Spring 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .
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8.044 L13B1 1. The System Fixed: E V N M or H P or E E < energy < E+ << E A complete set of independent thermodynamic variables is fixed. Many micro-states satisfy the conditions.
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2. Probability Density All accessible microscopic states are equally probable. Classical p ( { p, q } ) = 1 / E < H ( { p, q } ) E +∆ = 0 elsewhere accessible { dp, dq } = Ω( E, V, N ) 8.044 L13B2
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Quantum p ( k ) = 1 / E < k |H| k E +∆ = 0 elsewhere (1) = Ω( E, V, N ) k, accessible 8.044 L13B3
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= Let X be a state of the system specified by a subset { p”,q” } of { p,q } p ( X ) = except { p ,q } p ( { p, q } ) { dp, dq } 1 except { p ,q } { dp, dq } Ω (consistent with X ) = volume consistent with X = total volume of accessible phase space 8.044 L13B4
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3. Quantities Related to Ω Φ( E, V, N ) H ( { p,q } ) <E { dp, dq } = cumulative volume in phase space Φ( E, V, N ) ω ( E, V, N ) ∂E = density of states as a function of energy Ω( E, V, N ) = ω ( E, V, N )∆ 8.044 L13B5
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