**Problem**

Given a C*-algebra $\mathcal{A}$.

Consider dynamics $\tau:\mathbb{R}\to\mathrm{Aut}(\mathcal{A})$ and $\tau':\mathbb{R}\to\mathrm{Aut}(\mathcal{A})$.  
*(More precisely, strongly continuous one-parameter groups.)*

Denote their derivations by $\delta:\mathcal{D}\to\mathcal{A}$ and $\delta':\mathcal{D}'\to\mathcal{A}$.

Then one has:
$$\delta=\delta'\implies\tau=\tau'$$
*(Here, equality is meant in terms of operators resp. maps.)*

How do I check this?

For dynamics over Hilbert spaces I would proceed by:
$$i\frac{\mathrm{d}}{\mathrm{d}t}\|\varphi(t)\|^2=\langle H\varphi(t),\varphi(t)\rangle-\langle\varphi(t),H\varphi(t)\rangle=0$$
But for the C*-algebra case this path is not directly available.

**Disclaimer**

I hope to get a hint from here.  
*(I haven't got any respond yet from stack exchange.)*