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Removing problems... for now
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_toc.yml

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- file: lecture_files/Lecture8A
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- file: lecture_files/Lecture8B
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- file: lecture_files/Lecture9A
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- caption: Statistical Mechanics Problem Sets
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chapters:
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- file: problems/ps_1/problem_set_1
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- file: problems/ps_2/problem_set_2
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- file: problems/ps_3/problem_set_3
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- file: problems/exam_1_practice
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- caption: Molecular Simulation
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chapters:
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- file: lecture_files/Lecture9B
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- file: lecture_files/Lecture14A
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- file: lecture_files/Lecture14B
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- file: lecture_files/Lecture15
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- caption: Molecular Simulation Project
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chapters:
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- file: problems/simulation_project
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- caption: Thermodynamics
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chapters:
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- file: lecture_files/Lecture16
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- file: lecture_files/Lecture24
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- file: lecture_files/Lecture25
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- file: lecture_files/Lecture26
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- caption: Thermodynamics Problem Sets
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chapters:
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- file: problems/ps_4/problem_set_4
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- file: problems/ps_5/problem_set_5
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- file: problems/ps_6/problem_set_6
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- file: problems/exam_2_practice
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- caption: Appendices
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chapters:
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- file: appendices/notation

lecture_files/Lecture9B.md

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compared by recalling the ergodic hypothesis, which states that the
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time-average value of a system property $Y$ over a sufficiently long
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timescale $\tau$ is equivalent to the ensemble-average value of that
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same property (from [Lecture 2](Lecture 2)):
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same property (from [Lecture 2](Lecture2)):
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$$\begin{aligned}
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\frac{1}{\tau} \int_0^{\tau} Y(t) dt &= \sum p_i Y_i

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