In their book, Mr. Howe and Mr. Strauss note the roughly 80-year intervals between catalytic events in American history like the Declaration of Independence (1776), the attack on Fort Sumter (1861) and the bombing of Pearl Harbor (1941). They predicted the next crisis would begin around 2005 and reach its climax sometime before 2025.

“History is seasonal, and winter is coming,” they warn.

Precipitating each fourth turning, the authors wrote, is a breakdown of the existing civic order and the institutions that prop it up.

Mr. Bannon, who has said the Trump administration will see to the “deconstruction of the administrative state,” believes these institutions are already crumbling, and he seems more than happy to pilot the wrecking ball that demolishes them entirely.

In an interview, Mr. Howe recalls getting an email about 10 years ago from Mr. Bannon, whom he had never heard of at the time, asking if he would participate in a film about the book. “We kind of blew him off,” Mr. Howe, who is now a demographer at the investment firm Hedgeye Risk Management, said recently.

Mr. Howe, who eventually agreed to be interviewed for the film, said that Mr. Bannon seemed to have no qualms about the destruction part of the cycle. “There is something beneficial about the creative destruction that comes with a fourth turning,” Mr. Howe said. “There has to be a period in which we tear down everything that is no longer functional.”

Mr. Bannon’s suspicion of powerful institutions and the men and women who run them might seem at odds with his personal conservatism. He is a Catholic, a former Navy officer and a traditionalist in many ways. But Peter Schweizer, an author and frequent collaborator with Mr. Bannon on films and books, said Mr. Bannon believes the nation’s elites arrogantly underestimate their own role in creating crises and then overestimate their ability to solve them.

“I do think the reason this theory is so powerful in Steve’s mind is it kind of goes to the heart of his problem with elites,” Mr. Schweizer said. “He does have a skeptical view of the limitations of human intellect. This notion that a few smart guys know how to quote unquote run a global economy is just laughable to him.”