Conditioning, Correlation and Entropy Generation in Maxwell’s Demon

Abstract

Maxwell's Demon conspires to use information about the state of a confined molecule in a Szilard engine (randomly frozen into a state subspace by his own actions) to derive work from a single-temperature heat bath. It is widely accepted that, if the Demon can achieve this at all, he can do so without violating the Second Law only because of a counterbalancing price that must be paid to erase information when the Demon's memory is reset at the end of his operating cycle. In this paper, Maxwell's Demon is analyzed within a "referential" approach to physical information that defines and quantifies the Demon's information via correlations between the joint physical state of the confined molecule and that of the Demon's memory. On this view, which received early emphasis in Fahn's 1996 classical analysis of Maxwell's Demon, information is erased not during the memory reset step of the Demon's cycle, but rather during the expansion step, when these correlations are destroyed. Dissipation and work extraction are analyzed here for a Demon that operates a generalized quantum mechanical Szilard engine embedded in a globally closed composite, which also includes a work reservoir, a heat bath and the remainder of the Demon's environment. Memory-engine correlations lost during the expansion step, which enable extraction of work from the Demon via operations conditioned on the memory contents, are shown to be dissipative when this decorrelation is achieved unconditionally so no work can be extracted. Fahn's essential conclusions are upheld in generalized form, and his quantitative results supported via appropriate specialization to the Demon of his classical analysis, all without external appeal to classical thermodynamics, the Second Law, phase space conservation arguments or Landauer's Principle.

Conditional Action and Imperfect Erasure of Qubits

“…There exists a vast amount of literature on Maxwell's demon and related questions [10,11,20]. Among them is an article that comes rather close to the results of the present work, namely [21], that deals with Szilard's engine and where we read in the abstract:…”

Conditional Action and imperfect Erasure of Qubits

“…There exists a vast amount of literature on Maxwell's demon and related questions [19]. Among them is an article that comes rather close to the results of the present work, namely [15], that deals with Szilard's engine and where we read in the abstract:…”

“…Following [4] we want to explicitly construct a measurement dilation of J of the form (15), see also the analogous construction for a Maxwell instrument in [1].…”

Comment on ‘A note on heat reservoirs and the like’

“…This implies that all intensive variables in the surroundings are spatially uniform, an idealization which is at the core of the definition of reservoir in thermodynamics, the distinction between a work reservoir and heat reservoir being related with its entropy. A work reservoir does not change its entropy as it interacts with the system [6,7], unlike a heat reservoir which interacts with the system by experiencing an entropy variation S e D given by [5,6]…”