I'll respond to these last few points, and then step out of this thread. I don't know what backgrounds everyone else is coming from and have tried to do a good job of explaining things. I can't prove via the internet what my background is and what I do for a living, but I know what I'm talking about when it comes to primary cells.
I'm sure we have had this debate before at some length, but I do not agree with the statement above. The same number of electrons can pass through a resistor, yet the resistor doesn't get discharged at all. There are various electrochemical pathways through a cell and not all the current passing through has to pass via the expected discharge reaction. Under varying conditions of temperature and imposed electrical gradient other pathways for the charge carriers are possible that do not involve the same degree of discharge.
One atom of lithium gives up one electron. That is the "electrochemical pathway" in this type of cell, ie. the half-cell reaction that occurs.
When I have the time and patience I will do a quantitative experiment to measure this. If I find I cannot measure it with a meter I will admit I am wrong.
I wish you all the best in your endeavor. I hope you have a meter that measures electron flow, as voltage of cells will not give you an accurate measurement of their depth of discharge, nor will it allow you to infer their remaining capacity.
I admit I am in over my head here but lets suppose that instead of a coil of wire in this series circuit, we have four LED dice also in series. Now the same number of electrons, 3n, may flow through all four die in this circuit but that doesn't mean that the power provided by these electrons will be shared equally! By the same logic (could be erorr), I can imagine the three batteries not providing equal amounts of work, power, watts to this system either. You have three people all pushing the same car and they are all moving at the same speed as the car but you have no idea how much power each is providing nor if all three will be able to continue at the contribution of effort they presently are.
Your car analogy would be more akin to 3 cells in parallel, and in that case a different amount of current could flow through each cell.
Cells in series can contribute different amounts of power, and therefore work, to the total, because P=VI, and the voltage (V) of individual cells can vary. However, since current (I) through each cell in series is the same, they each undergo the same number of redox reactions and therefore use up the same amount of active materials. Remaining capacity is determined based on starting capacity and the amount of material that has already reacted.
The cells may be matched at the start or they may not be. Even if they are matched at the start, they won't stay matched if one is operating under ideal thermal conditions and another isn't. I see no justification that a series circuit restricts components to equal amounts of energy being provided? It has a nice symmetry to it but that doesn't make it so, does it?
Since Power=Volts*Amps, and Energy=Power*Time, matched cells could supply different amounts of power and energy when run in series, but this would be be dependent on different voltages of the cells. The total capacity used up in each of them would be the same, however.
I also believe this is not accurate. Despite my being 100% certain that there are different residual voltages of primaries inserted from same batch/box at the same time because I have measured them numerous time with my Fluke 189 DMM, and it repeats in the same pattern time after time.
The OCV of a discharged CR123A cell can not give you a meaningful idea of its remaining capacity. Depth of discharge in a primary cell depends solely on how much active material has reacted, and how much the capacity was at the start.
It ignores the difference in electical conductance pathways within individual cells related to the cumulative and changing internal resistances, and heat influences relative to cell position on a stack of serial cells.
I think you're saying that my statement of equal electron flow through cells in series "ignores the difference in electical conductance pathways" etc? The way cells in series work is that the same number of electrons go through each of them. That's all there is to it. You can have a low voltage cell in the middle, or the top, or the bottom of a stack, and it'll have the same number of electrons going through it as every other cell in the stack.
If anyone would like to discuss these points further, feel free to send me a PM.