The countdown has started. Manchester City now need just five wins from their remaining 10 games to secure a third Premier League title in seven years. If everything goes as serenely as it has done for most of the season, they could sew it up at Tottenham Hotspur on the night of Saturday 14 April. Circle it in your diary. It would be the coronation of a superbly slick and worthy champion team and the latest layer to Pep Guardiola’s managerial legend.

As for Arsenal, a more macabre countdown is in train. Arsène Wenger has pledged to fight into next season – the last on his managerial contract – but nobody believes he can stay beyond the summer. On this evidence, his players are the principal naysayers.

After the 3-0 humbling at City’s hands in Sunday’s Carabao Cup final, they needed a performance to restore a measure of pride. Instead they got another one of those 90 minutes when their fragility was exposed in glaring fashion.

Arsenal have not lost this heavily at home to City since they dropped the Woolwich from their name, but there was nothing surprising about the result. Their self-belief has come to feel non-existent and the manner in which they were picked off by City in the first half reflected the sense of drift.

Leroy Sané made the difference. The City winger helped set up goals for Bernardo Silva and David Silva before he scored the third himself and Arsenal were left to consider a 30-point chasm that has opened up between themselves and their opponents.

It was an occasion when the home support appeared to vote with their feet. The Emirates was half-empty and at kick-off time there was the feel of an early round cup replay. The biting cold was a factor but – on paper, at least – this was one of the showpiece fixtures of the season. The low attendance laid bare the supporter disenchantment.

Wenger’s team had actually started well. With Aaron Ramsey prominent, they hustled and probed. Ramsey cut back a cross that hit Vincent Kompany and forced Ederson into a smart save while Henrikh Mkhitaryan also worked the City goalkeeper.

But it took only one flicker from City to see them in front and, very quickly, Arsenal’s confidence disintegrated. “You go up by the stairs, you go down by the lift,” Wenger said of the difficulty in building belief and the ease with which it can slide.

Arsenal’s movement and spontaneity abandoned them, but not nearly as noticeably as their resolve at the back. It felt as though City would score with every forward thrust before the interval.

Sané was the catalyst. Showing his balance, control and acceleration, he left three Arsenal players for dead before working it wide right for Bernardo Silva. Sead Kolasinac decided to show the winger inside, on to his favoured left foot, and the finish was curled beautifully into the far corner.

Arsenal tried to look forwards and they had half-chances in the first half. But they were cut to shreds on the counterattack and, if it was easy to wince at the defending, it was also pertinent to scrutinise the lack of defensive midfield cover. Arsenal were grotesquely open.

That said, City’s cohesion and ruthlessness was really something. Sané was the architect of the second goal, dropping his shoulder to destroy Shkodran Mustafi before squaring for Sergio Agüero. He touched through for David Silva, who fired high inside Petr Cech’s near post. City’s third came with indecent haste. Agüero spun clear and they worked the ball with precision via Kevin De Bruyne and Kyle Walker to Sané, who had got in on Héctor Bellerín’s blindside. He finished almost apologetically.

Agüero ought to have added a fourth before the interval, only to be denied by Cech, and there were the inevitable boos from the home crowd at half-time. A small section of the Arsenal support chanted that their players were not fit to wear the shirt.

Arsenal even threw in a penalty miss early in the second-half – Ederson springing to his left to deny Pierre-Emerick Aubameyang, after Nicolás Otamendi had fouled Mkhitaryan – and it would have been worse for them had Cech not saved from Agüero on 78 minutes. The stadium was practically empty of Arsenal fans at full-time but those who did stay jeered the players as they left the field. It felt like the end for Wenger.