I meet Jake Gyllenhaal in a makeshift production office in an industrial estate outside Boston, Massachusetts. He is bright-eyed and sitting in a bare corner room. He closes the door on his dog, a big Alsatian, which roams outside among a team of assistants staring at screens and eating lunch. He has been here for six weeks making Stronger, a film based on the life of Jeff Bauman, who lost his legs in the Boston Marathon bombing and then identified one of the killers, who he had stood next to in the crowd.

Gyllenhaal, who has a legendary work ethic, is both starring in and producing the film. He’s got to know Bauman well. “The irony is that, however terrible the situation was, it gave him a real meaning and purpose,” he says. “Jeff is quite a character. A hilarious person. The movie is very funny. It is a story of someone who had to learn how to become a father and an adult through an unbelievably difficult and horrific situation. It is a story of how to grow up.”

Having watched the last half-dozen films he has made back to back, I suggest to Gyllenhaal that he seems lately drawn to exploring the difficulties of such rites of passage; perhaps it’s the curse of his boyish looks. His latest release, Demolition, comes at the question obliquely. Davis, a cool, disaffected Wall Street banker, loses the wife he is not sure he loves suddenly, unexpectedly, and then tries to work out what to do next. To begin with, he feels not much at all. Then he starts to destroy everything about his hated former life, literally, with a sledgehammer and JCB. Directed by Jean-Marc Vallée (who made Dallas Buyers Club), Gyllenhaal offers a compulsive study of the unhinged strangeness of grief you don’t often see on screen.

“I think apathy is a feeling,” he says of the character. “I think that it is disrespected as a feeling. And I think this movie respects it. Not feeling, or not knowing how you feel, is a very large part of life.”

At various points in the film, Davis tries to summon up “appropriate” responses, watching himself weep in a mirror, trying to behave like they do in the movies, something Gyllenhaal is at pains to avoid.

“I think conventions override our lives all the time,” he says. “And then the universe delivers something unexpected, and convention no longer works. In movies, change tends to be some cathartic epiphany that happens in a moment with a swell of music. But this is a subtle change. From 10 to 10-and-a-quarter. You don’t see the flower bloom, but you wake up in the morning and it has.”

Gyllenhaal studied Buddhism at Columbia University – “the closest I could find to a course in abstract thinking,” he says with a smile – and from time to time as he talks you can hear traces of it. “I am a big proponent of continuous self-reflection,” he says, then pauses, reflects, smiles again. “I don’t mean to be too lofty.”

His interest in Buddhism, in openness to the present moment, informs his acting. “I start off by crossing out stage direction in a script,” he says, “anything that suggests in advance how you are supposed to be feeling or behaving. There is a scene in that Meryl Streep movie on a white water raft [The River Wild]. Her family is kidnapped and a guy pulls out a gun and her first response to seeing the gun is to laugh. And then she gets terrified. I love those microcosmic honest details.”

Gyllenhaal is a friendly, spirited presence. He doesn’t take things lightly but is never quite in earnest. When you ask about his life, he replies with answers about work – and though he is notoriously guarded, not all of this sounds like evasion.

He tends to divide his career – and his life – into a before and after. The shift happened about six years ago, just before he turned 30. After his early, edgy successes the cultish Donnie Darko and his Oscar-nominated performance alongside Heath Ledger in Brokeback Mountain, his career appeared to follow the Hollywood money. In 2010 he played the lead in the $200m Disney video-game adaptation Prince of Persia: The Sands of Time and the part of a Viagra salesman in the limp romcom Love and Other Drugs opposite Anne Hathaway (“dishonest nonsense”, according to the Guardian). Gyllenhaal wasn’t convinced that was all he was good for.

He took a breath. And then immersed himself in more challenging, less obvious films, beginning with the acclaimed low-budget drama End of Watch. To prepare, he spent five months working alongside real cops in the LAPD, on one occasion witnessing a murder during a drugs bust. After a life flirting with make-believe, the reality got to him, he says. In some ways, he has never looked back.

The change coincided with other shifts in his life. “A lot of things were redefining themselves. Not all of them good.” There was the death of his friend Heath Ledger. His parents, both film- makers, separated, leaving him and his actor sister Maggie, though long left home, “trying to figure out a way of the family still being together. People were moving and changing. I moved from Los Angeles to New York City.” The world of film seemed “more than usually absurd”. He made a pact with himself: to make it more meaningful. He wanted to find exactly what he was capable of.

The string of films he has made since have tested those limits. For Everest Gyllenhaal filmed in the Alps, Iceland and Everest base camp for three months (“It was worse for the crew – the actors talked about getting frostbite; the crew actually had it”). For recent boxing epic Southpaw he spent half a year in a professional gym. In Nightcrawler, a brilliantly unsettling film about an ambulance-chasing TV journalist, Gyllenhaal became feral-eyed, scarily thin. He suggests the shape-shifting, his literal body of work, is instinctive and necessary.

“When I started to learn the dialogue for Nightcrawler, the words and the punctuation were so particular that my body started to respond to it in a certain way,” he says. “I had this animal idea, like a coyote. I grew up in Southern California, and at night you could hear them howling sometimes as they tore apart an innocent animal, so I thought it should be like that. Coyotes always look sickly and have crazy eyes and wander round in the shadows. I could see that worked as a concept, and so I shaped myself to that idea.”

Gyllenhaal grew up in a Hollywood family: his father, Stephen, is a director; his mother, Naomi Foner, an Oscar-nominated screenwriter. Paul Newman and Jamie Lee Curtis were godparents. Donnie Darko, he suggests, was “a pretty accurate representation of my experience of adolescence”. It’s tempting to suggest that his masochistic dedication is a response to a perception that his entry into the business was gilded. Is it?

“Maybe,” he says. “I am certainly aware in interviews that it is brought up. ‘Gilded’ is a particular word for you to use. I am aware of how it looks.”

But he believes his particular ethic is more an ingrained part of his character than a reaction to perceptions of his background. “It’s part of my ancestry, I think, somewhere. My grandfather on my mother’s side was second-generation Jewish American. His father was a tailor from Poland, and he became a surgeon. He was the pride of his family. My father is from a long line of hard-working Swedes. Both were men who got up at 4.30 in the morning to start work. Pushing yourself both physically and mentally has always been a part of my life. From an early age, my dad would wake me up early to go for a run.”

Although gossip columns have tried hard over the years to link Gyllenhaal with possible partners – Taylor Swift, Reese Witherspoon, his Southpaw co-star Rachel McAdams – he suggests that all the hard work has come at the expense of any long-term romance. In interviews Gyllenhaal has routinely said, in a vague manner, that he has been in love two or three times. I wonder, at one point, if he has always lived on his own as an adult.

“You mean, like, roommates?” he says, innocently.

No, relationships.

“Have I always?” He pauses for a moment, as if to try to remember. “No, I have lived with girlfriends sometimes. My house is always open to all my friends.”

There is another short pause that says he has nothing more to say on the subject. I wonder what he would like to do in the next six years.

He talks about doing more theatre – he has starred in two plays by the young British writer Nick Payne. He has inevitable ambitions to direct: “I would like to be watching people more talented than me play a scene and not have to sully it with my own lack of talent,” he says, not entirely modestly.

And what about beyond work?

“My dad, the Swede, said something beautiful the other day,” he says. “He said: ‘Jake, you’ve got to remember to have fun, too’. I had to go: ‘Oh? So it’s OK now? I’ve done enough?’ And he was like: ‘Yeah, why not turn that switch on?’” He laughs. And then he’s restless to get back to work on his movie.

Demolition is out on 29 April