Manitunc, I'm not sure I understand what you are not understanding. Energy is proportional to power (factored by time). Power is proportional to voltage times current. As you undoubtedly realize, in a passive biamp configuration there is no connection between the mid/hi amp and the low frequency section of the speaker, and there is no connection between the low frequency amp and the mid/high frequency section of the speaker. As a result of the high impedance that is presented by each section of the speaker at frequencies that it is not intended to reproduce, there will be little or no current flow at those frequencies, hence little or no power will be generated or delivered at those frequencies, hence there will be little or no energy to be diverted, absorbed, dissipated, or consumed at those frequencies.
I would draw an analogy with turning on a light fixture via a switch on the wall. When the switch is in the off position it presents a high (essentially infinite) impedance to the AC that is supplied through the house wiring. Therefore the light fixture draws no current and consumes no power or energy. Similarly, the high impedance of the mid/hi crossover at low frequencies prevents any current, power, or energy from being drawn from the mid/hi amp in response to the low frequency content (i.e., the low frequency spectral components) of the output voltage of that amp. Similarly, the high impedance that the low frequency crossover has at high frequencies prevents any current, power, or energy from being drawn from the low frequency amp in response to the mid/high frequency content of the output voltage of that amp.
Think of the output voltage of each amp as being a summation of many different frequencies. The amount of current that is drawn from the amp at each of those frequencies depends on the impedance of the speaker at each of those frequencies.
Regards,
-- Al
