# Is there a link between entropy and the loss function of logistic regression?

entropy is a logarithmic measure of the number of states with significant probability of being occupied:

$${\displaystyle S (X)=-\sum _{i}p_{i}\log p_{i},}$$

consider the case where $$X \in \{0,1\}$$

$$P(X=1)=p, \quad P(X=0)=1-p, \quad where \quad 0\leq p \leq 1$$

then, the entropy is in this form(equation_1)

$$S = -plog(p) -(1-p)log(1-p)$$

the loss function of logistic regression is in the form (equation_2)

$$-ylog(\hat y) -(1-y)log(1-\hat y)$$

equation_1 look like equation_2, is there a link between them?