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> I find that slow walking is way more tiring than going fast.

The physics is probably something like: A leg is a pendulum, so its length determines the natural frequency, which corresponds to a gait requiring least energy. Move away from that frequency and you have to do work.

I agree, I especially notice it when forced to trudge up the stairs to exit the subway.

When the stairs are crowded the pace is set by the slowest person on the staircase.

On the rare occasions where I find the stairs empty, and I can run up, I find it less taxing.

In our family we call it the museum shuffle.

You need to get your legs swinging nicely to be efficient

Yes! I get extremely tired when I walk in a museum as I need to look at things. At the end of the day I am extremely exhausted but if I look at the "mileage" it is very low. I wonder if there's a more scientifically sound explanation for this phenomenon

It's sensory overload. Which is indeed physically exhausting.