Let $A$ be an automorphism on tori $\mathbb{T}^d$. It is well known that the topological entropy $$ h(A)=\sum_{\lambda} \max\{0, \log|\lambda| \} $$ where $\lambda$ goes through all eigenvalue of $A$ with multiplicity.

Consider the case when $h(A)>0$. I would like to ask what are the lower bounds $$ \inf_{A\in SL(d,\mathbb{Z}),h(A)>0} h(A) $$ and $$ \inf_{A\in SL(d,\mathbb{Z}),h(A)>0, d\ge 2} h(A). $$ Thanks.