To be fair, I'm not 100% sure what you mean by entropy. My understanding of a universal commonality in Imperial decline through history is that by it's nature, Empires are in a constant state of pressures from within to separate, the pressure is maintained by a largely strong state, and it is when such a strong state weakens that the pressure breaks out. Empires by the very definition are single-state polity that has numerous ethno-cultural groups within it that have, often, different views of how to best govern themselves, and that puts pressure on the state to address the those grievances. When grievances become too large, and the state is unable to contain them, Imperial decline begins, often, rapidly.
Saying that, I think the US (and to an extent Canada) is a super unique element of Human History. Before the US, imperialism manifested itself as one particular power would come to dominate several regional ethnic groups – but maintain supremacy over those ethnic groups in their geographic areas. For example, the Roman Empire conquered the Greeks, the Egyptians, the Levantine kingdoms, Gauls, etc, but many of these ethnic groups already had long established their regional presence for centuries, and maintained that under the Roman Empire (largely, the expulsion of Jews from Judea, and renaming to Palestine was ethnic cleansing). This pattern is similar to many Empires throught the ages.
The US is unique, because instead of conquering groups of people and incorporating them into the Imperial order, the reality was that the US, as a nationality is composed of multi-ethnic groups, that were not conquered, but largely, immigrated to. The Americans with Italian ancestry, were not conquered by the US. The Americans with French or German ancestry were not conquered.
The fundamental diference between the EU and the US is that the EU is composed of numerous nation-states that have entirely unique and very entrenched ethno-cultures. A Frenchman is different than a Spaniard, and in turn is different than a German, or a Hungarian. Not only do they speak fundamentally different languages, they have entirely different cultural views. Someone from Poland to move to Spain would have a hard time adapting to the new country they are in, they would need to first learn the language, then they would need to get with the local cultural vibe, and nuances. Someone from Los Angeles can move to New York, Texas, Florida, Washington, or even Portland Oregon and already speak the same language, largely have similar cultural values and rules.
The biggest divide in America today is not ethno-cultural division, despite what we make it out to be. The biggest divide in America today is between the demographic changes of Metropolitan versus Non-Metropolitan areas. This is also the reality in many places such as the UK. And this is going to come to serious political head in the next several years.
I leave this.
By 2040 30% of the American people will be represented by 70% of the Senate. 70% of the American people will be represented by 30% of the Senate. If you think this a long ways off, keep in mind, 2001 was 20 years ago. We are coming up to the halfway point from the 9/11 to when this political crisis will occur.