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Let's not complicate things. My system is a Mixmaster and a bowl of
cake batter. It has two terminals. Mixmasters can be run perfectly
well off DC mains because they have universal (AC/DC) motors, as
anyone watching an old TV next to a running Mixmaster will readily
perceive. Let's say I run my Mixmaster on DC. My system dissipates
energy, it has an IV characteristic, and the power dissipated P = IV.
I can define R for this system by your causal relation: R = P/I^2.
Like the light bulb however, this relation will yield a variable
resistance. Unlike the light bulb, electrical resistivity plays no
important part in dissipating energy in this system.