Gibb's Entropy

$S=-k_B\sum _s{p}_s\ln p_s\ge 0$

• Measures uncertainty of the system
• $p_i=P({\psi }_s)$, or is the probability of a microstate $s$
• By equiprobability postulate, $p_s=P({\psi }_s)=\frac{1}{\Omega }$, where $\Omega$ is the multiplicity function
  • Reduces to regular entropy under this condition
  • Uniform $P({\psi }_s)$ maximizes uncertainty and therefore Gibb’s entropy as well
• If we were 100% certain of the state being for example ${\psi }_1$, then $p_1=1$ while $p_s$ for $s\ne 1$ is 0, which would mean that $S=\dots \ln (1)=0$