If the mind is a heat engine, what work does it do?
The Landauer-Bennett Principle describes the minimal energy cost of maintaining a logical distinction against ambient temperature by the formula kTln2, in effect making the maintenance of a logical distinction the work of a heat engine.
The origin of computational thermodynamics can be traced to Szilard's single gas molecule model of the bit. Work can be extracted from a division of the phase space of the single gas molecule if one has knowledge of which side of the division the molecule is on. Szilard's bit model emphasizes the logical distinction of the R or L placement of the piston direction. Knowledge of this binary distinction can be applied as a piston shaft which converts the logical distinction (the division of the phase space) to a physical compression of a piston head that can perform work.
These actions of making a measurement, and inserting a division, compress the phase space of the gas while generating one bit of information. A coupled memory storage device undergoes a similar compression of the information storage capacity phase space. There is no known lower limit to the energy costs of these actions. As the gas molecule performs work on the piston head, the coupled information storage phase space loses compression. Resetting the memory involves purging entropy to the environment. The energy cost kTln2 is incurred in resetting (recompressing) the memory register.
Objects which continue to perform work over time, such as biological objects, must repeatedly expel entropy to the environment, and therefore must exist in an open system energy gradient. Such objects form the subject of dissipative systems.
For those interested in further notes on brain, computation, and thermodynamics, see papers posted on my blog