Entropic Fluctuations in Statistical Mechanics II. Quantum Dynamical Systems
Bibliographic record
Abstract
Abstract The celebrated Evans–Searles, respectively Gallavotti–Cohen, fluctuation theorem concerns certain universal statistical features of the entropy production rate of a classical system in a transient, respectively steady, state. In this paper, we consider and compare several possible extensions of these fluctuation theorems to quantum systems. In addition to the direct two-time measurement approach whose discussion is based on Benoist et al. (Lett Math Phys 114:32, 2024. https://doi.org/10.1007/s11005-024-01777-0 ), we discuss a variant where measurements are performed indirectly on an auxiliary system called ancilla, and which allows to retrieve non-trivial statistical information using ancilla state tomography. We also show that modular theory provides a way to extend the classical notion of phase space contraction rate to the quantum domain, which leads to a third extension of the fluctuation theorems. We further discuss the quantum version of the principle of regular entropic fluctuations, introduced in the classical context in Jakšić et al. (Nonlinearity 24:699, 2011. https://doi.org/10.1088/0951-7715/24/3/003 ). Finally, we relate the statistical properties of these various notions of entropy production to spectral resonances of quantum transfer operators. The obtained results shed a new light on the nature of entropic fluctuations in quantum statistical mechanics.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.005 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".