2. If you take advantage of sleep states, it is possible to reach single-digit uA but this is difficult. Even the leakage currents of your capacitors (0.1uA to 10uA, depending on chemistry and conditions) starts to overwhelm your microcontroller.
3. Case in point. Internal leakage of most batteries is in the 1uA to 100uA range.
4. Alkaline (AA, AAA, AAA, and 9V) and CR2032 batteries are very very low leakage.
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2 years might be on the easy side, especially if you use AA batteries. That way a 10uA leak isn't really that big a deal. This is aiming at a 150uA circuit or less which is fine.
With a bit of effort, it's not too hard to run a circuit for 5 years. But you do need to really watch the leakage currents and carefully design it. That's under 70uA with the AA batteries.
10years is probably pushing it even with an Alkaline or Lithium CR2032, but it's theoretically doable.
I didn’t read the datasheet but I imagine it has to have a lower power mode than that. Much larger MCUs can manage an average power consumption far lower and power off the same battery for periods measured in years, not days.
This is simple enough you’d think you’d be able to power it off an EM field directly!
In any case, Tomagachi is famously a 32kHz toy. There's a lot you can do at 32kHz.
I'm not sure what you'd do with that, but I think as power consumption drops to 0 on these sorts of thing it might make some remote sensing applications cheaper/easier to deploy, if you could just deploy it with a battery and forget about it for a year or two.