SITTING with a friend in a cafe, you order a cappuccino and your buddy orders a milkshake. But as you go to take a sip of your coffee, you see a roiling boil, steam rising from the mug at an increasing rate. Astonished, you look up to tell your friend, then stop dead: his tongue is stuck to the now-frozen milkshake. Terrified and confused, you both run to your car and start the engine, but then notice the fuel gauge going up – your engine is sucking in heat and exhaust fumes and turning them into petrol and air.
This has never happened and almost certainly never will. But the key word here is “almost”. Although processes that involve the exchange of energy don’t behave like this at the scale of our everyday experiences, at the level of atoms and molecules they can and do run backwards.
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Physicists first acknowledged the possibility of this kind of violation of the forward flow of time more than a century ago. Yet it is only recently that we have started to get to grips with what this might mean for the many critical processes that underpin life itself.
Our growing understanding of what drives – and limits – these processes, is not only upending traditional notions of energy, but also exposing new clues relating to perplexing questions about human biology, including how some neurological diseases take hold. Now, researchers have even set their sights on applying these ideas to understanding one of the greatest mysteries of all, the origin of life.
The industrial revolution of the 18th and 19th centuries saw hard graft increasingly replaced by engine power. As steam engines came on the scene, engineers also set about improving the design and efficiency of existing labour-saving “engines”, like the waterwheel and windmill. This new industrial world represented an exciting playground for natural philosophers, where they could start to dissect the mystery of energy and the rules governing how it is transformed into useful work. By 1860, Rudolf Clausius and William Thomson (later Lord Kelvin) had laid it all out in two laws, later extended to four. The laws built on early insights from the likes of Sadi Carnot and James Joule, and could be applied not just to engines, but all processes in nature. The science of energy – – was born.
You can think of thermodynamics in terms of a casino. The first law of thermodynamics says that you can’t create energy, only transfer it, in the same way that a gambler’s potential winnings are limited by the cash in their bank account and the house’s money.
The second law is based around a concept called entropy, which, roughly speaking, is a measure of the tendency for energy to disperse or spread out as time progresses. High entropy means high disorder and low energy. The second law says that, in any natural process, entropy cannot shrink – in other words energy can’t be gained or things become more orderly. It is the same as saying that on any trip to the casino, given enough time, you will always come home with less cash than you brought.
However, this doesn’t stop you from winning a few games of blackjack along the way. Bringing it back to thermodynamics, these chance wins are the rare interactions between atoms and molecules where entropy is actually lost instead of gained, as if the process were running backwards in time.
In 1878, James Clerk Maxwell had already cottoned on to this loophole, writing in a book review for Nature: “The truth of the second law is therefore a statistical not a mathematical truth, for it depends on the fact that the bodies we deal with consist of millions of molecules… Hence the second law of thermodynamics is continually being violated.”
Small wins
For natural processes, like your cup of coffee inevitably going cold, violations in the form of a few energy gaining interactions make no difference to the overall trend towards a state with the lowest energy and most disorder, known as maximum entropy. Essentially, in our everyday world, the house always wins – unless you are cheating the casino, which equates to pumping outside energy into a process in thermodynamics terms. But the nanoworld is more like zooming in on an individual blackjack table. Observing small groups of particles, scientists have witnessed players go on incredible winning streaks.
Way back in 2001, at the Australian National University in Canberra and his colleagues . They were using the laser as “optical tweezers”, now a common technique for grabbing tiny objects with a light field. In their experiment, the bead’s curved surface acted like a lens, bending the laser light and exerting a force that kept the bead at the beam’s centre. Using this force, they slowly dragged the bead through the water. According to Clausius and Kelvin’s thermodynamics, no matter how many times the experiment was repeated, the bead should have happily followed the beam.
Instead, over the course of hundreds of repetitions, the bead occasionally pushed ahead of the beam. “The bead extracted ambient heat from the water and converted this heat into work to move against the ‘natural’ motion of the focus of the laser beam,” says Evans.
Although lasting only about 2 seconds at a time, these little acts of rebellion were violations of the second law of thermodynamics. Essentially, the researchers had witnessed the bead beating the house.
Not only was this the first time violations had been observed over these time and length scales, but the numbers also matched a modern twist on the second law of thermodynamics that Evans and his collaborator at the University of Queensland, Australia, had cooked up in the early 1990s. This tinkered with the second law so it could be studied with statistics. Where the traditional law is hardwired so that entropy always increases as time moves forward – coffee cools, engines burn petrol and so on – their stochastic theory explained how entropy could rise or fall for tiny, individual processes while still ensuring that, averaged out at larger scales, it always increased.
More generally, the fluctuation theorem showed how different thermodynamics is when you zoom in to the nanoscale. There, whatever you are studying is continually bombarded by surrounding molecules, creating an element of randomness that makes the system jiggle around. This jiggling causes fluctuations in energy and violations of the second law of thermodynamics, and even a blurring of the arrow of time.
“At our scale, eggs go splat and you never see entropy going down,” says at the Santa Fe Institute in New Mexico, who specialises in thermodynamics . “As we go to smaller and smaller scales, we’re going to have a greater probability of seeing backward processes.”
These aren’t backward processes in the same way that a car can be driven backwards in reverse gear. A backward process is more like a Slinky travelling up a flight of stairs or a splattered egg reconstituting itself: impossible at our scale of the world, where time appears to be firmly set in the forward direction, but not in the nanoworld. There, time is still inclined to go forward, but is no longer shackled to just one direction. This slight preference to going forward at the level of an individual molecule gradually firms up time’s thermodynamic arrow as we add more and more molecules, giving the impression that everything always runs forward.
Arriving at a time when nanotechnology was starting to take off commercially, Evans’s 2001 experiment and its mind-bending consequences catalysed frenzied work. Scientists derived new fluctuation theorems for various specialised scenarios as well as generalisations. They attempted to combine fluctuation theorems with quantum theory and other research fields. And they conducted countless experiments violating the second law that validated the theorems in different settings.
“It’s not a like a car going in reverse, it’s like a broken egg reconstituting itself”
Researchers could immediately see how these theorems could help them get to grips with the thermodynamics of small systems, which seemed a likely coup for nanoscale devices and electronics. However, it was in the messy world of biophysics – the study of biological systems with physics where existing techniques were more limited – that they proved to be a truly unique scientific tool. This was thanks to an experiment to test an idea first proposed in 1997 by , who is now at the University of Maryland.
, as it is now known, is similar in spirit to Evans’s and Bernhardt’s fluctuation theorem, but with work – the energy a force produces and transfers to or from an object to move it – replacing entropy as the quantity of interest. Just as entropy fluctuations were included in the original fluctuation theorem, Jarzynski incorporated work fluctuations in his. This allowed him to define a way of measuring the maximum amount of energy that can be freed from a real-world system to perform useful work: the free energy difference.
, a team led by at the University of California, Berkeley, repeatedly unfolded and refolded a single molecule of RNA. Half of the time they pulled the molecule apart very slowly, allowing energy and forces to spread evenly at each stage. This allowed them to scrutinise the process using standard thermodynamics and write down a firm value for the free energy difference. The rest of the time they tugged at the RNA very rapidly, leading to a process whose work could only be analysed using Jarzynski’s equality. “When you do it quickly, then each time you do the experiment, you get a different value for work,” says Jarzynski. “Repeating the experiment many times, these work fluctuations form a distribution of values from which you can extract an average.” Amazingly, the values for free energy difference from standard thermodynamics and Jarzynski’s equality agreed.
A unique tool
The simple, yet elegant demonstration by Bustamante and his team showed how fluctuation theorems and, more generally, stochastic thermodynamics could be wielded to gain information from real-life nanosystems that traditional thermodynamics can’t access. Traditional thermodynamics only describes systems close to equilibrium, where no energy enters or leaves and everything happens smoothly and slowly. In the real world, almost nothing is in equilibrium. Instead, most systems are in a state of constant flux, with energy flowing in and out of them all the time. Being able to extract practical thermodynamic values like work from a messy, real-life system out of equilibrium was a huge step forward.
What’s more, there may be ways to exploit these tools on much bigger systems. “The same theorems apply no matter what the scale of the system is,” says Wolpert. “They apply at the level of human society just as well as they apply down at the level of single RNA molecules.”
Building full stochastic thermodynamic descriptions of ever-bigger living systems may provide a picture of how perhaps the most precious phenomenon on Earth manages to keep itself constantly out of equilibrium, relentlessly fighting against disorder – life itself. Wolpert also thinks it could pin down the physics behind cell-level natural selection and thereby the origin of life. He isn’t alone. “To the extent that the origin of life is to be understood in terms of interactions between different molecules, stochastic thermodynamics provides us with proper theoretical tools for analysing those problems,” says Jarzynski.
Starting at the molecular level, biophysics researchers have latched onto these tools and conducted a swathe of experiments pulling at various biomolecules with some interesting results already. The aim has been to understand the mechanisms underpinning the nanoscale biological equivalents of steam engines.
Molecular motors are proteins that convert available energy into mechanical motion. They play a fundamental role in various processes essential to life, like muscle contraction, DNA transcription and moving materials around cells, such as neurotransmitters and hormones.
Until recently, studies of molecular motors were limited by their simplified nature. Ultimately, they didn’t replicate the intricate, interdependent functioning of the motors or the complex environment of the cell. But Kumiko Hayashi and Shinsuke Niwa at Tohoku University in Japan have found a way to truly capture how various molecular motors work in their natural habitat.
In 2018, Hayashi and Niwa tried out a new, non-invasive technique on worms to look at how molecular motors called kinesins and dyneins transport materials back and forth between motor neurons along their axons, which transmit nerve signals. They were able to use fluctuation theorems to estimate the molecular motors’ energy from only the fluctuating movements of their cargo of materials. From this, they found that these , like ants working in tandem.
Interestingly, comparing healthy worms with worms that had a gene associated with correct function of the molecular motor deleted, Niwa discovered that fewer motors worked to transport cargo in the mutant worms than in the healthy ones, which can lead to weaker transport and even cargo being delivered to the wrong location.
Hayashi also points out that other researchers have recently pinned down the cause of hereditary spastic paraplegia, a rare disorder that causes weakness and stiffness in people’s leg muscles, to mutations of motor proteins transporting neuronal cargoes. She thinks her work with Niwa clarifies the key physical mechanism underpinning this disease. More broadly, Hayashi is optimistic that , by helping unpick mechanisms of other neurological diseases, such as Huntington’s, Parkinson’s and Alzheimer’s.
But to get a broader picture of health, disease and even life itself, Wolpert and others working on bigger systems need to account for a rich and complex hierarchy of interacting subsystems. For instance, each cell in the human body contains many intertwined parts at different scales performing specialised jobs. Capturing how energy is transported in these kinds of scenarios is monumentally difficult. Yet they are making inroads.
Theories about information – how it can be quantified, stored and communicated – have a rich history of interplay with theories of thermodynamics. Looking at how information flows through big systems, “there may start to emerge patterns that govern thermodynamic properties that have to do with interactions among all those subsystems”, says Wolpert. He believes that information flow – and more generally, information transformation – will play “a key role in understanding the overall thermodynamics” of systems like a cell.
“This new approach could pin down the physics of cell-level natural selection – and thereby the origin of life”
Already, Wolpert has to encompass multiple interacting parts. This is allowing him, at least theoretically, to start analysing how thermodynamics depends on the communication structure between the given system’s subsystems. However, he is far from naive about the scale of the task. “It’s going to be ongoing work for many, many years.”
What is clear is that when it comes to even starting to answer questions about the origins and persistence of life, our new understanding of thermodynamics will be crucial. If experience so far is anything to go by, you might gamble on it exposing a messy, noisy reality, where change is governed by random fluctuations that can even bend the rules of time. As to what this refined perspective will ultimately reveal, all bets are off.
