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Why does hot water shoot out of my reusable coffee cup when I invert it during cleaning?

This is a weaker form of the thermos-squirting effect. Sloshing the hot water (even gently) increases its surface area and therefore increases the evaporation rate into the air inside the cup. This ...
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Why inverse flow of separable Hamiltonian with even kinetic energy can be written like this?

The idea is to show that the "momentum-flipped" $\phi_N\varphi_t\phi_N$ obeys the correct differential equation to be $\varphi_t^{-1}$: The chain rule says $$ \partial_t( \phi_N\varphi_t\...
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