There's no military conflict between China and Japan – nor, really, even a threat of so much as a minor skirmish. But there is a constant volley of harsh words, a chain of linguistic clashes that has, now, become a globe-trotting affair. Most recently, the two countries exchanged (un)pleasantries on Swiss stages at the World Economic Forum in Davos. And China has made clear that, come the Sochi Olympics, its leaders will have no contact with Japanese Prime Minister Shinzo Abe, after he visited Tokyo's controversial Yasukuni Shrine and rekindled animosity between the two countries.

Mr. Abe is unapologetic, and observers have suggested the rift is unlikely to close until he leaves office. That could be a few years yet.

There appears to be little cause for hope.

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But maybe there is. History suggests the times of sharpest dispute between the two countries tend to result in the most meaningful resolution. And Japan, both publicly and behind closed doors, is working hard to mend frayed relations, and quickly.

Indeed, among those most hopeful about improving ties are officials in Japan's own Ministry of Foreign Affairs. They stand at the front lines of the Asian "cold war" – and they suggest a breakthrough might be possible.

The reason? Some time in the fall (the date has not yet been set), China will play host to APEC meetings. Mr. Abe will "certainly visit Beijing" at the time, one official said in a background briefing with the Globe and Mail. "And there could be some bilateral [meeting] at that time."

That doesn't leave much time to sort things out, given China has quite publicly said it has no interest in high-level talks between the two countries. Earlier this month, China's Foreign Ministry spokeswoman Hua Chunying said: "He himself has closed the door of dialogue between China and Japan. The Chinese people don't welcome him." And it may be more a reflection of Japanese optimism than reality. But it's also a marching order from Mr. Abe himself, who on Tuesday in Tokyo reiterated: "I am actively seeking contact with China and South Korea."

For Japan's diplomatic workers, then, the mandate is clear: try to be soothing.

"We will try not to create any unexpected situations. No incidents. No conflicts," the official said. "We have this [APEC] diplomatic date in mind and we try to improve the relations by then."

Such an outcome seems, on the face of it, difficult to fathom – at least not without some significant statement from Mr. Abe to mollify China. And Mr. Abe has seen domestic gains from tweaking Beijing, not least in a bump in popularity polls.

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But there is precedent for the unexpected between the two nations. Friction may be long-standing, but so are attempts at resolution. Before a late 2012 flareup over East China Sea islands both countries claim, negotiators had nearly completed an agreement to formalize Sino-Japanese contact over military matters. The deal would have seen regular meetings between ministry of defence officials, a hotline between the People's Liberation Army and Japan's Self-Defense Forces, and a mechanism for those forces to communicate on water and in the air. That deal was abandoned when the government of Japan said it had signed a deal to buy the disputed islands, and no talks have since taken place. But the text still exists of what could form an important blueprint for agreement.

Students of the island dispute say there is reason to believe some sort of détente – even co-operation – is again possible. One is James Manicom, a research fellow at the Centre for International Governance Innovation in Waterloo. He has written a book on the subject: "Bridging Troubled Waters."

"A lot of people think I'm nuts because I'm actually optimistic about the China-Japan maritime relationship. Nobody believes me," he said at a recent speech in Tokyo. The long-standing marine territory dispute between the two countries is "a story about confrontation, it's a story about brinksmanship, but at the end of the day it's also a story about co-operation."

And, he says, the past 20 years have shown that "co-operation follows crisis." There's no denying that crisis has once again arrived.

Mr. Manicom's observations are instructive, too, for the broader relationship between Tokyo and Beijing – although any hope must be tempered by the reality that "co-operation" is very different from "agreement."

"The best that you can hope for is a very informal, very flimsy, very tacit effort at dispute avoidance," Mr. Manicom said. "That's not great, that's not the western model of preferring a formal institutionalized, robust settlement, perhaps. I just don't see that happening. But I am optimistic that China and Japan can avoid conflict."