The third law of thermodynamics says, in its simplest form, that the entropy of a perfect crystal drops to zero as its temperature approaches absolute zero, and that reaching absolute zero itself is physically impossible through any finite process. It sounds like an abstract rule about cold things, but it sets hard limits on everything from quantum computers to the structure of black holes. The law has been around for over a century, and physicists are still finding new corners of nature where it applies, bends, or surprises.
What the Law Actually Claims
The third law has two closely related statements that are sometimes treated as separate principles. The first, usually called the Nernst heat theorem after the German chemist Walther Nernst who proposed it in 1906, says that as a system’s temperature drops toward absolute zero, its entropy approaches a definite, minimum value. For a perfectly ordered crystal with no defects, that minimum is zero. Nernst originally called this his “New Heat Theorem,” and later referred to it as the Third Law of Thermodynamics.1Journal of Fluids Engineering. The Third Law of Thermodynamics: A Half-Century Appraisal of the Nernst Heat Theorem The idea is that at absolute zero, a perfect crystal has only one possible arrangement of its atoms, and since there is only one way to be in that state, the disorder (entropy) is zero.
The second statement is the unattainability principle: no sequence of physical operations, no matter how clever or idealized, can bring a system all the way to absolute zero in a finite number of steps. You can get extraordinarily close, but the last sliver of temperature can never be fully removed. These two ideas reinforce each other. Because entropy must smoothly approach zero, each successive cooling step extracts less and less heat, and the effort required to shave off each remaining fraction of a degree grows without bound.2Physics Letters A. Principle of Unattainability of absolute zero temperature, the Third Law of Thermodynamics, and projective quantum measurements
Why You Can Never Quite Get to Absolute Zero
Think of cooling like squeezing water out of a sponge. At first, a firm squeeze releases a lot. But the drier the sponge gets, the harder you have to squeeze for each remaining drop, and you will never get the last molecule of water out no matter how strong your grip. Cooling works the same way: the colder a system already is, the less thermal energy is left to extract, and each incremental step demands exponentially more effort.
Every real cooling technique confirms this. Evaporative cooling, laser cooling, and adiabatic demagnetization all run into the same wall. Each method can push the temperature lower, but the rate of progress slows asymptotically. The unattainability principle is not just a practical limitation of current technology; it is built into the structure of quantum mechanics itself. As a system approaches its ground state, the possible transitions that could remove energy become fewer and fewer, until there is simply no physical process left that can extract the last bit of heat.3Physics Letters A. Principle of Unattainability of absolute zero temperature, the Third Law of Thermodynamics, and projective quantum measurements
How Close Scientists Have Actually Gotten
Just because absolute zero is unreachable doesn’t mean physicists haven’t gotten breathtakingly close. The record holders are experiments with ultracold atomic gases, specifically Bose-Einstein condensates, clouds of atoms cooled so thoroughly that they begin behaving as a single quantum entity. A group at MIT cooled a sodium condensate to about 450 picokelvin, which is 450 trillionths of a degree above absolute zero.4PubMed. Cooling Bose-Einstein condensates below 500 picokelvin They achieved this by gently weakening the magnetic trap holding the atoms and then evaporating the hottest atoms away, leaving only the coldest behind.
Other experiments have reached the low-nanokelvin range. Caesium atoms, for instance, have been evaporatively cooled in magnetic traps to temperatures as low as 8 nanokelvin, pushing the phase-space density to within a factor of four of what is needed for Bose-Einstein condensation.5Journal of Optics B: Quantum and Semiclassical Optics. Strong evaporative cooling towards Bose–Einstein condensation of a magnetically trapped caesium gas These temperatures are staggeringly low. The cosmic microwave background, the faint afterglow of the Big Bang that fills all of space, sits at about 2.7 kelvin. These lab experiments produce conditions a billion times colder than the background temperature of the universe itself.
The pattern in all of these experiments is the same: each new generation of cooling technology pushes the floor lower, but the gains shrink. Going from microkelvins to nanokelvins was hard. Going from nanokelvins to picokelvins was much harder. The third law predicts exactly this diminishing return, and every experiment so far has obeyed it.
When Entropy Doesn’t Quite Reach Zero
The classic statement of the third law says entropy goes to zero at absolute zero for a perfect crystal. But not all materials are perfect crystals, and this is where things get interesting. Some materials retain a small amount of entropy even as they approach absolute zero, a phenomenon called residual entropy. The most famous example is ordinary water ice. The hydrogen bonds in ice allow the hydrogen atoms to sit in multiple slightly different arrangements without changing the crystal’s energy. Even at absolute zero, if you could somehow get there, the ice would still have many possible configurations, so its entropy would not be zero.
Magnetic materials can show an analogous effect. In a class of materials known as spin ices, the magnetic moments of atoms are arranged on a lattice in a way that is geometrically frustrated, meaning no single arrangement of the magnets can simultaneously satisfy all of the competing interactions. The result is that many different arrangements have exactly the same energy, and the system retains disorder down to its lowest temperatures. The disorder in these spin ice materials is precisely analogous to the proton disorder in water ice.6Science. Spin ice state in frustrated magnetic pyrochlore materials
Does residual entropy violate the third law? Not exactly. The law, carefully stated, applies to systems that can reach true thermodynamic equilibrium. A system with residual entropy is typically stuck in a metastable state: it has many nearly equivalent configurations but cannot easily shuffle between them at very low temperatures because the thermal energy needed to make the switch has disappeared. Some physicists frame this as the system being “kinetically frozen” rather than being in its true ground state. When theorists analyze lattice models rigorously, they find that the question of whether the third law holds comes down entirely to what happens with ground-state degeneracies across all possible boundary conditions.7Journal of Statistical Physics. The third law of thermodynamics and the degeneracy of the ground state for lattice systems If the ground state is unique, entropy reaches zero. If many ground states exist, residual entropy persists.
The Coldest Known Place in the Universe
Outside the laboratory, the coldest known object in the universe is the Boomerang Nebula, a dying star about 5,000 light-years from Earth. It is a pre-planetary nebula, meaning a star in a brief transitional phase between two stages of stellar death. The star’s outer layers are being expelled at enormous speed, and that rapid expansion has cooled the gas to about 1 kelvin, well below the 2.7 kelvin background temperature of space.8The Astrophysical Journal. The Coldest Place in the Universe: Probing the Ultra-cold Outflow and Dusty Disk in the Boomerang Nebula
That might not sound impressive compared to picokelvin laboratory experiments, but the scale is utterly different. The Boomerang Nebula’s cold gas spans light-years. Achieving temperatures below the cosmic microwave background on that scale requires a massive, sustained outflow that acts like a cosmic refrigerator. ALMA telescope observations confirmed that the nebula really is colder than the background radiation, making it the only known natural object in the universe to hold that distinction.9The Astrophysical Journal. ALMA Observations of the Coldest Place in the Universe: The Boomerang Nebula The third law still applies: the nebula’s gas has finite entropy, and no natural process will push it the rest of the way to absolute zero.
Why Quantum Computers Care About the Third Law
Superconducting quantum computers operate at temperatures around 10 to 20 millikelvin, deep inside a dilution refrigerator. At those temperatures, thermal noise is low enough that delicate quantum states can survive long enough to perform calculations. But “low enough” is not zero, and the third law guarantees that true zero is not coming. Every millikelvin of residual temperature introduces noise that degrades quantum information.
One specific problem is the wiring. The qubits themselves sit at the bottom of the refrigerator, but the control lines that carry microwave signals to them stretch upward to room-temperature electronics. Even with careful filtering and attenuation, these interconnects act as a conduit for thermal noise. Research on prototypical drive lines has found that in the limit of zero applied power, the noise reaching the quantum processor is equivalent to that of a blackbody with a temperature between roughly 63 and 71 millikelvin, several times warmer than the processor itself.10PRX Quantum. Inherent Thermal-Noise Problem in Addressing Qubits That extra noise limits qubit lifetimes, introduces dephasing, and caps how accurate quantum gates can be. The third law is not just abstract here: it is a concrete engineering constraint.
Researchers are fighting back with creative approaches. One promising idea is a quantum-circuit refrigerator that uses thermal noise itself as a resource. Experiments have shown that injecting carefully engineered artificial thermal noise into a circuit can actually reduce the effective temperature of a resonator from roughly 300 millikelvin down to about 130 millikelvin.11Physical Review Research. Noise-driven quantum-circuit refrigeration The concept is a bit counterintuitive: you are using heat to cool things down, essentially redirecting thermal energy to do useful work in resetting qubits. These techniques may eventually allow waste heat inside a quantum processor to serve as the power source for resetting qubits between calculations. None of these methods get around the third law, but they push the practical floor lower.
Even the fundamental energy cost of erasing information ties back to temperature. Landauer’s principle says that erasing a single bit of information in a thermal environment costs at least a tiny amount of energy proportional to the temperature. The colder the environment, the cheaper the erasure. Research has shown that using non-standard thermal states, like squeezed thermal states that naturally arise in pulse-driven electronics, can exponentially reduce the energy cost of erasure compared to the standard Landauer bound.12PubMed. Landauer’s Erasure Principle in a Squeezed Thermal Memory The third law ensures you can never reach zero temperature and therefore never get free information erasure, but the gap between theory and practice is narrowing.
Quantum Refrigerators and the Speed of Cooling
The pursuit of colder temperatures has led to work on the theoretical limits of quantum refrigerators, tiny systems that use quantum mechanical processes to pump heat from a cold reservoir to a hot one. These devices face a fundamental tradeoff: the faster you try to cool something, the less effectively you cool it. Research on quantum absorption refrigerators has demonstrated that there is a tradeoff between the steady-state cooling rate and the minimum time it takes the refrigerator to reach that steady state.13PubMed. Quantum speed limit constraints on a nanoscale autonomous refrigerator In other words, you can cool something well or cool it quickly, but not both at once.
This tradeoff is rooted in the same physics as the third law. As you approach lower temperatures, the quantum states available to your refrigerator become more constrained, and the speed at which quantum systems can evolve hits fundamental quantum speed limits. The third law appears here not as a single rule to be followed but as a reflection of deeper constraints woven into quantum mechanics itself.
Black Holes and the Third Law by Analogy
One of the stranger chapters in the story of the third law involves black holes. In the 1970s, physicists noticed that the equations governing black holes bear a striking resemblance to the laws of thermodynamics. A black hole has a quantity called surface gravity that plays the role of temperature, and its event horizon area plays the role of entropy. The “third law of black hole mechanics” says that you cannot reduce a black hole’s surface gravity to zero through any finite physical process, just as you cannot cool a material to absolute zero.14arXiv. The Third Law of Black Hole Dynamics in Lovelock Gravity
A black hole with zero surface gravity is called an extremal black hole. For a charged black hole, this would mean its charge is maxed out relative to its mass. For a spinning black hole, it would mean spinning as fast as physically possible. The third law of black hole mechanics predicts that you can never quite push a black hole to that extreme. As the surface gravity approaches zero, the range of allowed perturbations shrinks, creating a kind of dynamical barrier that prevents the final step.
This analogy has held up remarkably well in four-dimensional spacetime, which is the spacetime we live in. But recent numerical simulations in five-dimensional vacuum gravity suggest the analogy may break down in higher dimensions. Researchers found that extremal black holes, those with zero surface gravity, can form from non-rotating black holes or collapsing gravitational waves in finite time in five dimensions, violating the black hole version of the third law.15Physical Review Letters. Violating the 3rd law of black hole mechanics in vacuum gravity This doesn’t mean the ordinary third law of thermodynamics is wrong in our universe, but it does suggest that the deep connection between gravity and thermodynamics has limits that physicists are still mapping out.
How the Third Law Shapes Everyday Material Science
Far from black holes and picokelvin labs, the third law has quietly practical consequences for anyone working with materials. Because entropy must go to zero smoothly as temperature drops, the heat capacity of every material must also approach zero as temperature approaches absolute zero. Heat capacity measures how much energy it takes to change a material’s temperature by one degree, and the third law dictates that this quantity shrinks and approaches zero at low temperatures. This is something you can measure and verify for any solid.
This constraint matters for calculating what are called standard thermodynamic quantities: the entropy, enthalpy, and Gibbs energy of a substance at room temperature. All of these are computed by integrating heat capacity data from near zero kelvin up to the temperature of interest. The third law anchors the bottom of that integral. Without it, you would have no defined starting point, and thermodynamic tables for chemical reactions would be full of arbitrary constants. Researchers have shown that heat capacity data for pure elements from zero kelvin to room temperature can be accurately described using functions that respect the third law’s constraint, and these fits allow precise calculation of standard entropies and related quantities for elements like iron, aluminum, silver, and gold.16Journal of Phase Equilibria and Diffusion. Revisiting the Extension of SGTE Heat Capacity Data to Zero Kelvin: Combining Classical Fit Polynomials with Debye–Einstein Functions
In practical terms, this means the third law is the reason chemists and engineers can look up standardized values for chemical reactions and trust that they are consistent. Every entry in a thermodynamic reference table implicitly relies on the third law to set the zero-point of entropy. It is one of those laws that most people never hear about but that underpins an enormous amount of applied science.
Common Misconceptions
The most widespread misunderstanding about the third law is that it merely says “you can’t reach absolute zero.” That is one consequence, but the law says something deeper: it specifies what happens to entropy as you approach zero, and it tells you that the approach must be asymptotic rather than abrupt. A related misconception is that absolute zero means all motion stops. Quantum mechanics forbids this. Even at absolute zero, atoms retain what is called zero-point energy, a minimum amount of motion required by the uncertainty principle. A system at its ground state is not motionless; it is as still as quantum mechanics allows, which is not quite still at all.
Another common confusion involves the relationship between the three laws of thermodynamics. People sometimes assume the laws were discovered in numerical order and that the third law was some kind of grand finale. In reality, the numbering is a historical accident. The second law (entropy tends to increase) was understood before the first law (energy is conserved) was rigorously formulated, and the third law came decades later as an independent insight from Nernst’s work on chemical reactions near absolute zero. There is even a “zeroth law,” which was formalized after all the others and deals with the basic concept of thermal equilibrium. The laws are numbered by logical priority, not chronological order, and the numbering was applied after the fact.
People also sometimes wonder whether the third law means cold things are somehow “more perfect” than hot things. Not exactly. A system at very low temperature is in a highly ordered state with very few accessible configurations, which means it has low entropy. But “low entropy” is not the same as “perfect” in any meaningful physical sense. A glass, for instance, has residual entropy at low temperatures because its disordered atomic structure gets frozen in. Glasses are not less real for failing to reach zero entropy; they just are not perfect crystals.