Do power supplies have to heat up? Is there a fundamental reason why a power supply, say, from 120v AC to 12v DC, has to lose some power to heat dissipation? 
I am not asking why current engineering solutions do; I'm aware that rectifying capacitors act as resistors. The question is whether it's theoretically possible to create a device with, say, a 120v AC input and 12v DC output, or there is a physical (rather than engineering) obstruction to that.
EDIT: based on the comment that mere wires would make any device necessarily lossy, let me rephrase.
Is it theoretically possible to create a voltage converter with input/output voltage/power $V_{\text{in}},P_{\text{in}},V_{\text{out}},P_{\text{out}}$ with $P_{\text{out}}>(1-\epsilon)P_{\text{in}}$, where $\epsilon$ is arbitrarily small?
EDIT 2: Al Nejati's reference to Carnot's limit is perfect: this is exactly what I was asking about. A fundamental physical efficiency limit, not an engineering challenge.
 A: If what you're asking is: Is there some kind of efficiency limit to power conversion, like for example the Carnot limit for heat engines, the answer is: no, there is not. It is not forbidden by physics to have a 100% efficient electrical power conversion devices, and some large industrial transformers achieve 98% efficiency.
But even things like mere copper wires dissipate some power. Sure you could design a power supply based on, for example, superconductors, but you would need some energy to keep the superconductors cold.
In practice, the closer you try to get to 100% efficiency, the harder it becomes to increase efficiency, and systems turn out very bulky, expensive, and with lower power density.
The fundamental reason for all of this is that you are trying to push up against the limits of the 2nd law of thermodynamics. A 100% efficient power conversion device must not increase entropy and must therefore be a reversible process. Achieving true reversible processes on a macroscopic scale is not possible in practice because you must battle against not only internal entropy, but also environmental sources of entropy such as heat, which destroy your system's reversibility.
A: It is not just an issue of the inevitable presence of lossy wires connecting various parts or parasitic losses of semiconductor devices (diodes or transistors) in switching applications, there is also a fundamental problem in any rectification, namely, that it must also involve signal filtering. To achieve ideal rectification you need ideal filters, ones that not only are lossless but can also reject the undesired harmonic content completely, and of course there are no such filters. Any harmonic content not rejected is a loss of conversion efficiency. Note, too, that a switching rectifier may generate an infinity of harmonics so a few resonators even if made of ideal lossless components will not do the job.
A: Even we create such a device, there will always be loss of energy. And it depends if the loss of energy is in the form of heat or something else.
Moreover, 
Power= V×i(current) and
Heat disspiated=i$^2$RT
Since, heat is proportional to the square of current supplied, the device will eventually loose some heat.
