Computing Entropy: Understanding Maxwell's Demon

In 1871, James Clerk Maxwell proposed that a being, able to measure the microscopic parameters of a physical system and act accordingly, might be able to violate the Laws of Thermodynamics. The being became known as Maxwell's Demon. Investigations conducted over the course of a century have placed well-de ned thermodynamic bounds upon the action of Maxwell's demon. It is the purpose of this work to review those investigations which fall in the information theoretic domain. Special attention is paid to algorithmic information theory as it applies to the characterization of information contained in the physical microstate. Logical irreversibility and missing information are also examined in order to derive limits upon the actions of Maxwell's demon and to reformulate entropy from the point of view of devices capable of measuring and manipulating physical systems.