Available to watch online this week, the Starship Chicago film was made to help save the building that German-born, Chicago-based architect Jahn completed in 1984. The building is currently at risk of demolition, as the state department has put it up for sale.
During the 16-minute documentary, producer and director Eddy interviews Jahn and James R Thompson – the governor of Illinois who the building was named after – as well as architects, critics, political writers based in Chicago, and the president of Landmarks Illinois.
He hopes their responses will reinforce the architectural importance of the building to Chicago's heritage.
"I wanted to make an architecture documentary that is personable, funny, and overall human," Eddy told Dezeen. "It's very hard to translate the language of glass, steel and stone into genuine human emotion, but if you try hard enough you can do that."
The Thompson Center is revered as one of Chicago's best examples of the postmodern architecture style, which was developed in the late 1970s as an ideological reaction against the utopian ideals of modernism.
Governor James R Thompson selected Jahn's glassy, curved 17-storey building over "shoeboxes", as he was looking for a statement building to host the state government's Chicago headquarters. It measures nearly one million square feet (92,903 square metres), and is nicknamed The Spaceship after its futuristic shape.
"The building was an opportunity statement of representing government building and connecting it to the city," says Jahn in the documentary. "It wasn't just another office building. It shouldn't have been another office building."
"The fact is in terms of the art of architecture at that point, the building was ahead of its time," he adds.
To mimic historic state capital buildings in the US, Jahn added a dome to the top of his structure, but sliced it in half at an angle. When seen from above, the glass offers views into to a massive atrium, which is encircled by offices above a food court and a transit station entrance.
Other decorative features that have divided opinion are the building's blue and red exterior paneling, intended to evoke the colours of the American flag. "It was a special government building, the building should not have some neutral palette," Jahn said.
Although aiming to save the centre from demolition, Eddy's documentary picks up on a number of issues that have famously plagued the project. Initially, the large expanses of glazing resulted in overheating, so cooling towers had to be fitted, while other reports suggest that workers in the building use umbrellas to shade themselves from glare and the sun.
Repairs for the building were estimated at $100 million (£64.7 million) when governor Bruce Rauner announced plans to sell it at auction in 2015.
At the time, Jahn accused the state of deliberately letting the building fall into disrepair – a rhetoric that is also echoed by many in Eddy's film. The participants call for a range of alternative uses for the building, like remodelling it as a hotel or a shopping mall.
Despite a recent revival in interest in the style, the Thompson Center is the latest postmodern building threatened with demolition or significant changes.
Snøhetta's recently unveiled plans to replace the iconic granite base of the AT&T Building triggered outcry from several members of the profession – including Eddy, who organised the petition and protest against the project.
Starship Chicago premiered at the Architecture Film Festival Rotterdam last month. Its first US screening occurred at the one-day MAS Context: Analog Chicago event, which took place in the city on 21 October 2017.
The premiere of Eddy's Thompson Center film also comes as Chicago's recent bid for Amazon's second headquarters offers the online retailer its pick of 10 sites in the city. One includes the Thompson Centre, making its fate more threatened.
The film was released on MAS Context's website on 6 November 2017, and is available to watch until 12 November 2017.