Lecture 15 Lecture 15 ——The Canonical Ensemble The Canonical Ensemble Chapter 5, Chapter 5, Wednesday February 13Wednesday February 13thth•Exam 1 statistics•The Canonical Ensemble•The Boltzmann probability distribution•The partition function•Entropy and the canonical ensemble•The bridge to thermodynamics through ZReading: Reading: All of chapter 5 (pages 91 All of chapter 5 (pages 91 --123)123)I will assign homework on FridayI will assign homework on Friday0 204060801000246810Number of studentsScore (%)Exam 1 StatisticsExam 1 StatisticsMode &Median58.5%iiinSSN==∑()2iiinS SNσ−=∑σ≈ 20%The Canonical EnsembleThe Canonical EnsembleUUAAThermal reservoir attemperature TUUBBUUCCUUDDUUNN............System ASystem BSystem CSystem DSystem NUURRThe Canonical EnsembleThe Canonical EnsembleUUAA•The systems themselves (the ensemble) represent the thermal reservoir at temperature T.•The energies of the various quantum states may fluctuate, but they are all presumed to exist at the reservoir temperature T.UUBBUUCCUUDDUUNNSystem ASystem BSystem CSystem DSystem NThe Canonical EnsembleThe Canonical EnsembleSystem AM systemsThe bridge to thermodynamics through The bridge to thermodynamics through ZZ()exp / ;jjZEkT=−∑jsrepresent different
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