Does shrinking a semiconductor die necessarily mean that the power used will go down in a measurable way?

Question

If a manufacturer takes a mixed-signal IC and does a die shrink, does that mean that the power consumption will go down in a real or measurable way? For example, can the shrink by itself result in a 10% decrease in power consumption?

Answer 1

no, but usually when they do a die shrink, they also lower the voltage requirement (example: from 2.7v to 1.8v), which means less power.

Answer 2

Not necessarily so. The thermal management is very important in this case. However it is a known fact that the smaller the semiconductor the less power it requires and the less heat dissipation will evolve.