  Ovadia and Rodriguez-Hertz defined neutralized Bowen open ball as
$$B_n(x,e^{-n\epsilon})=\{y\in X: d(T^jx, T^jy)<e^{-n\epsilon}, \forall 0\leq
j\leq n-1\}.$$ We introduce the notion of neutralized Bowen topological entropy
of subsets by neutralized Bowen open ball, and establish variational principles
for neutralized Bowen topological entropy of compact subsets in terms of
neutralized Brin-Katok local entropy and neutralized Katok's entropy.
