In The Long 20th Century, Giovanni Arrighi sets out an ambitious theory of the cyclical rise and decline of hegemony. Unfortunately, he provides relatively little quantitative evidence to back up his claims.
Energy consumption provides a window into these cycles. Energy consumption per capita is a good proxy for industrial development. If we plot the degree to which hegemonic powers exceed world energy consumption per capita, we get a good idea of their status.
When we do this for Britain, the US, Japan, and China, we do see cycles. Despite the attention paid to China, it's per capita consumption is still very small. Interesting, the US, UK, and Japan are now all in a free fall.
Also, the fact that US energy consumption exceeds UK consumption in the early 19th century should be treated with skepticism, as all data this far back are very rough estimates.