Problem 1: Short Answers (a) What is the Shannon entropy of a probability distribution that puts...

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Problem 1: Short Answers (a) What is the Shannon entropy of a probability distribution that puts 100% probability on a single microstate and 0% on all the others? (b) What is the Shannon entropy of a probability distribution that puts an equal proba- bility of 1/2 on some number of different microstates, and 0 on all the others? (c) Consider a two-level system with energy levels 0 and e (where e > 0). Which is bigger: the Shannon entropy of the canonical distribution at low T, or the Shannon entropy belles of the canonical distribution at high T? (d) Recall the Maxwell relation aT av = as V (1) And recall that for a system described by pressure and volume, work was -PdV, while for a magnet, it is BodM. Write the Maxwell relation for magnets that corresponds to Eq. (1). Problem 1: Short Answers as ybod oils out teed to wolf for or at 979d7 bus igiz rgia et ei ted TWT bas 80.V to arst ni Osterleyd (a) What is the Shannon entropy of a probability distribution that puts 100% probability on a single microstate and 0% on all the others? (b) What is the Shannon entropy of a probability distribution that puts an equal proba- bility of 1/2 on some number of different microstates, and 0 on all the others? E (c) Consider a two-level system with energy levels 0 and (where > 0). Which is bigger: the Shannon entropy of the canonical distribution at low T, or the Shannon entropy hells of the canonical distribution at high T? pl ei owi od (d) Recall the Maxwell relation sds.bios ai 10350 anoiisusul lauris OT dzrav IS as \v (1) 999 And recall that for a system described by pressure and volume, work was -PdV, while for a magnet, it is BodM. Write the Maxwell relation for magnets that corresponds 101s to Eq. (1). Problem 1: Short Answers (a) What is the Shannon entropy of a probability distribution that puts 100% probability on a single microstate and 0% on all the others? (b) What is the Shannon entropy of a probability distribution that puts an equal proba- bility of 1/2 on some number of different microstates, and 0 on all the others? (c) Consider a two-level system with energy levels 0 and e (where e > 0). Which is bigger: the Shannon entropy of the canonical distribution at low T, or the Shannon entropy belles of the canonical distribution at high T? (d) Recall the Maxwell relation aT av = as V (1) And recall that for a system described by pressure and volume, work was -PdV, while for a magnet, it is BodM. Write the Maxwell relation for magnets that corresponds to Eq. (1). Problem 1: Short Answers as ybod oils out teed to wolf for or at 979d7 bus igiz rgia et ei ted TWT bas 80.V to arst ni Osterleyd (a) What is the Shannon entropy of a probability distribution that puts 100% probability on a single microstate and 0% on all the others? (b) What is the Shannon entropy of a probability distribution that puts an equal proba- bility of 1/2 on some number of different microstates, and 0 on all the others? E (c) Consider a two-level system with energy levels 0 and (where > 0). Which is bigger: the Shannon entropy of the canonical distribution at low T, or the Shannon entropy hells of the canonical distribution at high T? pl ei owi od (d) Recall the Maxwell relation sds.bios ai 10350 anoiisusul lauris OT dzrav IS as \v (1) 999 And recall that for a system described by pressure and volume, work was -PdV, while for a magnet, it is BodM. Write the Maxwell relation for magnets that corresponds 101s to Eq. (1).