A lot of explanations on the internet say that the negative end of a battery has a relative abundance of electrons while the positive end relatively lacks electrons. Thus, when the two ends are connected, the electrons flow from the negative to the positive until there is a balance (zero voltage state).
If this were the case, then why can't you run a wire from the negative end of one battery to the positive end of a second battery and expect current to flow from the electron-plentiful negative terminal of battery 1 to the electron-deficient positive terminal of battery 2?
Take the water example. If you have a big jug of water suspended in the air connected to an empty jug down below, water will flow down and fill the bottom jug. There's no circuit. The water jug up top will simply empty its "charge" down into the water jug below. If you put a water wheel in the middle you would still get work. No apparent circuit needed.
If you rubbed yourself on carpet, electrons rub off the carpet molecules and get attached to you, making you negatively charged with a surplus of electrons. If you touch a metal doorknob electrons will jump from you to the doorknob, but there's no apparent circuit either between you and the doorknob, especially considering the doorknob itself terminates into the wood of the door. Yet there is still current without a complete circuit.
If an internal wire became dislodged inside of a metal case, and the metal case was connected to earth, current would flow from the mains down to literal dirt. But there's also no apparent circuit, just one end with a relative abundance of electrons and another end with a relative deficiency of electrons.
Work is produced when electrons flow, just as a water wheel turns when water molecules flow past the wheel, pushing it. So movement of particles, to me, is the only requirement for work. A complete circuit isn't required if all you want is movement - you just need something to move from A to B, no?