Summations and calculus gives me fits so please verify my results on these 2 issues:(adsbygoogle = window.adsbygoogle || []).push({});

1. Z = summation ( exp ( - B*E(s)) ) where the sum is over s

d/dB of ln(Z) = d/dB (ln (exp(-BEo) + exp(-BE1) + ... exp(-BEn))

= (exp(-BEo) + exp(-BE1) + ... exp(-BEn))^-1 +

(-E0*exp(-BEo) + -E1*exp(-BE1) + ... -En*exp(-BEn))

= summation ( E(s) * exp(-B*E(s)) / summation ( exp(-B*E(s))

which is also the average value of E when Prob(E(si)) = exp(-BE(si))

2. does d/dT of exp( -E/kT) = -E/k * exp(-E/kT) * -(1/T^2) =

E/k* 1/T^2 * exp(-E/kT) ?

If you're curious, these come up in Boltzmann statistics in thermal physics.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Derivatives of ln of summation

Loading...

Similar Threads for Derivatives summation |
---|

I CDF of summation of random variables |

I Derivation of the Cantor set |

**Physics Forums | Science Articles, Homework Help, Discussion**