Two advances would be crucial to solving Maxwell’s demon.
The first was by the American mathematician Claude Shannon, regarded as the founder of information theory. In 1948, Shannon showed that the information content of a message could be quantified with what he called the information entropy. “In the 19th century, no one knew about information,” said Takahiro Sagawa, a physicist at the University of Tokyo. “The modern understanding of Maxwell’s demon was established by Shannon’s work.”
The second vital piece of the puzzle was the principle of erasure. In 1961, the German American physicist Rolf Landauer showed that any logically irreversible computation, such as the erasing of information from a memory, would result in a minimal nonzero amount of work converted into heat dumped into the environment, and a corresponding rise in entropy. Landauer’s erasure principle provided a tantalizing link between information and thermodynamics. “Information is physical,” he later proclaimed.
Maxwell’s demon was at core an information-processing machine: It needed to record and store information about individual particles in order to decide when to open and close the door.
https://www.quantamagazine.org/how-maxwells-demon-continues-to-startle-scientists-20210422/