Let's assume that $X$ is a discrete random variable, which can take any value from the set $\{x_0,\dots,x_n\}$ with the probability mass function $P(X)$. We can calculate the entropy of $X$ as follows,
$\text{Ent}(X) = -\sum\limits_{i=1}^n {P(x_i) \log P(x_i)}$
In above we assumed that the random variable $X$ has a stationary distribution. Can we define entropy for a non-stationary random variable?