Based on the passage provided, what is the difference between Amdahl's law and the law of diminishing returns?

Context: Amdahl's law is often conflated with the law of diminishing returns, whereas only a special case of applying Amdahl's law demonstrates law of diminishing returns. If one picks optimally what is to be improved, then one will see monotonically decreasing improvements as one improves. If, however, one picks non-optimally, after improving a sub-optimal component and moving on to improve a more optimal component, one can see an increase in the return. Note that it is often rational to improve a system in an order that is "non-optimal" in this sense, given that some improvements are more difficult or require larger development time than others.

Amdahl's law does represent the law of diminishing returns if one is considering what sort of return one gets by adding more processors to a machine, if one is running a fixed-size computation that will use all available processors to their capacity. Each new processor added to the system will add less usable power than the previous one. Each time one doubles the number of processors the speedup ratio will diminish, as the total throughput heads toward the limit of 1/.

This analysis neglects other potential bottlenecks such as memory bandwidth and I/O bandwidth. If these resources do not scale with the number of processors, then merely adding processors provides even lower returns.

An implication of Amdahl's law is that to speed up real applications which have both serial and parallel portions, heterogeneous computing techniques are required. There are novel speedup and energy consumption models based on a more general representation of heterogeneity, referred to as the normal form heterogeneity, that support a wide range of heterogeneous many-core architectures. These modelling methods aim to predict system power efficiency and performance ranges, and facilitates research and development at the hardware and system software levels.

Answer: The law of diminishing returns represents a special case of the application of Amdahl's law. The passage provides an example of a scenario where Amdahl's law represents the law of diminishing returns. In this scenario one is running a fixed sized computation that will use all available processors to their capacity and is considering what sort of return can be achieved by adding more processors to a machine. Applying Amdahl's law tells us that each new processor added to the system will add less usable power than the previous. In other words, each new processor yields diminishing returns.