The Szilard engine

Leo Szilard introduced his famous model more than 60 years after Maxwell introduced his intelligent being. Szilard simplified the problem in two ways: He reduced the macroscopic gas of Maxwell to a single molecule, and the demon’s sorting was based on its location rather than its speed. Szilard’s engine is

The four-step Szilard engine described in the text

Figure 9.2: The four-step Szilard engine described in the text. The small rectangles show the memory state at each step. N is the standard state and (R.L) denote that the molecule is in the (right, left) sides of the partition.

depicted in Fig. 9.2, and it acts as a pressure demon. It creates a pressure differential that can be used to do work on an external load, e.g., by lifting a weight as shown in parts (c) and (d) of Fig. 9.2.

Step 0 of the Szilard engine cycle has the entire volume V of a cylinder is available to the molecule, as shown in Fig. 9.2(a). The small, upper-right rectangle labeled N represents the demon’s memory state N, which stands for no data. The four steps of the engine are:

  • 1. (a) —> (b). A partition is placed into the cylinder, dividing it into two equal chambers. The memory state remains N.
  • 2. (b) —> (c). The demon determines the side in which the molecule resides. The molecule is shown in the right in Fig. 9.2(b) and (c). The demon’s measurement is recorded and the memory state is now R.
  • 3. (c) —» (d). The partition is replaced by a piston, and the recorded result is used to couple the piston to a load, namely a weight (shown here pulling the piston rightward) that is lifted by work W. In this process, the gas pushes the piston to the left end of the cylinder. The energy lost by the gas is replenished by a heat process moving energy Q = W from an energy reservoir at constant temperature to the gas during the volume expansion. The memory state remains R.
  • 4. (d) —> (a). The partition is removed and the demon’s memory state is changed to N. In addition, the pulley configuration constitutes a second memory of the side the molecule was in after piston placement in (b) and the pulley must be removed. This erases that second memory.

Key Point 9.4 Repeating the process ad infinitum, using the Szilard engine, a Maxwell’s demon could convert an arbitrary amount of energy via a heat process, to work lifting a weight. This would violate the Kelvin-Planck form of the second law of thermodynamics, converting energy from a single reservoir completely to work.

There are a number of loose ends and nuances of the Szilard engine that should be mentioned.

  • 1. For the Szilard engine cycle, the load must be varied continually, e.g., using grains of sand, matching the average force on the piston by the molecule to keep the process slow and quasistatic. Szilard and most subsequent researchers did not mention the need for a variable load.
  • 2. Just how the demon determines which chamber the molecule is in after partition placement is not specified.
  • 3. A one-molecule gas is not an everyday occurrence and is not macroscopic. Thus, applying normal thermodynamics is questionable.
  • 4. A demon is a physical entity that presumably contains sufficiently many molecules to possess a temperature. If it continually receives energy input via light signals (or other means), its temperature will rise unless it transfers energy to its surroundings. This would confound the basic puzzle, and such energy exchanges are usually neglected.
  • 5. If a lamp is used to generate light signals, photons that miss the demon will heat up the gas and or container walls. Such phenomena threaten the assumption of constant-temperature operation, and most treatments of Maxwell’s temperature-demon ignore these details.

Despite such concerns, the Szilard model has been taken seriously and has been the subject of many research articles for over 90 years.

Szilard observed: “One may reasonably assume that a measurement procedure is fundamentally associated with a certain definite average entropy production, and that this restores concordance with the second law. The amount of entropy generated by the measurement may, of course, always be greater than this fundamental amount, but not smaller.” He further identified the “fundamental amount” to be />• In 2. His observation was the beginning of information theory. Interestingly, as discussed in the next section, it is now believed it is not measurement that must generate sufficient entropy to prevent violation of the second law of thermodynamics, but rather erasure of the information recorded by that measurement.

The ingenuity of Szilard’s engine is striking. It allows thermodynamic analysis and interpretation, and also entails a binary decision process. Thus, long before the existence of modern information ideas and the computer age, Szilard had the foresight to focus attention on the information associated with a binary process. In doing so he discovered the binary digit, or ‘bit’ of information. Szilard’s observation that an inanimate device could effect the required tasks - obviating the need to analyse the thermodynamics of complex human observers, was a precursor to cybernetics.

Key Point 9.5 Although Szilard did not fully solve the Maxwell’s demon puzzle through his one-molecule gas, he identified the three central issues of information gathering as we understand them todaymeasurement, information, and memory—and he established the underpinnings of information theoi'y and its connections with physics.

 
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