The following is an extract from our Lost in Space-Time newsletter. Each month, we dive into fascinating ideas from around the universe. You can sign up for Lost in Space-Time here.
One of the more absurd things about science is that you can spend years studying and reading about the universe’s deepest mysteries – dark matter, quantum gravity, the nature of time – and still get tripped up by something deceptively simple. Nobel-prizewinning theoretical physicist Richard Feynman famously confessed that as a student he didn’t really understand why mirrors flip images left to right rather than up and down. I’m no Feynman; I know how mirrors work. But I’ve had my own humbling reckoning with the obvious: temperature.
We’ve known that things can be hot or cold since the first cave-child stuck their hand in a fire and got yelled at by a concerned parent. But what we mean by temperature has changed a lot over the centuries, and continues to evolve today, as physicists push it into weirder, quantum corners.
My own brush with this came by way of my partner, who once asked: “My beautiful and stunningly intelligent wife, didn’t you study physics? Then tell me, can a single particle have a temperature?” I may be paraphrasing here slightly, but that was basically his question.
Now, his initial hunch was right: no, it can’t, not really. Most science enthusiasts know that temperature isn’t something you can assign to just one particle. The business of hot and cold only makes sense as a property of systems with many, many particles – things like gas-filled pistons, pots of coffee or stars. That’s because temperature, as we normally define it, is a kind of shorthand. It captures the average energy of a system’s microscopic components once they’ve bounced around and spread their energy out evenly, reaching a state known as equilibrium.
Imagine it like a ladder, with each rung representing a different energy level. The higher the rung, the more energy a particle has. When there are lots of particles, we expect them to be spread out across the rungs predictably. Most particles settle near the bottom, a few have enough energy to climb one rung higher, and fewer higher than that. The result is a smooth, declining number of particles as you go up the ladder.
But why do we define temperature this way? Sure, it’s an average, but there’s nothing in mathematics that forbids us from taking the mean of a dataset with a single point. If there’s one tall person in a room, we don’t blink at calling the average height of people in that room 6 feet. Why not do the same here?
It’s because temperature isn’t just descriptive, it’s predictive. For the scientists trying to harness the power of fuel, fire and steam in the 17th and 18th centuries, it was most useful for a temperature to tell them what would happen when two systems interacted.
That’s what gave rise to the zeroth law of thermodynamics, the last of these laws to be established but the most fundamental. It goes like this: if a thermometer reaches 80°C in a cup of warm water, and also reaches 80°C in a cup of warm milk, then if we mix the two liquids, there should be no net exchange of heat between them. This might sound obvious – banal, even – but it’s the bedrock of classical thermometry.
And it only holds because large systems behave in statistically stable ways. Tiny fluctuations in energy between specific particles get washed out and the law of large numbers allows us to write generalisable outcomes.
Thermodynamics is strange in that way. Unlike, say, Isaac Newton’s laws of motion, which work just fine for one falling apple or a thousand, thermodynamic laws only emerge at scale. They rely on averages, ensembles and the mathematical magic that happens when your particle count climbs into the billions.
So: single particles don’t have temperatures. Case closed.
Or so I thought. But just when I felt ready to move on, physics threw me a curveball. The first dead giveaway that things are about to get really weird is that many quantum systems are composed of very few particles that never have stable properties.
Tiny systems – like individual atoms or singular spins – can be trapped states that never really settle. Some are even deliberately engineered to resist the peaceful state of equilibrium entirely. So, if temperature is supposed to describe what happens after things calm down, then doesn’t our definition of temperature fall apart?
What exactly is temperature?
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Physicists have been working hard to retool temperature from the foundations up, considering what it even means to have temperature in the quantum realm.
In the same spirit as the pioneers of thermodynamics, researchers are now asking not what temperature is but what it does. If we take a quantum system and connect it to something else, which way does the heat move? Can the system warm up its neighbour? Can it cool it down?
In the quantum world, the answer can be both! Let’s go back to the temperature ladder that particles can climb. In the classical world, the rules of temperature here are simple. When two ladders (two systems) interact, energy always flows from the system with more particles on higher rungs to the one with fewer.
But a quantum system doesn’t obey the same rules. Quantum systems could have no particles on the bottom rung, and instead have them all crowded on rungs higher up. They could have patchy distributions of particles equally spread out on all rungs. Superposition also makes it possible for particles to exist between rungs. When quantum mechanics comes into play, our ladder is no longer what physicists call “thermally ordered”.
This makes it hard to predict how heat might flow if one ladder were to interact with something. To deal with that, physicists have developed a curious solution: let quantum systems have two temperatures. Imagine a sort of reference ladder that represents a simple thermal system. One temperature tells you the hottest such ladder your system can still pull heat down from. The other tells you the coldest ladder that your system can push heat up to. Outside this bracket, heat flows in a predictable direction, but inside it, the outcome depends on the exact nature of the quantum system. It’s the new zeroth law of thermodynamics, something that can help us restore logic to how heat flows in the quantum world.
These two bounds reflect the system’s potential to give or take energy, regardless of whether it’s in a state of equilibrium. Crucially, these temperatures depend not just on energy, but on how that energy is structured: how quantum particles or states are distributed across energy levels, and what kind of transitions the whole system supports.
And like their thermodynamical predecessors, quantum physicists are interested in making their systems do work. Imagine two atoms that are entangled – their properties are so closely correlated that measuring one affects the other. Now expose one atom to the environment. When that atom gains or loses energy, it tugs on the invisible quantum link connecting the pair. Breaking or degrading that link has a cost, like snapping a stretched rubber band. This creates a flow of heat that wouldn’t happen without the quantum link, which can then be harnessed – by coupling the atom to a tiny quantum “piston” – to perform work, until the entanglement is used up. By assigning hot and cold effective temperatures to any quantum state, researchers can determine when a system can reliably transfer heat, extract work or drive tasks such as refrigeration and computation.
If you’ve made it this far, here’s my confession: I argued with my partner that a single particle could have temperature, despite his intuition being correct. Being a sore loser sent me spiralling down a major rabbit hole – and at the bottom, I’ve found that we’re both right, sort of. A single particle can’t have a temperature, but it can have two.
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