After more than 100 years of debate featuring the likes of Einstein himself, physicists have finally offered up mathematical proof of the third law of thermodynamics, which states that a temperature of absolute zero cannot be physically achieved because it's impossible for the entropy (or disorder) of a system to hit zero.

While scientists have long suspected that there's an intrinsic 'speed limit' on the act of cooling in our Universe that prevents us from ever achieving absolute zero (0 Kelvin, -273.15°C, or -459.67°F), this is the strongest evidence yet that our current laws of physics hold true when it comes to the lowest possible temperature.

"We show that you can't actually cool a system to absolute zero with a finite amount of resources and we went a step further," one of the team, Lluis Masanes from University College London, told IFLScience.

"We then conclude that it is impossible to cool a system to absolute zero in a finite time, and we established a relation between time and the lowest possible temperature. It's the speed of cooling."

What Masanes is referring to here are two fundamental assumptions that the third law of thermodynamics depends on for its validity.

The first is that in order to achieve absolute zero in a physical system, the system's entropy has to also hit zero. 

The second rule is known as the unattainability principle, which states that absolute zero is physically unreachable because no system can reach zero entropy.

The first rule was proposed by German chemist Walther Nernst in 1906, and while it earned him a Nobel Prize in Chemistry, heavyweights like Albert Einstein and Max Planck weren't convinced by his proof, and came up with their own versions of the cooling limit of the Universe.

This prompted Nernst to double down on his thinking and propose the second rule in 1912, declaring absolute zero to be physically impossible.

Together, these rules are now acknowledged as the third law of thermodynamics, and while this law appears to hold true, its foundations have always seemed a little rocky - when it comes to the laws of thermodynamics, the third one has been a bit of a black sheep.

"[B]ecause earlier arguments focused only on specific mechanisms or were crippled by questionable assumptions, some physicists have always remained unconvinced of its validity," Leah Crane explains for New Scientist.

In order to test how robust the assumptions of the third law of thermodynamics actually are in both classical and quantum systems, Masanes and his colleague Jonathan Oppenheim decided to test if it is mathematically possible to reach absolute zero when restricted to finite time and resources.

Masanes compares this act of cooling to computation - we can watch a computer solve an algorithm and record how long it takes, and in the same way, we can actually calculate how long it takes for a system to be cooled to its theoretical limit because of the steps required to remove its heat.

You can think of cooling as effectively 'shovelling' out the existing heat in a system and depositing it into the surrounding environment. 

How much heat the system started with will determine how many steps it will take for you to shovel it all out, and the size of the 'reservoir' into which that heat is being deposited will also limit your cooling ability. 

Using mathematical techniques derived from quantum information theory - something that Einstein had pushed for in his own formulations of the third law of thermodynamics - Masanes and Oppenheim found that you could only reach absolute zero if you had both infinite steps and an infinite reservoir.

And that's not exactly something any of us are going to get our hands on any time soon.

This is something that physicists have long suspected, because the second law of thermodynamics states that heat will spontaneously move from a warmer system to a cooler system, so the object you're trying to cool down will constantly be taking in heat from its surroundings.

And when there's any amount of heat within an object, that means there's thermal motion inside, which ensures some degree of entropy will always remain. 

This explains why, no matter where you look, every single thing in the Universe is moving ever so slightly - nothing in existence is completely still according to the third law of thermodynamics.

The researchers say they "hope the present work puts the third law on a footing more in line with those of the other laws of thermodynamics", while at the same time presenting the fastest theoretical rate at which we can actually cool something down.

In other words, they've used maths to quantify the steps of cooling, allowing researchers to define set speed limit for how cold a system can get in a finite amount of time.

And that's important, because even if we can never reach absolute zero, we can get pretty damn close, as NASA demonstrated recently with its Cold Atom Laboratory, which can hit a mere billionth of a degree above absolute zero, or 100 million times colder than the depths of space.

At these kinds of temperatures, we'll be able to see strange atomic behaviours that have never been witnessed before. And being able to remove as much heat from a system is going to be crucial in the race to finally build a functional quantum computer.

And the best part is, while this study has taken absolute zero off the table for good, no one has even gotten close to reaching the temperatures or cooling speeds that it's set as the physical limits - despite some impressive efforts of late

"The work is important - the third law is one of the fundamental issues of contemporary physics," Ronnie Kosloff at the Hebrew University of Jerusalem, Israel who was not involved in the study, told New Scientist.

"It relates thermodynamics, quantum mechanics, information theory - it's a meeting point of many things."

The study has been published in Nature Communications.