Linearity and Passivity
the question is 'Does linearity imply passivity ?
No,in pure mathematical sense answer would be No.
Consider an input signal x(t) and a linear system whose output is Y(t)=-2x(t)
Now energy delivered by input = take limit from 0 to t and assuming initial condition zero then energy delivered by input  at time t  would be
E= ∫x(t)Y(t)= ∫x(t).(-2x(t))&lt;=0 for all t&gt;=0 and so it is not a passive system .
And hence linearity doesn't imply passivity.
Anyone interested in edits are welcome as I didn't use MATHML code