The demonless quantum Szilard engine of Aydin, Sisman, and Kosloff shows that even without a Maxwell's demon, the logically irreversible localization of the working particle by quantum measurement carries the Landauer cost and saves the second law; their analysis was restricted to a single particle in a symmetric box operated quasistatically. The open problem is to extend that complete Landauer-consistent thermodynamic account of the demonless cycle to the regimes the source analysis did not cover: many-particle working fluids obeying Bose-Einstein or Fermi-Dirac statistics with quantum degeneracy and chemical potential (including when partition removal ceases to be trivial), asymmetric partition placement and confinement shape effects, adiabatic and sudden (non-quasistatic) protocols, and realistic rectification devices in which the microscopic loci of the implicit-erasure entropy production can be identified. The multi-particle quantum-statistics question has so far been answered only for demon-assisted engines, leaving the demonless extensions open.

Background

Szilard's engine is a thought experiment in which a single gas molecule is confined in a box, a partition is inserted in the middle, and an observer (Maxwell's demon) measures which side the molecule is on; knowing the outcome, the molecule is allowed to expand isothermally against the partition and convert heat from a single thermal bath into kTln⁡2kT\ln 2 of work (with kk Boltzmann's constant and TT the bath temperature). The apparent violation of the second law is resolved by Landauer's principle, the statement that erasing one bit of information dissipates at least kTln⁡2kT\ln 2 of heat, which the demon must pay to reset its memory. A quantum Szilard engine treats the working substance quantum-mechanically; the founding analysis of Kim, Sagawa, De Liberato, and Ueda (PRL 2011) derived the extractable work for an arbitrary number of particles with quantum statistics and showed that insertion and removal of the partition are genuine thermodynamic processes with their own energy costs. Aydin, Sisman, and Kosloff (Entropy 22, 294, 2020) analyzed a demonless variant: no which-side information is acquired or used, yet heat is still dissipated, because work extraction requires the particle to be localized on one side, and localization by quantum measurement (a projective measurement collapsing the superposition of 'left' and 'right' into one outcome) is itself a logically irreversible operation carrying the Landauer cost. They argued that any demonless engine needs rectification — the conversion of bidirectional particle motion into unidirectional work output — and that rectification always implies implicit erasure: the rectifying many-to-one map from the two opposite microscopic outcomes (left/right, or opposite current phase) onto a single work output destroys the information that distinguishes them and therefore must generate entropy, in contrast to the explicit resetting of a stored memory bit that Landauer's principle prices. Their work and heat expressions include quantum-confinement corrections via the quantum boundary layer framework (a systematic description of the layer near a wall in which wave-function depletion modifies the density of states and hence all thermodynamic quantities of a confined gas). For indistinguishable particles, Bose-Einstein statistics (any number of particles per state, valid for bosons) and Fermi-Dirac statistics (at most one particle per single-particle state, valid for fermions) must replace Maxwell-Boltzmann statistics; in degenerate regimes the chemical potential, the free-energy derivative with respect to particle number, enters the bookkeeping explicitly. Prior multi-particle results exist only for demon-assisted engines: Cai, Dong, and Sun (PRE 2012) gave a fully quantum multi-particle treatment with a demon whose memory is erased, Bengtsson et al. (2017) showed enhanced work for attractive bosons, and Zhuang and Liang (2014) treated arbitrary spin. Finite-time operation was likewise studied only with a demon performing a finite-time measurement (Zhou, Ma, Sun, 2024). The demonless single-particle quasistatic symmetric analysis therefore stands alone, and its authors explicitly flagged its extensions — quantum statistics, degeneracy, asymmetric insertion, non-quasistatic protocols, and concrete rectification devices — as open.

Problem Statement

Extend the demonless quantum Szilard engine analysis of Aydin, Sisman, and Kosloff beyond the single-particle, symmetric, quasistatic box: a complete Landauer-consistent quantum-thermodynamic account of the demonless cycle in the regimes it did not cover. Specifically: (1) Many-particle working fluids of indistinguishable particles obeying Bose-Einstein or Fermi-Dirac statistics: determine the energetics of partition insertion, localization by measurement, expansion, and partition removal per cycle, including quantum-confinement corrections modified by quantum statistics, the role of degeneracy entering through the chemical potential, and the conditions under which partition removal ceases to be thermodynamically trivial; (2) asymmetric partition placement and confinement-shape effects: quantify how they alter the work and heat exchanges relative to the symmetric case; (3) non-quasistatic protocols: characterize what new features adiabatic and sudden (as opposed to quasistatic) insertion, measurement, expansion, and removal introduce into the work, heat, and entropy balances; and (4) rectification and implementation: the source analysis deliberately treated the abstract conceptual engine rather than physical realizations, while arguing that any demonless engine needs rectification and that rectification always implies implicit erasure; extending the thermodynamic account toward realistic rectifying work-extraction devices — including where in such devices the entropy production constituting the implicit erasure microscopically arises — remains open. In every extension, the analysis must state how the localization cost and the kTln⁡2kT\ln 2-per-bit Landauer bookkeeping are modified by quantum statistics and degeneracy, and must reduce in the appropriate limits to the single-particle quasistatic demonless result and agree with the demon-assisted multi-particle analyses (Kim et al. 2011; Cai et al. 2012) on the subprocess energetics shared with them (insertion, removal, and measurement-localization costs under quantum statistics). These four extensions are the constituent regimes of the single complete account requested here.

References

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