Maxwell's demon

The Maxwellian demon or Maxwell's demon is a by Scottish physicist James Clerk Maxwell in 1871 published a thought experiment similar to Laplace's demon, with whom he is the second law of thermodynamics in question. The dilemma that resulted from this thought experiment, was by many famous physicists worked (for example Feynman ) and repeatedly led to new insights. 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 information bit is, (the Boltzmann constant and the absolute temperature of the system ). Even today, inspired the Maxwellian demon theoretical physics. Outside of physics was the Maxwellian demon because of the fascination that triggers this dilemma, even into art.

The dilemma of the Maxwell's demon

The original thought experiment describes a container which is divided by a partition which contains a small closable opening. Both halves contain air of the same temperature initially. A being that can "see" the molecules can - the name demon got it later - opens and closes the connection opening so that gather the fast molecules in one hand and the slow molecules in the other half of the container.

Under ideal conditions, must be applied to open and close the opening in the partition wall, no energy. Could still operate with the resulting difference in temperature, for example, a heat engine. It would thus have to do work, and at the same time relative to the initial state, no further change other than the end of a lowering of the temperature in the container. Thus, the second law of thermodynamics would be ( "It is impossible to construct a cyclically operating machine that causes nothing more than raising a load and cooling of a heat reservoir. " ) Violated and you would have found a perpetual motion machine of the second kind.

Solution attempts

James Clerk Maxwell in 1871

Maxwell himself looked into the problem created by him only a clear indication of the fact that the second law is statistical in nature, so is only valid at the macroscopic level. If you choose the total number of molecules small enough, it is even likely that even with constantly open connection temporarily significant temperature differences between the two container halves occur.

Lord Kelvin in 1874

William Thomson, later Lord Kelvin, introduced the term " Maxwell's demon" and realized that this is critical to its employment in the "Sort", which can be realized in other ways ( cf. sedimentation). It addition to the original " temperature demon " postulated the possibility of other demons that transform into kinetic energy eg heat energy by sorting on the direction of motion directly, separate salt solutions in concentrated solution and pure water or gas mixtures for individual gases. Everywhere he saw in this Order, the reversal of the "natural" process of dissipation.

Even Max Planck and others employed at that time with the Maxwell's demon. In general, you just thought he was "unnatural" and looked at the problem with it as completed or at least purely academic. After all, he had brought some clarity in his newly formed thermodynamics.

But Maxwell had a more fundamental issue raised when it was discovered by then. With the dynamics of the molecules and with the help of statistics could be explained though why thermodynamic processes occur spontaneously in their "natural " direction. Why it should not be possible, however, to enforce such a process with skilful use of technical means in the opposite direction, so that was not to explain. The second law, which is only an empirical law, but requires exactly this irreversibility.

Leo Szilard 1929

Szilárd put 1929 in front of a sensational Habilitation About the Decrease of Entropy in a Thermodynamic System by the Intervention of intelligent beings. He simplified the model initially radically by reducing it to a single molecule. The nature brings in this model, the partition (which is now more like a piston ) when the molecule is located in a predetermined one-half of the container. The molecule now pushes the piston dividing wall to the outside and done this work on a weight. This heat is absorbed from the environment, so that the temperature remains the same. Then the cycle repeats. With each cycle reduces ambient heat, while the potential energy of the weight increases by the same amount. The other hand, must first perform a measurement by observing a half of the container for each cycle, the nature: If the molecule is not? Thus, by measuring binary information is obtained. This information must be recorded in a memory, at least in the short term.

The matter was now manageable. The only interaction of the substance with the one-molecule gas is the measurement. The thermodynamic Entropieverringerung can, so the second law is not violated, are thus compensated for by an entropy production of the same amount by the measurement. The value of this entropy S calculated Szilárd from the thermodynamic processes to S = k ln 2, with the Boltzmann constant k

This means that the stored measurement information to the S = k · ln some form of these 2 had include entropy. This was for the first time, albeit still quite blurred, of an entropy of information the speech. The Maxwellian demon had contributed to the basis of information theory. Where the entropy is to be found precisely in the system of measurement, information and memory, Szilárd was not yet set.

Léon Brillouin 1951

Brillouin asked in 1951 precisely after the measurement, the "seeing" of the demon. See in the literal sense ultimately means a sampling of molecules with light, even if all other wavelengths are also possible. This sampling means taking into account the quantum nature of light, the interaction of two particles, a molecule and a photon, by impact. Brillouin could now relatively easy to show that in this bumper getting enough entropy is free to comply with the second law, if it is assumed that the energy of the photon must be large enough to deliver the demon general information can. The demon seemed done that yet clear open question about the exact location of the entropy in an unspectacular way in Szilárd.

Brillouin went further in his interpretation, however, he saw the photon as a transmitter of ( " bound " ) information and postulated for the first time a direct link between the imported Shannon entropy of information and thermodynamic entropy, 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 in the sense of preserving a corresponding entropy increase in the gas. The demon can more than compensate for this again just then.

However, the requirement of the measurement with photons proved excessive restriction which could also be avoided.

Rolf Landauer and Charles Bennett 1961/1982

Landauer not dealt with the Maxwell's demon, but with information storage. He was able to show in 1961 on the model of a potential well that deleting - in the sense of resetting in a rewritable state - a bit physically stored information is always the previously known entropy must release, now known as Landauer principle. He set a context for the logical irreversibility of the erase operation forth. Logically reversible operations such as writing and reading, however, cause no entropy or energy release. In order for a physical relationship was for what had Brillouin physically irrelevant called "free" information detected. But it was Charles Bennett showed in 1982 that the application of the Landauer principle to the memory of Maxwell's demon, the gas exactly the missing entropy is again supplied to satisfy the second law, while on the other hand, the measurement can be performed with as little dissipation. According to Bennett, the swinging door of Maxwell's demon - swinging doors must swing forcibly after a gas particle has passed through the door. Just as the closed door causes the passage of a gas particle in the seemingly " right" direction, causes the swinging door to the passage of a gas particle in the opposite direction. The swinging door is a localized overheating condition represents the excess power is preferably used in the particle acceleration of the gas in the opposite direction. The proportion of closed doors to swinging doors is independent of the gas density ( Boltzmann statistics ).

Orly R. Shenker provides a detailed analysis of Landauer's theses from 2000, several errors in reasoning landau, which could be especially an illegal equating the Dissipationsbegriffe of information theory and thermodynamics lead back. She points out that the Landauer principle is based on the second law of thermodynamics. Since the validity of the second law to be proved by the solution of the problem of Maxwell's demon, arises an illegal circular reference. Bennett and Landauer so do not refute Maxwell's demon, in the sense that they prove the validity of the second main theorem for Maxwell's demon, but show it is repugnant exactly where Maxwell's demon against the 2nd law.

Oliver Penrose 1970

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