Non-equilibrium stationary states from the equation of motion of open systems
Bibliographic record
Abstract
A BBGKY-like hierarchy is derived from the non-equilibrium Redfield equation. Two further approximations are introduced and each can be used to truncate and solve the hierarchy. In the first approximation such a truncation is performed by replacing two-particle Green's functions (GFs) in the hierarchy by their values at equilibrium. The second method is developed based on the cluster expansion, which constructs two-particle GFs from one-particle GFs and neglects the correlation part. A non-equilibrium Wick's Theorem is proved to provide a basis for this non-equilibrium cluster expansion. Using those two approximations, our method of solving the Redfield equation, for instance, of an N-site chain of interacting spinless fermions, involves an eigenvalue problem with dimension $2^{N}$ and a linear system with dimension $N^2$ in the first case, and a nonlinear equation with dimension $N^2$ in the second case, which can be solved iteratively via a sequence of $N^2$ linear systems. Other currently available direct methods correspond to a linear system or an eigenvalue system with dimension $4^N$ plus an eigenvalue system with dimension $2^N$. As a test of the methods, for small systems with size N=4, results are found to be consistent with results made available by other direct methods. Although not discussed here, extending both methods to their next levels is straightforward. This indicates a promising potential for this BBGKY-like approach of non-equilibrium kinetic equations.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| 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".