Physicist Solves 120-Year-Old Thermodynamics Puzzle and Corrects Einstein

The paper argues that the third principle of thermodynamics follows from the second principle, rather than being a separate or independent concept.

Professor José María Martín-Olalla of the University of Seville has published a paper addressing a thermodynamics problem that has remained unresolved for 120 years. In doing so, he corrects an idea proposed by Albert Einstein more than a century ago.

The paper links Nernst’s theorem, an experimental observation from 1905 stating that entropy exchanges approach zero as temperature approaches zero, directly to the second principle of thermodynamics. Published in The European Physical Journal Plus, the study extends the implications of the second principle, which states that entropy in the universe tends to increase.

The historical problem of absolute zero

The problem surrounding Nernst’s theorem emerged in the early 20th century, during investigations into how matter behaves at temperatures near absolute zero (minus 273 degrees Celsius). Walther Nernst received the Nobel Prize in Chemistry in 1920 for his contributions to this field.

To explain his findings, Nernst argued that absolute zero must be unreachable. Otherwise, one could theoretically construct an engine that uses absolute zero as a coolant to convert all heat into work, violating the principle that entropy always increases. He used this reasoning to formally state his theorem in 1912.

Soon after, Albert Einstein challenged the argument by noting that such an engine could not actually be built, and therefore it posed no real threat to the second law of thermodynamics. As a result, Einstein separated Nernst’s theorem from the second principle and classified it as a third, independent principle. That interpretation has now been overturned.

In the demonstration presented, Professor Martín-Olalla introduces two nuances that were omitted by Nernst and Einstein: the formalism of the second principle of thermodynamics, on the one hand, requires the existence of the engine imagined by Nernst, and, on the other hand, that this machine be virtual; the engine does not consume any heat, does not produce any work, and does not question the second principle. The concatenation of both ideas allows us to conclude that entropy exchanges tend to zero when the temperature tends to zero (which is Nernst’s theorem) and that absolute zero is inaccessible.

Rethinking temperature and physical abstraction

Martin-Olalla points out, “a fundamental problem in thermodynamics is to distinguish the sensation of temperature, the sensations of hot and cold, from the abstract concept of temperature as a physical quantity. In the discussion between Nernst and Einstein, temperature was merely an empirical parameter: the absolute zero condition was represented by the condition that the pressure or volume of a gas became close to zero. Formally, the second principle of thermodynamics provides a more concrete idea of the natural zero of temperature. The idea is not related to any sensation, but to that engine imagined by Nernst but which has to be virtual. This radically changes the approach to the proof of the theorem.”

The study points out that the only general property of matter near absolute zero that cannot be related to the second principle of thermodynamics is the cancellation of heat capacities, also compiled by Nernst in 1912. However, Martin-Olalla proposes a different formalization: “The second principle contains the idea that entropy is unique at absolute zero. The cancellation of specific heats only adds that this unique value is zero. It seems more like an important appendix than a new principle.”

The professor at the University of Seville points out that the publication of this article is a first step towards the acceptance of this novel point of view: “The students on the thermodynamics course I teach were the first to learn about this demonstration. I hope that with this publication the demonstration will become better known, but I know that the academic world has a great deal of inertia.”

Reference: “Proof of the Nernst theorem” by Jose-María Martín-Olalla, 13 June 2025, The European Physical Journal Plus.
DOI: 10.1140/epjp/s13360-025-06503-w

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