Rigorous results on approach to thermal equilibrium, entanglement, and nonclassicality of an optical quantum field mode scattering from the elements of a non-equilibrium quantum reservoir
Bibliographic record
Abstract
Rigorous derivations of the approach of individual elements of large isolated systems to a state of thermal equilibrium, starting from arbitrary initial states, are exceedingly rare. This is particularly true for quantum mechanical systems. We demonstrate here how, through a mechanism of repeated scattering, an approach to equilibrium of this type actually occurs in a specific quantum system, one that can be viewed as a natural quantum analog of several previously studied classical models. In particular, we consider an optical mode passing through a reservoir composed of a large number of sequentially-encountered modes of the same frequency, each of which it interacts with through a beam splitter. We then analyze the dependence of the asymptotic state of this mode on the assumed stationary common initial state <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>&#x03C3;</mml:mi></mml:math> of the reservoir modes and on the transmittance <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>&#x03C4;</mml:mi><mml:mo>=</mml:mo><mml:mi>cos</mml:mi><mml:mo>&#x2061;</mml:mo><mml:mi>&#x03BB;</mml:mi></mml:math> of the beam splitters. These results allow us to establish that at small <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>&#x03BB;</mml:mi></mml:math> such a mode will, starting from an arbitrary initial system state <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>&#x03C1;</mml:mi></mml:math>, approach a state of thermal equilibrium even when the reservoir modes are not themselves initially thermalized. We show in addition that, when the initial states are pure, the asymptotic state of the optical mode is maximally entangled with the reservoir and exhibits less nonclassicality than the state of the reservoir modes.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".