How small/compact can a pump or other mechanism be, that would allow compressing gas (or liquid) to pressures of excess of 10GPa, continuously?

Throughput may be minuscule, of order of milligrams per hour; even lower is acceptable. Also, for "size of the device" let us count all the necessary infrastructure: if it requires energy of a nuclear power plant to operate, it's not compact. Let's say we have some 30 watt of energy "for free"; anything above that goes out of our "compactness budget".

There's abundant heat sinking capacity, but any extra heating goes out of our "budget". Operating (ambient) temperature - choose anything between 40K and 400K as you like. It should have operational lifetime of at least a year, preferably ~10 years.

(clarifying: "continuous" - we can assume a small "buffer" container on the output side, emitting the pressurized gas at rate that is the average of the intake speed, so short "discontinuity" like piston motion is fully acceptable - simply keep the "buffer" above 10GPa with losses of order of assumed average input (1mg/hour, or less if required, but fairly constant).)