What I mean by passivity of impulse response is that the energy of impulse response for this system is less than the input impulse signal energy.
For example, in a discrete-time system, considering the impulse response, the input is Kronecker delta function $δ[n]$, and the output is the impulse response $h[n]$. Suppose that $$ h[n]=\sqrt2/2 , n=1,2 $$ and $h[n]$ is 0 for any other components. In discrete-time system, We calculate the energy of the signal with $$ Energy = \sum_{n=-\infty}^{\infty} |h(n)|^2 $$ Therefore, the energy of the impulse response is 1, and the input signal energy($δ[n]$) is also 1, which means the system is passive for this input signal.
Then considering another input signal $δ[n] + δ[n-1]$, the energy of this input is 2. The output can be derived by convolution of impulse response and this input signal. We get: $$ y[n]=\sqrt2/2 , n=1,3 $$ $$ y[n]=\sqrt2 , n=2 $$ and $y[n]$ is 0 for any other components. The energy of this output is 3, larger than the input energy. Therefore, It seems that the passive impulse response doesn't necessarily make a system passive. But if a system is passive, the impulse response of the system should always be passive. Am I right with this conclusion? or can anyone give a rigorous proof for this?