Some advanced textbooks define entropy by the formula S=−k∑sρ(S)ln⁡ρ(S). Where the sum runs over all microstates accessible to the system and P(s) is the probability of the system being in microstate s. (a) For an isolated system, P(s)=1x2.Ω for all accessible states s. Show that in this case the preceding formula reduces to our familiar definition of entropy. (b) For a system in thermal equilibrium with a reservoir at temperature T P(s)=e−E(s)x2.kTx2 Z. Show that in this case as well, the preceding formula agrees with what we already know about entropy.

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rogreenhoxa8 · Accepted Answer

a) S=kln⁡mho    b) S=ET−FT

Some advanced textbooks define entropy by the formula S=-k\sum_s \rho (S)\ln\rho (S).Where the sum runs over all microstates accessible to the system

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