Professor challenges Einstein and solves a 120-year-old mystery

After 20 years of re‑examining dusty notebooks and paradoxes, physicist José Martín‑Olalla, a professor at the University of Seville, says he has closed one of the oldest open loops in entropy and thermal science.

His new proof shows that entropy changes must disappear as temperature heads toward absolute zero, directly from the Second law of Thermodynamics.

Entropy and thermodynamic laws

Entropy is all about the natural tendency of things to move from order to disorder. The Second Law of Thermodynamics lays it out clearly: in any closed system, entropy always increases over time.

That means energy spreads out, things fall apart, and chaos slowly takes over unless you actively do something to keep order.

Think of your bedroom – if you don’t clean it, it gets messier by itself. That’s entropy at work. It’s also why no machine is perfectly efficient; some energy always escapes as useless heat.

There’s also the Third Law of Thermodynamics, which says that as something gets closer to absolute zero – the coldest temperature possible – its entropy, or disorder, approaches zero. Everything would be perfectly still and ordered, at least in theory.

And the First Law of Thermodynamics? It reminds us that energy can’t just appear or vanish – it can only change forms. So while the total amount of energy in a system stays the same, the useful part of it slowly runs out, thanks to entropy.

Nernst and the laws of entropy

Walther Nernst’s 1905 heat theorem stated that entropy differences fade to nothing when a system cools to 0 degrees kelvin (0 K), or about ‑459 °F.

The idea became a cornerstone of low‑temperature chemistry after Nernst’s 1920 Nobel lecture.

Yet the theorem never had a clean thermodynamic proof. It sat beside the empirical findings that specific heats also shrink near 0 K, giving teachers two loose ends to present whenever cryogenics showed up in class.

Because entropy law underpins chemical equilibria, critical‑point physics, and even memory devices, an unproven limit left nagging doubts. Could there be exotic materials that slip through the cracks?

Einstein, entropy, and a “third law”

Albert Einstein spotted a loophole in 1906. He argued that Nernst’s hypothetical Carnot engine working with a 0 K reservoir could never be built, so the theorem was not tied to the second law at all.

Textbook writers followed Einstein and promoted a “third law” as an extra postulate: entropy approaches a constant value, often set to zero, at absolute zero.

That constant became a tidy teaching device, but it also carved a conceptual rift between everyday heat engines and the unattainable cold frontier.

Virtual engine settles the argument

“The formalism requires the existence of the engine Nernst imagined, and also that this engine be purely virtual,” Martín‑Olalla explained.

He revisited the logic by insisting on the strict wording of the second law’s Carnot statement. If a reversible engine assesses a reservoir, it must exchange heat in exact proportion to temperature. 

Virtual means no heat leaves the cold reservoir, no heat enters from the hot side, and therefore no work comes out.

The engine turns into a paper loop, yet its bookkeeping is still valid. By tracing that loop, Martín‑Olalla shows that all entropy transfers collapse to zero at 0 K.

Because the proof needs only the second law and a Carnot thermometer, it sidesteps the separate postulate about vanishing heat capacity.

The unattainability of zero follows automatically: adiabatic expansion cannot sneak a real material to a temperature where entropy jumps would have to be negative.

What this means for absolute zero

A direct link between the Nernst limit and the second law tightens the definition of absolute zero.

It is no longer just where molecular motion would stop, or where gas pressure extrapolates to nothing, but the point where a reversible Carnot cycle folds into a line, delivering no area and therefore no work.

The proof also clarifies why entropy at 0 K must be unique for any homogeneous substance. If two states at the same temperature had different entropies, a Carnot path could produce work without heat flow, breaking the second law.

Why does any of this matter?

Researchers chasing quantum refrigerators or solid‑state cooling devices often confront design targets within a few millikelvin.

The new work confirms that they will always need at least two reservoirs, no matter how clever the qubit control scheme becomes.

Chemical thermodynamics gains a sturdier base as well. Setting entropy to an absolute reference simplifies reaction databases and avoids small but compounding errors in free‑energy tables used for battery and fuel‑cell modeling.

The second principle contains the idea that entropy is unique at absolute zero. [Canceling specific heats] “seems more like an appendix than a new principle,” Martín‑Olalla noted. Students, meanwhile, can drop one axiom from their cheat sheets. 

Shifting entropy and thermodynamic laws

For centuries, absolute zero was approached through physical indicators like pressure, volume, or kinetic energy.

Early scientists believed that when a gas exerted no pressure, it had reached the coldest possible state. This view, grounded in mechanical intuition, made sense in an era without formal thermodynamic laws.

Martín‑Olalla’s approach reframes this thinking. Instead of relying on external measurements, he defines 0 K using the internal logic of the Carnot cycle, where no heat flows and no entropy is exchanged.

This removes the need for empirical proxies and gives a universal, formal definition of temperature’s natural floor.

Martín‑Olalla emphasized the value of introducing this proof to students early. He acknowledged the resistance that often meets reinterpretations of established theory.

Although he believes the academic world has strong inertia, he believes the argument might resonate with a new generation of physicists seeking internal consistency if the theorem is rooted in the second law itself, rather than a loosely attached third principle.

The study is published in The European Physical Journal Plus.

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