What makes it hard to lower energy and power consumption for a computation: looking for serious but pedagogical reference

Question

I would like to get "general" culture about what limits engineers in reducing the power and energy consumption to compute.

Please correct me if I am wrong but for power, I know that there are two parts in electronics consumptions:

$$P=P_d+P_s, \text{ with }P_d \propto f$$

Where \$P_d\$ is the dynamic consumption; it scales proportionally with the frequency of transistor switching, \$f\$, (hence the computer's clock speed), and \$P_s\$ is the static consumption (it is a constant).

Conclusion 1: going faster increases power consumption because of the dynamic consumption.

About energy, I would naïvely expect that the faster the computation goes, the lower the energy it consumes because the static consumption will vanish for a fast computer (while the dynamic consumption would be a constant given the fact \$P_d \propto f\$). An implicit assumption here is that whenever my computation has finished, I turn it off the computer to save energy (see comments for why I say so). However it seems the answer is more subtle (see after Eq. (2) in this paper). It says:

We will dissipate more energy if we switch faster

Hence, I am very confused.

Basically, I am looking for a pedagogic reference to someone unfamiliar with the domain to understand the general challenge to reduce computation's consumption (in power and energy). The ideal would be a technical book that has a pedagogical introduction to the domain (so that an non expert like me could understand, the fact it is a technical book would reassure me on the scientific validity). I am also interested in pedagogic answers here (but I would really like having a nice reference).

[edit]: If the consumption can be reduced by making some parameter (for instance a voltage drop) closer to 0, then I want to know what forbids engineer to do so. My overall question is really to understand the practical issue engineer face if they want to drastically reduce the consumption.

Answer 1

Dynamic consumption is reduced by reducing the number of nodes that change state (linear), by reducing the capacitance of each node (linear), and especially by reducing the supply voltage (proportional to square of voltage). Capacitance tends to drop as device size drops.

For a given technology, doing a calculation quickly or slowly is not much different in terms of total energy per calculation.

However, because of the way device physics works, decreasing the supply voltage tends to increase quiescent power consumption because leakage is higher.

There are limits to how small devices can be made and how thin insulators can be, both technical and economic. Those limits have historically tended to trend in a fairly predictable manner (Gordon Moore's law). But, as they say, past performance does not guarantee future results,

Answer 2

To add to the existing answers, reliability is really the limiting factor; we seek to use the minimum amount of energy possible per bit or per bit wise operation, but will eventually have a bit energy so low that it’s near the noise floor of our equipment and so errors will occur more frequently. In most applications we prefer to spend more energy and get a reliable result and so the bit energy is well above the noise floor. In practice, changing the clock speed has little effect on power consumption since the static power consumption is much lower than the dynamic power.

Answer 3

Landauer's Principle sounds like what you're looking for. It's the thermodynamic minimum energy to erase one bit of information.

That's the information theoretic, ideal, minimum energy. When we run a practical computer, its actual implementation, in terms of bias currents, charging capacitive nodes etc, dissipates many, many orders of magnitude more energy than this, because our computational technology is still pretty stone-age.

We can try to optimise our computation for lower energy by reducing voltage swings, and the distances we send information to other cells (the capacitance we have to charge up), and by switching things off when there's nothing to do.