What is a quantum afterburner

Günter Sturm, ScienceUp Sturm and Bomfleur GbR,
Camerloherstrasse 19, D-85737 Ismaning,
Quanten.de Newsletter, July 1st, 2003,
ISSN 1618-3770

Are you sitting at your desk with a steaming cup of coffee? Then I wish you the following does not happen: You accidentally bump into the cup, it falls down and breaks, whereby the coffee is distributed on the carpet. Something like that is annoying, but possible at any time. This can easily happen, and it may have happened to you yourself.

Has this already happened to you? The hot coffee on the carpet suddenly cools down. The resulting energy is used by the coffee to flow towards the cup, which also cools down and flies back onto the table with the coffee. Impossible, you say? Well, energetically not at all. If we assume that both the coffee and the cup cool down by 70 ° C, then - roughly estimated - the energy released is 1000 times the energy that would be required to "fly" back onto the desk. So it would be possible.

But it's unlikely. So unlikely that it has not happened anywhere in the universe since the existence of the universe. So there must be another quantity besides energy that determines the "course" of the universe. This size is called entropy.

What is this entropy and what are its effects? And what does all of this have to do with quantum mechanics? Read on, in this order we will cover the topic.

The third theory

Physical theories are valid until they have been refuted by experiments. Tests at the beginning of the last century showed that the mechanics - now called "classic" - fail with very small dimensions. A new theory was needed, quantum mechanics.

It was also shown that the classical mechanics are no longer correct for objects that move approximately at the speed of light. Einstein's theory of relativity replaces classical mechanics here. And although both theories cannot yet be combined in a new "unified" theory, both are considered correct today.

There is a third important theory that emerged about 100 years ago: The thermodynamics. This theory deals with the relationships between the macroscopic properties of systems. Quantities such as heat, work, energy and also entropy are used. And here, too, the following applies: There is nothing against this theory. With its system of partial differential equations, it is self-contained, even of "mathematical beauty".

One for all

Thermodynamics explains the course of all macroscopic phenomena - up to the end of the universe - with four main principles. The so-called zeroth law defines the temperature measurement. The first law is nothing else than the energy conservation law known from school: Energy can neither "be lost" nor be generated from "nothing". The second and third law describe entropy, that mysterious quantity that z. B. determines the course of chemical reactions, imposes a natural limit on the efficiency of heat engines and prevents our cup from flying.

Everything over and over again?

Three terms are important to understand entropy: the system, its environment and the processes between the two. The system is - to put it simply - the observed object (e.g. coffee cup with coffee) that is in contact with its environment (the rest of the universe). In certain processes, the system can exchange both energy (heat or work) and matter with the environment. Can such an exchange be reversed at any time? Can the same thing happen over and over again?

If so, one speaks of one reversible process. And this is where entropy comes in. If one writes the change in entropy of the entire universe delta SUniv as the sum of the entropy changes in the system delta SSyst and the environment (rest of the universe) delta SEnv, then for reversible processes:

However, a process is only reversible if the system is constantly in equilibrium with its environment, i.e. all processes take place in infinitely small steps. In practice, this means that the changes would have to take place infinitely slowly, although this sentence is not entirely correct in the "thermodynamic sense", since time is brought into play here. However, the cup suddenly falls and breaks, so this is an irreversible, irreversible process. The following applies here:

Overall, the following applies to the entire entropy in the universe for all processes (reversible and irreversible):

Entropy can only be created in the universe, but never destroyed. This distinguishes it from energy, which can neither be created nor destroyed.

At the end of the universe

It is not only through Douglas Adams that we know what is in store for us at the end of the universe. Thermodynamics also makes a statement here: The end of the universe is a state of maximum entropy, the so-called "heat death".

But the second law has other consequences than the heat death of the universe and the ban on coffee cups from flying. One of the most important is the impossibility of building a heat engine (thermal power station, car, refrigerator, ...) that does nothing but convert heat into work. When converting heat Q into work W, part of the heat - and thus also entropy - has to be transferred to a colder reservoir. Here, colder means colder than the system that does the work.

Entropy what are you

So far we have not yet been able to imagine anything descriptive under entropy. The statistical interpretation of thermodynamics, which interprets entropy as a degree of disorder, helps here. This explains the heat death of the universe as a state of maximum disorder in which all matter is evenly distributed in space. And our coffee cup problem becomes clear too: Coffee in the cup and cup on the desk: in good condition. Coffee on the floor, broken cup: there is disorder.

In order for the cup to fly back onto the table, all the atoms in the coffee and in the cup would have to give up their disordered heat movement, move in a certain direction, come together to form a cup of coffee and then fly onto the desk. Very, very unlikely.

What does all of this have to do with quantum mechanics?

Thermodynamics is not only compatible with quantum mechanics, it can even be combined. A separate theory, statistical thermodynamics, calculates the properties of macroscopic systems from the microscopic properties of the individual particles. The central term here is the sum of states, i.e. the sum of all possible quantum mechanical energy Ej of a system:

In principle, all other thermodynamic quantities such as energy or entropy can be calculated from this partition function Z.

No quantum mechanical peculiarities in thermodynamics?

But! This is shown by a recently presented theoretical model by physicist Marlan O. Scully [1] from Texas A&M University. Let us remember again the heat engine described above. The theoretically best possible efficiency of a heat engine can be given as a consequence of the second law as follows:

The efficiency is only determined by the temperature difference between the hot and cold reservoir. A single, isolated heat reservoir can never do any work; some of the heat always has to be dissipated to a colder reservoir. If both heat reservoirs are at the same temperature, the efficiency is zero.

Scully now presented a theoretical approach that could break this so-called "Carnot limit": The presented reversible and closed process works more efficiently than Carnot allows. His "photon steam engine" can work from one using the quantum mechanical coherence single Remove the heat reservoir. The role of steam is played by photons, the heat reservoir consists of hot atoms that exchange energy with the photons via emission and absorption processes. If quantum coherence is generated in the hot atoms, the temperature Tp from TH to be different. Therefore, in the case of TH = Tt, so off only one Heat reservoir, work to be done.

And the second law?

This still applies, also in quantum mechanics. The experiment does not violate the validity, since the generation of the coherence costs extra energy and entropy. So the whole entropy of the system also increases with a photon steam engine. The only special thing here is that work is done by a single heat reservoir.

However, this would make it entirely conceivable that a quantum heat engine as a "quantum afterburner" would one day increase the efficiency of internal combustion engines.

Günter Sturm


[1] "Extracting Work from a Single Heat Bath via Vanishing Quantum Coherence", Marlan O. Scully, M. Suhail Zubairy, Girish S. Agarwal, Herbert Walther, Science 299, 862-864 (2003).

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© 2003 ScienceUp Sturm und Bomfleur GbR, all rights reserved. Non-commercial reprinting and reproduction permitted provided the source is acknowledged ScienceUp Sturm und Bomfleur GbR, www.ScienceUp.de

Get interested? As an introduction to thermodynamics, I recommend the following two textbooks in physical chemistry, which are aimed at students of chemistry and other natural sciences in their first semesters. In addition to thermodynamics (from a predominantly chemical point of view), both books also offer a basic introduction to quantum physics.

Ira N. Levine
"Physical Chemistry"

Hardcover, McGraw-Hill Companies 2001, ISBN 0072534958
More information at Amazon.de

Peter W. Atkins
"Physical chemistry"

Hardcover, Wiley-VCH 2001, ISBN 3527302360
More information at Amazon.de