For definite states \$$i, j \in D\$$, define:

\$H_{i,j} = (\Gamma_{i}'(0))(j)\$

This is the instantaneous rate of change of the probability of being in state \$$j\$$, given that the chain began in state \$$i\$$.

Loosely speaking, it is the rate at which probability flows from definite state \$$i\$$ to definite state \$$j\$$.