Maxwell's demon

The Maxwell demon or Maxwell demon is a thought experiment published in 1871 by the Scottish physicist James Clerk Maxwell , with which he questions the Second Law of Thermodynamics . The dilemma that resulted from this thought experiment was worked on by many well-known physicists (e.g. Feynman ) and led to new insights several times. There was a relationship between information and energy, similar to the relationship between mass and energy in Einstein's formula . The minimum energy to process bits of information, is ( the ${\ displaystyle E = mc ^ {2}}$ ${\ displaystyle E}$ ${\ displaystyle n}$ ${\ displaystyle E = nkT \ ln 2}$ ${\ displaystyle k}$ Boltzmann constant and the absolute temperature of the system). Even today, Maxwell's demon inspires theoretical physics . Outside of physics, Maxwell's demon also found its way into art because of the fascination that this dilemma creates. ${\ displaystyle T}$

The dilemma of the Maxwellian demon

The “demon” opens and closes the flap to allow particles of greater speed (red) from A to B and smaller particles (blue) from B to A.

The original thought experiment describes a container that is divided by a partition that contains a small closable opening. Both halves contain air initially at the same temperature . A being that can “see” the molecules - it was later called a demon - opens and closes the connecting opening so that the fast molecules collect in one half of the container and the slow molecules in the other.

Under ideal conditions, no energy has to be expended to open and close the opening in the partition wall. Nevertheless, one could use the resulting temperature difference z. B. operate a heat engine . One would thus work do and would at the same time compared to the initial state ultimately no further change except for a reduction in the temperature in the tank. This would violate the second law of thermodynamics (“It is impossible to construct a periodically working machine that does nothing more than lift a load and cool a heat reservoir.”) And a perpetual motion machine of the second kind would have been found.

Attempted solutions

James Clerk Maxwell 1871

Maxwell himself saw in the problem he created only a clear indication of the fact that the second law is statistical in nature, i.e. only applies in the macroscopic range. If the total number of molecules is chosen to be small enough, it is even likely that there will be significant temperature differences between the two halves of the container, even if the connection is constantly open.

Lord Kelvin 1874

William Thomson , who later became Lord Kelvin, introduced the term “Maxwell's demon” and recognized that the critical thing about his occupation is “sorting”, which can also be achieved in other ways (cf. sedimentation ). In addition to the original “temperature demon”, he postulated the possibility of other demons, e.g. B. convert thermal energy directly into kinetic energy by sorting according to the direction of movement, separate salt solutions into concentrated solutions and pure water or gas mixtures according to individual gases. Everywhere he saw in this sorting the reversal of the “natural” process of dissipation .

Even Max Planck and other busy at this time with the Maxwell's demon. In general, it was simply thought of as "unnatural" and considered the problem to be settled, or at least purely academic. After all, he had brought some clarity to the thermodynamics that had just emerged .

But Maxwell had raised a bigger problem than had been realized by then. With the dynamics of the molecules and with the help of statistics it could be explained why thermodynamic processes take place spontaneously in their “natural” direction. But why it shouldn't be possible to force such a process with the skilful use of technical means in the opposite direction could not be explained. The second law, which is only an empirical proposition, demands exactly this irreversibility.

Leó Szilárd 1929

In 1929 Szilárd presented a sensational habilitation on the reduction of entropy in a thermodynamic system during interventions by intelligent beings . He first radically simplified the model by reducing it to a single molecule. In this model, the being brings in the partition (which is now more of a piston) when the molecule is in a predetermined half of the container. The molecule now pushes the piston partition outwards and does work on a weight. Heat is absorbed from the environment so that the temperature remains the same. Then the cycle repeats itself. With each cycle, the heat of the environment decreases while the potential energy of the weight increases by the same amount. On the other hand, for each cycle the being must first take a measurement by observing one half of the container: is the molecule in it or not? Binary information is thus obtained through the measurement. This information must be retained in a memory, at least for a short time.

The matter was now manageable. The entity's only interaction with the one-molecule gas is measurement. So that the second law is not violated, the thermodynamic entropy reduction can only be compensated for by generating entropy of the same amount through the measurement. The amount of entropy calculated Szilárd to from the thermodynamic processes , with the Boltzmann - constant . ${\ displaystyle S}$ ${\ displaystyle S = k \ cdot \ ln 2}$ ${\ displaystyle k}$

This means that the information stored with the measurement had to contain this entropy in some form . This was the first time, although it was still rather vague, there was talk of an entropy of information . The Maxwellian demon had contributed to the foundation of information theory. Szilárd has not yet been able to determine exactly where in the system of measurement, information and storage the entropy is to be found. ${\ displaystyle S = k \ cdot \ ln 2}$

Léon Brillouin 1951

Brillouin asked more precisely in 1951 about the measurement, the "seeing" of the demon. Seeing in the literal sense ultimately means scanning the molecules with light, even if completely different wavelengths are conceivable. Taking into account the quantum nature of light, this scanning means the interaction of two particles, a molecule and a photon, through collision. Brillouin was able to show relatively easily that with this collision there is always enough entropy released to keep the Second Law, if it is assumed that the energy of the photons must be large enough to be able to provide the demon with information at all. The demon seemed to have been settled, and Szilárd's still open question about the exact location of the entropy generation was resolved in an unspectacular manner.

Brillouin went further in his interpretation, however, he saw the photons as a transmitter of ("bound") information and for the first time postulated a direct connection between the entropy of information introduced by Shannon in 1948 and thermodynamic entropy, for which he multiplied Shannon's entropy by a constant. He then formulated the “negentropy principle of information”, which remained controversial: the information itself is negative entropy (negentropy) and causes a corresponding increase in entropy in the gas in the sense of conservation. The demon can then at most just compensate for this.

However, the requirement of measuring with photons turned out to be too severe a restriction that could also be circumvented.

Rolf Landauer and Charles Bennett 1961/1982

Landauer was not concerned with Maxwell's demon, but with information storage. In 1961 he was able to show on the model of a potential pot that the deletion - in the sense of resetting to a rewritable state - of a bit of physically stored information always has to release the already known entropy , known today as the Landauer principle . He made a connection to the logical irreversibility of the deletion operation. Logically reversible operations such as writing and reading, on the other hand, do not cause any entropy or energy release. This proved a physical connection for what Brillouin had called physically irrelevant “free” information. But only Charles Bennett showed in 1982 that with the application of the Landauer principle to the memory of Maxwell's demon, the exact missing entropy is fed back into the gas in order to fulfill the Second Law, while on the other hand the measurement can be carried out with as little dissipation as desired. According to Bennett, the swinging door of the Maxwellian swinging door demon is forced to swing after a gas particle has passed the door. Just as the closed door causes a gas particle to pass in what appears to be the "correct" direction, the swinging door causes a gas particle to pass in the opposite direction. The swinging door represents a state of local overheating. The excess energy releases it preferably by accelerating the gas particle in the opposite direction. The proportion of closed doors to swinging doors is independent of the gas density ( Boltzmann statistics ). ${\ displaystyle k \, \ ln 2}$

Orly R. Shenker sees in a detailed analysis of Landauer's theses from the year 2000 various errors in Landauer's argument, which could be traced back to an inadmissible equation of the dissipation concepts of information theory and thermodynamics. It indicates that the Landauer principle is based on the second law of thermodynamics. Since by solving the problem of Maxwell's demon the validity of the Second Law is to be proved, an inadmissible circular reference arises . Bennett and Landauer do not refute Maxwell's demon in the sense that they prove the validity of the Second Law also for Maxwell's demon, but they show exactly where the Maxwell's demon violates the Second Law.

Oliver Penrose 1970

Penrose dealt with Maxwell's demon in 1970 and, without knowing Landauer's work, even before Bennett came to the same conclusion with a statistical argument on entropy: If the memory of the demon is full, it can only be used again after it has been reset. This reduces the possible states of the overall system. The application of a statistical entropy definition to the memory then also leads to Landauer's result.

literature

Charles H. Bennett : Maxwell's Demon Spectrum of Science, Jan 1988, p. 48.
James Clerk Maxwell : Theory of Heat. 1871
Harvey S. Leff (Eds.), Andrew F. Rex (Eds.): Maxwell's Demon 2: Entropy, Classical and Quantum Information, Computing. Institute of Physics Publishing, Bristol 2003, ISBN 0-7503-0759-5

Web links

Commons : Maxwell's demon - collection of images, videos and audio files

Orly R. Shenker: Logic and Entropy. (2000)

Individual evidence

↑ z. B. in the novel Homo faber by Max Frisch

[1] z. B. in the novel Homo faber by Max Frisch