Martingale drift of Langevin dynamics and classical canonical spin statistics.
basic_science · Level V
Where this comes from
- Record sourced from PubMed, PMID 38366522.
- Also identified by DOI 10.1103/PhysRevE.109.014106.
- No licence information is recorded for this record.
- Because redistribution is not established, this page shows the abstract only. Follow the links below for the full text.
Abstract
A martingale is a stochastic process that encodes a kind of fairness or unbiasedness, which is associated with a reference process. Here we show that, if the reference process x_{t} evolves according to the Langevin equation with drift a(x) and if a(x_{t}) is a martingale, then its amplitude is the Langevin function, which originally described the canonical response of a single classical Heisenberg spin under static field. Furthermore, the asymptotic limit of x_{t}/t obeys the ensemble statistics of such a Heisenberg spin.