Question

Integrals over the Fermi–Dirac and Bose–Einstein distributions define a “poly” form of this function. The replica trick takes advantage of the fact that this function of Z is equal to the limit as n approaches zero of “Z-to-the-n, minus one, all over n.” The expected value of the energy is equal to the negative partial derivative of this function of Z with respect to beta. The Helmholtz free energy is equal to kT times this function of the partition function. Stirling’s formula approximates this function of n-factorial. (10[1]-5[1])The negative sum over all states of “p times this function of p” defines the Shannon entropy, while Boltzmann’s definition of entropy is equal to k times this function of the number of microstates. For 10 points, name this function, the inverse of the exponential function. ■END■ (10[2])

ANSWER: natural logarithm [or natural log or ln; accept polylogarithm]
<Physics>
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PlayerTeamOpponentBuzz PositionValue
Roxanne Tang (UG)Ohio State AMichigan A8610
Leo Tao (UG)Michigan CMichigan B86-5
Emmett Bicknell (DII)CedarvilleKenyon13310
Dennis Yang (DII)Michigan BMichigan C13310