A forgotten cup of coffee will gradually cool down as its heat flows into the cooler surrounding air, but in the quantum realm, it appears this experience can be turned on its head. As a result, we may need to update the second law of thermodynamics, a fundamental principle of physics that states heat energy always flows from hot to cold.
Dawei Lu at the Southern University of Science and Technology in China and his colleagues have seemingly broken this law with a molecule of crotonic acid, which contains atoms of carbon, hydrogen and oxygen. The researchers used the nuclei of four of its carbon atoms as qubits, which are the basic building blocks of quantum computers and can store quantum information. When used in computation, researchers normally control the quantum states of the qubits with bursts of electromagnetic radiation, but in this case, the team leveraged this control to make heat flow from a colder, lower-temperature qubit towards a hotter one instead.
This would never spontaneously happen to something in our macroscopic world, like a cup of coffee, as it would require extra energy to fuel the backwards flow. But in the quantum setting, other forms of fuel are available – in this case, a form of quantum information called “coherence”. “By injecting and controlling this quantum information, we can reverse the direction of heat flow,” says Lu. “We were excited.”
The fact that the laws of thermodynamics break down in the quantum realm is perhaps unsurprising, as they were laid down in the 19th century, about 100 years before the formalisation of quantum physics. To fix this issue, Lu and his colleagues calculated each qubit’s “apparent temperature,” which is a modification of conventional temperature that accounts for some of an object’s quantum properties, like coherence, and saw the second law of thermodynamics become satisfied again and heat flow from a higher apparent temperature to a lower one.
Roberto Serra at the Federal University of ABC in Brazil says that quantum properties like coherence can be considered a type of thermodynamic resource analogous to how, for example, heat is a resource that is used to make a steam engine work. He says that when these quantum, microscopic resources are manipulated, thermodynamics laws can be apparently broken. “But the usual laws of thermodynamics were developed thinking that we do not have access to these microscopic states. This is just an apparent violation because we have to write new laws considering that we have this access,” says Serra.
The researchers now want to turn their heat-reversal experiment into a more practical protocol for controlling heat among qubits, says Lu. Beyond uncovering fundamental connections between quantum information and heat, finding new practical ways to cool qubits could improve quantum computers. This could be of great importance for the burgeoning quantum computing industry as, ultimately, even conventional computers can only work as well as they can avoid heating up, says Serra. %!s()
I’ve been in love with France ever since my first trip to Bordeaux in 2010. Friends I had met back in Thailand showed me around the area and introduced me to French culture. It was my first time in France and I loved the food, the wine, and the people.
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But that love became an obsession when, after Bordeaux, I stepped out of the Paris metro and onto the Champs Élysées. The lights, the energy, the mystique! There was magic in the air. I felt like I had known the city my entire life and I was simply returning home.
Since then, Paris has had a firm grip on my heart. Over the years, I spent countless visits exploring France and Paris in particular. I’ve run tours in the city and I spent a few months living there in 2019.
Last August, after yet another sojourn, I thought to myself, “What if I moved back?”
I was growing a bit tired of the NYC dating scene, the rising cost of living, and felt like creatively, I was in a rut. With AI coming for creators like me and the industry changing, I was a little lost on what, career wise, would come next.
In short, I needed a change.
And Paris seemed like the best place to go.
It’s cheaper than NYC, I had friends there already, I’ve always wanted to learn French, it would make a great base for exploring Europe, and I could start writing my next book there. There’s nothing like a change in scenery to get the creativity flowing!
But the question remained: how do you move to France?
After all, they don’t have a digital nomad visa, and you’re limited to three months if you visit on your regular Schengen tourist visa.
Well, it turns out that it’s not actually that hard. (And while I can only speak for Americans, I suspect the criteria are similar for Canadians, Aussies, Kiwis, and other “developed” nations.)
If you want to move to France, you have four main options:
Student visa
Long-term visitor visa
Entrepreneur
Talent visa
The student visa is pretty straightforward. You need to enroll in a full-time university program and show you have enough funds to support yourself (around 600 Euros per month). A friend is currently there on this visa, as she is doing a nine-month intensive French program to become fluent. You still have to apply for the visa, but if you’re enrolled in an accredited school, you’ll likely get approved. Another benefit to this visa is that you can work part-time on it!
But this visa is contingent on being in school, so if you leave or quit, it’s voided. However, when you are done, you can change this to a “job seekers” visa, which can give you up to another six months in France (or more depending on how long your program was).
I thought about applying for the entrepreneur visa, but the application process is pretty complex and can take months to be approved. You have to set up your business in France — and that is a lot of paperwork. You have to show that your business makes money, has clients (at least one of them being French), and can support you full time (you have to make at least the French minimum wage). They will scrutinize your assets and financials a lot and you’ll need to register your business in France and pay French taxes.
Additionally, France offers a talent visa. If you’re an expert in your field (with verifiable accreditations and accolades), this could be a good visa to apply for, especially if you plan to stay in France for a long time and want to physically work there. But, again, you’ll need to have some source of income and plan to do physical business in the France. If you’re not an academic but someone in the arts, you have to show how you are going to add to the “culture of France” in some way.
While I would meet the requirements for both those visas, the process for either would have been time consuming, and, since I’m not sure France is going to be my forever home, I decided not to go through that process.
So I went with the long-term visitor visa, officially called VLS-TS visiteur. This allows me to stay up to 12 months in France and is renewable in the country. It does come with a lot of restrictions, however: I can’t physically work here and I am not allowed into the French social welfare system.
It’s also the visa a lot of Americans (and most retirees) are coming in on. If you have passive income or retirement savings and just want to live in France, this is a good option for you. It allows you to set up a bank account and it can be renewed pretty much indefinitely.
The paperwork for this visa (which I’ll get into in a bit) essentially comes down to whether or not you can support yourself. French authorities want to make sure you won’t be a burden on the system.
My biggest question centered around whether or not I could “work” on this visa. A lot creators and digital nomads are applying for — and getting — this visa.
But remember: you aren’t allowed to work on this visa so how are you going to work if you can’t work?
So let me take a moment to talk about “work” from a legal standpoint.
As I mentioned, there’s no digital nomad visa that allows you to work in France. And the French tax office said last July that remote work is considered taxable — but there are no official laws that. That’s just their opinion and there’s been no progress in codifying that opinion. In fact, my visa doesn’t even come with a tax number, so it’s impossible for me to be taxed. I couldn’t pay taxes even if I wanted to.
The visa office asks how you’ll support yourself when you are in France and one of the sources of income they accept is “income from work.” I was very open that my means of support would be the income from this blog and my books.
The system there really hasn’t caught up to remote work. It still defines “work” as something you do physically that could take away a job from a French person.
So could I run walking tours in Paris? Nope. Could you work at a café? Nope.
But does writing this blog post count as work? After all, no one is paying for it. It’s a free resource. Does going to a café to work on the next great American novel count? What about my weekly newsletter that has affiliate links (that generate income) in it? Is writing that considered work?
The gray area is considerable, so the best thing to do is to talk to a lawyer. I recommend Daniel Tostado (yes, that’s his real name), one of the biggest American-French immigration lawyers in Paris. He has a huge law firm and regularly meets with government officials to clarify the rules on this. He gave me some solid advice.
For this long-term visitor visa, the application process is pretty easy. You go to the French government website, fill out your application, take the application number to the TLScontact website, and make an appointment. (France outsources the appointment process to this company, which then sends everything to the French consulate for approval.)
The main things you’ll want to demonstrate are that you have accommodation for 90 days on your application and enough income to support yourself. They just want to make sure you aren’t going to be a burden on the system. I went overboard. Here’s what I brought to my appointment:
The application (you need to bring a printout)
A confirmation of the appointment
Extra passport photos
Proof of accommodation (this can be Airbnbs, hotels, or someone’s home — if it’s the latter, make sure that they are the owner!)
A letter attesting I won’t work
A financial summary letter explaining why I am moving there and my source of income
Health insurance that meets French legal requirements (I used Mondassur.)
Three months of bank statements showing regular deposits
A second bank account, my tax returns, and my W-2
I didn’t need the second bank account, tax returns, or W-2 (they weren’t required) but the woman at the appointment said the more proof you had the better and it wouldn’t hurt. And another friend who got this visa didn’t bring beyond what was asked in the application form. But I wanted to take no chances!
At the appointment, the staff double-checks your paperwork, takes your biometric data, collects the fees, and then sends your passport to the embassy for processing. Officially, it takes up to 15 days to process your visa, but everyone I know seems to get it back within a week.
The worst part was not knowing if you are approved until your passport is returned. While you can track the progress of your application, you don’t know the verdict until your passport is back in your hands. While I was waiting (and anxiously spiraling), I looked on Reddit and found that most denials were for lack of income or issues with their accommodation, which seem to be the two most important things to have perfect on your application.
Once you get your visa back, you can enter France any time after the start date. After you enter, you have 90 days to register your visa with the state (they give you a little QR code with instructions). This allows you to “officially” be on this long-term visa. (It’s a more paperwork kind of thing.)
Once that is done, there’s nothing else to do and you can stay in France (and Europe) until your visa expires!
So, if you’re considering moving to France, these are your options. But, as always, I’m not a lawyer and this is not legal advance. In regard to work and other issues or questions, it’s important that you seek legal counsel and get their expert opinion!
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Why is there talk about a Pakistan spinner's action?
ByMatthew Henry
BBC Sport journalist in Kolkata
Amid the usual hullabaloo, there was one player who was mentioned more than the rest at the press conference before the highly anticipated match between India and Pakistan at the T20 World Cup.
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That player is Usman Tariq, the Pakistan spinner.
He might have only played four international matches but, right now, his bowling action is the most discussed anywhere in the world.
"He doesn't care about these things," said Pakistan captain Salman Agha.
"Since the time he has started cricket, these talks are going on about him.
"He doesn't care about these things."
So what is the history, what are the rules and what has been said about him?
Get in touch
Send us your questions
Who is Usman Tariq and why has his bowling action been controversial?
Image source, Getty Images
Image caption,
Tariq has taken 11 wickets in four T20s, including 3-27 against the United States at this World Cup
Tariq is a 28-year-old off-spinner from Pakistan. He has played just two first-class matches, instead concentrating on T20s.
After an initial season in the Pakistan Super League in 2023-24, he has become more prominent over the past year with a successful PSL and Caribbean Premier League in 2025, plus two matches in this winter's ILT20 in the United Arab Emirates.
But it is Tariq's bowling action that has made him so discussed.
He trots to the crease and pauses in his delivery stride, also coming to a complete stop, before slinging the ball down with a low-armed action.
During the warm-up series between Australia and Pakistan before this World Cup, Australia batter Cameron Green mimicked a side-arm throwing action after being dismissed by Tariq. He later apologised.
During the ILT20, England batter Tom Banton also appeared to suggest to the umpire that Tariq was throwing.
Tariq's action has twice been reported by on-field umpires during the Pakistan Super League, in 2024 and again in 2025, but he was cleared on both occasions.
What are the laws?
The regulations around whether a bowler is 'throwing' are simple.
Bowlers are not allowed to straighten their arm by more than 15 degrees from the time the arm reaches the shoulder in the bowling action.
"An illegal bowling action is a bowling action where the player's elbow extension exceeds 15 degrees between their arm reaching the horizontal and the ball being released," the International Cricket Council's playing conditions say.
Bowlers with suspected actions are first reported by the on-field umpires or match referee and then must undergo testing at an ICC-approved testing centre.
Tariq's action was cleared at the centre in Lahore, Pakistan.
The laws and regulations around Tariq's pause are less clearcut, with the issue falling under the "unfair play" section of the laws and playing conditions – rather than being explicitly defined by a law.
The on-field umpires can interpret the unfair play law, possibly using Law 41.5 which covers the "deliberate distraction or deception of batter" or the more broader laws around unfair play, to ensure the match goes ahead fairly.
"If the pause is obviously longer or shorter, or if he bowls without a pause, that will be considered deception" was one interpretation offered by former ICC umpire Anil Chaudhary this week.
"Everything seems OK up to now. I am not seeing anything wrong."
The issue came up in 2014 when former India spinner Ravichandran Ashwin paused in his delivery stride, resulting in a tightening of how umpires interpreted these laws.
The umpires are left to judge whether the length of a pause in a bowler's action is fair or unfair.
Image source, Getty Images
Image caption,
Tariq took 2-16 in his one match against Australia earlier this year
What has been said?
Tariq has said any flex in his action comes because he has "two elbows" in the joint.
Pakistan captain Salman said the spinner is his "trump card".
"He has been bowling very well for the past few months," Salman said.
"And he has also bowled very well in the league cricket he was playing before playing for Pakistan.
"You can say that he is a trump card for us."
India captain Suryakumar Yadav was seen mimicking Tariq's action in the nets before the encounter and backed his batters to succeed.
"He is a different character when he comes to bowl, but at the same time we cannot just surrender to him," Suryakumar said.
"We practise with similar type of bowlers and similar actions and we will try to execute what we are practising in net sessions."
This article is the latest from BBC Sport's Ask Me Anything team. %!s()
<p>Use BBC.com or the new BBC App to listen to BBC podcasts, Radio 4 and the World Service outside the UK.</p><p><a href="https://www.bbc.com/future/article/20250207-bbc-podcasts-are-now-available-on-the-bbc-website-and-app">Find out how to listen to other BBC stations</a></p><h2>Episode details</h2><img src="https://ichef.bbci.co.uk/images/ic/400x400/p0mtrstx.jpg" alt="" loading="lazy" /><p>Radio 5 Live,·04 Feb 2026,·30 mins</p><p>Available for over a year</p><p>We open Episode Five checking in at the airport with Haas driver Ollie Bearman as he prepares to take off for the final three races of the 2025 Formula 1 World Championship. But there’s only one thing on his mind - will he get the dreaded middle seat?
Fellow rookie Kimi Antonelli is also flying high as Formula 1 touches down for the Las Vegas Grand Prix. The Mercedes teenager takes a gamble on tyre strategy but will it pay off when the cars hit The Strip? Antonelli and his race engineer Pete Bonnington are looking back on the teenager’s rookie season in 2025. Bonnington, aka Bono, was one half of F1’s most successful driver-engineer pairing with seven-time World Champion Sir Lewis Hamilton, so how does it compare working with a rookie making his first steps into F1?
While the competition is nearly over on track, the race inside the team’s top-secret F1 factories has only just begun. It’s early December, and all the teams are pushing
hard to build a completely reimagined car for F1’s new era, when a new set of technical regulations are set to shake up the sport. At Mercedes, our F1 experts Sarah Holt and Holly Samos are given a guided tour by Chief Operating Officer Rob Thomas on the factory’s busiest day of the year.
As the sport prepares to move forwards into its new era, the dust is settling on the 2025 season at the finale in Abu Dhabi. There’s time for Bearman and his race engineer Ronan O’Hara to also give their verdict on his rookie season and formulate lessons to take into the British racer’s 2026 campaign. But the clock is ticking on Cadillac’s F1 debut… There are now less than 100 days to go until the US team joins the grid and team principal Graeme Lowdon is beginning to feel the pressure.
F1: Back at Base is an IMG Production for the BBC, hosted by Rosamund Pike.
Co-hosts & Executive Producers are Sarah Holt and Holly Samos.
Tottenham's decision to sack Thomas Frank was made almost immediately after Tuesday night's loss to Newcastle.
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Chief executive Vinai Venkatesham, in conjunction with sporting director Johan Lange, made the call - one the club had been reluctant to make.
But the sorry state of Tottenham's season meant not even Frank's biggest advocate could disagree with the decision.
Early on Wednesday morning, Venkatesham made the recommendation to the Lewis family - the club's ownership - to dispense with Frank.
In recent weeks a furious fanbase have directed their ire towards the Lewises amid a widely held belief that supporters' views about Frank were not being listened to.
According to conversations with those closely connected with the ownership, that was not the case - and the Lewis family were attuned to the widespread discontent from Spurs fans.
Of course, it would have been harder not to notice given the ferocity of ill feeling towards the Dane in recent weeks.
But given they effectively handed the running of the club to Venkatesham when appointing him chief executive last summer, it is fair to say the ownership have not sought to intervene - feeling a decision should be made 'on the ground'.
So, when the recommendation from Venkatesham to terminate Frank's employment arrived in the hours after the loss to Newcastle it was accepted immediately by the ownership board, who formally approved the decision.
All that was left was for Frank to be officially informed of his departure - a formality that took place on Wednesday morning in a meeting between the manager, Venkatesham and Lange.
Frank's appointment in June was welcomed at the time as a shrewd move.
He had done a superb job at Brentford to, firstly, earn promotion from the Championship and then, crucially, consolidate their position as a Premier League club.
But he lasted just eight months at Spurs amid player indiscipline, a split executive team and doubts over his tactical approach.
Frank's struggle to create a successful culture
Frank was intent on implementing a positive culture at Tottenham - having done so at Brentford - which was one of the factors behind the decision to appoint him as Ange Postecoglou's successor.
There have been instances, however, when Frank's efforts to build respectful working conditions for his players and staff were tested.
Towards the start of his reign, Frank dropped a player from Tottenham's starting XI after the squad member reported late for a pre-match meeting and then did not apologise for the indiscretion.
However, after being removed from the team the player did later apologise.
The way Frank handled apparent threats to his authority ultimately impressed some players, who liked the fact there were consequences for below-par behaviour.
An example came when Yves Bissouma was left in London for August's Uefa Super Cup against Paris St-Germain because of persistent lateness.
In recent days, meanwhile, Frank had no intention of stripping Cristian Romero of the captaincy despite the defender's social media outbursts against the club or his red card against Manchester United.
Romero is said to be more difficult to manage around the club's training centre, and it is claimed some players felt the Argentine has been afforded preferential treatment.
When Micky van der Ven and Djed Spence appeared to refuse to shake Frank's hand after the home loss to Chelsea, the manager defused the situation by insisting the players were simply "frustrated" before later revealing they had apologised.
There was always a sense Frank put his players before his own agendas. Certain members of the squad certainly appreciated that.
But that is not to say he left a positive impression on all of them.
In the opening weeks of his reign, some players are believed to have found Frank indecisive.
They were used to Postecoglou's big personality - although the Australian had become increasingly isolated during his final months in charge.
There were consistent reservations about Frank's tactical approach, too: concerns he was not assertive enough in matches and was too focused on adapting to the opposition rather than imposing Spurs' own strengths.
That image of Frank will do little to dispel the narrative the Tottenham job was simply too big for him.
Figure caption,
Thomas Frank's final interview as Spurs boss
'Tottenham considered replacing Frank in November'
Concerns over Frank's appointment have been lingering for months.
One leading executive recommended the Dane should be sacked after the 2-1 home defeat by Fulham on 29 November - Tottenham's third-straight loss after reversals to Arsenal and PSG.
Former Brighton head coach Roberto de Zerbi - who was managing Marseille at the time - was also pushed as a potential replacement.
But that recommendation was rejected with the club continuing to put their faith in Frank.
It is interesting that the club's leadership group, led by Venkatesham, stuck with Frank for as long as they did.
The Dane's appointment was ultimately led by Daniel Levy - Tottenham's divisive former executive chairman who unexpectedly departed after 24 years in September.
While Venkatesham was involved in the execution of the deal that took Frank across London, the groundwork was completed in advance of the CEO joining last summer.
With Levy gone, it appeared the easiest decision for Venkatesham would be to sack Frank given the increasing vitriol towards the head coach from fans.
But for Venkatesham, it was not as simple as that, despite the fact he knew it could increase his popularity.
For starters, Lange - who played a key role in Frank's identification as a leading candidate - was a close ally of his Danish compatriot.
However, it is also true to say Tottenham's former co-sporting director Fabio Paratici, who has since joined Fiorentina, was not overly convinced Frank was the best man for the job.
But there is also a sense during the post-Levy era at Spurs that after years of chopping and changing managers they would benefit from a period of stability.
Venkatesham saw first-hand at Arsenal what sticking with a manager when there are calls for his head can do for a club in Mikel Arteta, who has since established the Gunners as one of the best teams in Europe.
Likewise, there was a belief from within Tottenham's hierarchy that Frank had been dealt a rough hand given the campaign has been disrupted by injuries to key players.
There is also recognition that the squad needs repair work – particularly considering the departures of their two main sources of goals in Harry Kane and Son Heung-min.
Last season's top scorer Brennan Johnson has also left - although that was down to Frank deeming the Wales attacker was no longer part of his plans.
There is also a sense Tottenham's squad is lacking in leadership. It was why they signed England midfielder Conor Gallagher and tried to land Andy Robertson - both of whom have vast Premier League experience.
Ultimately, the foundations of Tottenham's faith in Frank were irreparably shaken after the home loss to relegation-threatened West Ham on 17 January.
Sources have suggested Spurs were close to ending Frank's reign after that defeat, which was attended by members of the Lewis family - Vivienne Lewis was confronted by an irate fan after the match.
Champions League victories over Borussia Dortmund and Eintracht Frankfurt bought Frank some time - but the loss to Newcastle extended Tottenham's winless league run to eight matches and proved to be the Dane's last.
Tottenham 'weigh up short-term appointment'
Figure caption,
Frank dismissal needed as Spurs in danger of relegation - Shearer
Venkatesham and the club's new leadership team will now be tasked with making their first appointment.
It remains to be seen whether they seek an interim manager with a view to appointing a permanent boss in the summer, or want a full-time choice immediately.
There is certainly consideration behind the scenes to the interim option given how drastically the managerial landscape will change in the summer.
One option until the end of the season could be John Heitinga, who joined Tottenham as an assistant coach last month. The former Netherlands defender managed Ajax this season and was part of Arne Slot's Premier League title-winning coaching staff at Liverpool.
For the long term, the most obvious development will be the potential availability of Mauricio Pochettino after the World Cup.
The USA head coach has made no secret of his desire to return to Tottenham one day - and supporters have made no secret of their wishes for him to return.
It seems like a perfect match. But Spurs will have to wait until after the World Cup to appoint Pochettino.
Even if it is not Pochettino, the likes of Oliver Glasner, Andoni Iraola and Marco Silva will be available for nothing in the summer.
Other World Cup coaches including Thomas Tuchel, Carlo Ancelotti and Julian Nagelsmann may also be obtainable.
So there is sense in buying time until the summer. Equally, however, the recent availability of De Zerbi, who left Marseille on Tuesday night, may interest Spurs.
De Zerbi is viewed as someone who can hit the ground running, a trait Tottenham could do with given their spiral towards the relegation zone.
Yes, he can be combustible. But if Spurs are looking for an instant impact, the Italian could fit the bill.
Sources are indicating Tottenham want an appointment in place by the time the players arrive back on Monday after a pre-planned five-day break.
Amid on-field troubles, there have also been off-field rumours for the club's hierarchy to deal with - amid persistent rumblings Spurs could be sold.
This is despite it being reinforced to staff that Tottenham are not for sale. That correlates with public messaging despite industry rumours the Lewis family are open to selling.
Former Newcastle owner Amanda Staveley has been heavily linked with a continued interest in Tottenham despite a statement in September that she does not intend to make a formal offer for the club.
Other consortiums, including groups from the USA, have also been linked with an interest in purchasing Spurs, while there were reports last week that Levy was looking at selling his stake in Tottenham after his departure.
Combined with the results on the pitch and the changes off it, it has been an uncertain time.
For now though, all the attention is on the dugout and how Tottenham replace Frank.
My detailed, 200+ page guidebook is made for budget travelers like you! It cuts out the fluff found in other guidebooks and gets straight to the practical information you need to travel and save money while backpacking around Europe. You’ll find suggested itineraries, budgets, ways to save money, on and off the beaten path things to see and do, non-touristy restaurants, markets, and bars, and much more! Click here to learn more and get started!
Image source, Getty Images
Image source, Getty Images
Image source, Getty Images