Do calculations require energy? A typical computer takes some energy "from the wall" while operating. I know that energy is spent on:


*

*Heating various components (psu/vrm/cpu/ram/ssd, so on)

*Fan/air motion to remove that heat (also vibrations, absorbed by case and surroundings)

*Magnetic emission from various chokes and long +5/+12v wires.


Let's consider that PC is disconnected from the network and has no attached devices and wires other than power cord. So that electric energy has no other ways out/wires to go. Then, all those waste-factors (mentioned above) are parasitic, in the sense that we want typically to avoid/lower them.
But the computer also does some meaningful process called calculation. For example, calculating a list of a prime numbers, or splitting very big number to prime factors - that is not an easy tasks - and that cannot just be done "instantly".
So the question is:  is there some other kind of "compute" energy (other than mentioned above)? Does the energy go somewhere else, other than mentioned above?
Or would I get exactly what we took out of the wall? (If we sum up heat + motion + emi waste, mentioned above).

I can even reword it: if we consider some theoretical recuperation device that would absorb every wasted watt of heat, emi and vibration from working PC (with 100% efficiency), and convert it back to electricity (also with 100% efficiency), would calculation run forever "for free"? Or is there some other energy leak spot?
 A: Computer do cause a decrease in the amount of usable energy, which is consistent with the second law of thermodynamics, but there is no violation of the first law; the total energy is constant, and can only be converted to other forms. There might be some energy stored as potential energy within the computer (for instance, the "1" state of a memory unit might hold more potential energy than the "0" state), but there is no energy destroyed by the computer.
A: Landauer's principle relates to the smallest theoretical amount of energy required for computation.
The principle asserts that the minimum energy required to erase one bit of information is:
$k T \ln 2$ 
where k is the Boltzmann constant (~1.38×10−23 J/K), T is the temperature of the environment, and ln 2 is the natural logarithm of 2 (~0.69315).
The derivation comes from the second law of thermodynamics and entropy.
From Wikipedia, the following paragraph illustrates how this compares with contemporary computers:

At 20 °C (room temperature, or 293.15 K), the Landauer limit
  represents an energy of approximately 0.0172 eV, or 2.75 zJ.
  Theoretically, room‑temperature computer memory operating at the
  Landauer limit could be changed at a rate of one billion bits per
  second with energy being converted to heat in the memory media at the
  rate of only 2.85 trillionths of a watt (that is, at a rate of only
  2.85 pJ/s). Modern computers use millions of times as much energy per second.

I suggest reading the whole article for more detail.
