Of the many qualities great athletes share, ruthlessness is among the most apparent. When Rafael Nadal and Novak Djokovic advanced to the third round of the French Open on day four, almost in tandem on the two principal stages, they crushed their opponents with such familiar ease that it seemed a shame only one of them can reach the final.

If they do meet to decide who is strongest on the opposite side of the draw to Andy Murray, who plays Slovakia’s Martin Klizan on Thursday, it looks likely they will leave a trail of bruised spirits behind them.

While Djokovic was tidying up his one‑sided match against João Sousa in a little over two hours, Nadal was embarking on an even quicker defeat of Robin Haase, his 74th win at Roland Garros, his personal fiefdom where he has only lost twice.

Djokovic defeated Sousa 6-1, 6-4, 6-3 on Suzanne Lenglen and now has given his personal Portuguese punchbag just 24 games in four matches. On the tournament’s showpiece court, Philippe Chatrier, the Spaniard who the French love to cheer saw off the stubborn Haase in 1hr 49min, winning a high‑quality contest 6-1, 6-4, 6-3 – the same score as Djokovic. Those contenders now have two quick wins each, the perfect start to any big tournament.

Murray has not been quite so explosive. He dropped a set against the string bean Russian Andrey Kuznetsov on Tuesday, although he recovered in blinding style to win 6-4, 4-6, 6-2, 6-0. The world No1, who seems to have not a friend among the experts here, now has a tricky assignment in his second match, against Klizan, one of the Tour’s more difficult customers. In his first-round match, the Slovak got into a row with French wildcard Laurent Lokoli, who refused to shake his hand at the end – in part because he believed Klizan was feigning injury after giving up the fourth set to love and then storming back to win in five sets.

Does Murray think the feisty Klizan – who he beat in Vienna last year, the only time they have met – would “try it on” with him? “I don’t know him that well,” he said, “but tanking sets is not good for the fans or anyone watching. For his opponent it’s a positive thing because he is basically handing a set over.

“[Was he] faking injury? I’ve no idea. I saw in some of the videos he had his calf pretty heavily strapped, so I don’t know if that was something he went into the match with or not [Klizan pulled out of three tournaments leading into this one]. But he obviously did OK to last something like three hours and 39 minutes.”

Murray said staying focused – which he found problematic against Djokovic in the Australian Open final two years ago – was an acquired skill. “It can be tough but I’ve played well over 800 matches on the Tour so I’ve seen pretty much everything. There wouldn’t be too much that would surprise me or shock me when I’m out there now. If he’s tanking sets against me, I’m happy with that. Maybe he doesn’t.”

One of the great non-handshakes between Klizan and Lokoli 😂 #RG17 pic.twitter.com/nihRTAGjEF — Eurosport UK (@Eurosport_UK) May 30, 2017

He expects a tough match. “He’s an unorthodox player. He’ll go through patches in the match where he is playing some unbelievable stuff and then he drops off a little bit and plays some strange shots – which may appear like he’s not interested, but that is how he plays the game. That’s what has been successful for him.”

The Scot also revealed he had considered asking Andre Agassi, whom he idolised growing up, to be his coach after splitting with Ivan Lendl in 2014. “I spoke briefly to Dani [Vallverdu] about it after I stopped working with Ivan the first time. I chatted to [the coach] Darren Cahill about it. But I didn’t think he would be able to give enough time for what I needed.” Which begs the question: how long will Agassi stay with Djokovic? “I don’t know what their setup is. They obviously want to see how it goes and how they enjoy spending time together at first. But I certainly haven’t spoken to him about doing that.”

On Court 6, there was pathos and tears of joy for Steve Johnson, bathos and some world-class racket-smashing for Borna Coric. After 3hr 53min the battling American, whose father died recently, sobbed uncontrollably in celebration of a 6-2, 7-6, 3-6, 7-6 win that booked him a third-round match against Dominic Thiem, who earlier beat Simone Bolelli 7-5, 6-1, 6-3.

The volatile Coric, meanwhile, lost it when Johnson put the winning forehand down the line out of his reach, thrashing the ground with the same venom he had earlier applied to his ground strokes. He was aware of Johnson’s sadness but struggled to control his own emotions, storming from the small court in a rage.Petra Kvitova, who rode into Paris on a wave of emotion after six months out recovering from a knife attack at her home in the Czech Republic, lost in her second-round match against Bethanie Mattek‑Sands, the American winning 7-6, 7-6.

“The tie-breaks showed that I don’t have [enough] matches under my belt,” Kvitova said. “Otherwise, I feel good. I’m happy I’m here and playing. The atmosphere on Court 1 was incredible. The fairytale ended; now I think it will be business as usual. I still have the motivation.”

As the sun set on Roland Garros, the lights went out on Aljaz Bedene’s campaign after a rousing struggle against the Czech Jiri Vesely, who won 6-3, 6-3, 4-6, 6-3 in two hours and 52 minutes on Court 3. He then tackled the controversy about supposedly abandoning Great Britain to play in the Olympics for Slovenia. Bedene insisted he was committed to his fight with the International Tennis Federation to qualify for his adopted country in the Davis Cup, which is the door-opener for the Olympics.

“It looked like it was finished, that fight,” Bedene said. “So, when I said my dream was to play Olympic Games, I contacted Stephen Farrow [the lawyer who has handled his case for British qualification with the ITF on behalf of the Lawn Tennis Association]. When I read those things online [that he was prepared to turn his back on Great Britain], it was awkward. Until it looks like it’s done, it’s not done. I’ve been fighting for so long.”

On the possibility of playing Davis Cup for Slovenia, he said: “I haven’t considered that at all. My first priority is to keep fighting [to play for Great Britain] and see what happens.”