@article{0b8033f0b13c441b9737b720d5944148,
title = "Entropic turnpike estimates for the kinetic Schr{\"o}dinger problem",
abstract = "We investigate the kinetic Schr{\"o}dinger problem, obtained considering Langevin dynamics instead of Brownian motion in Schr{\"o}dinger{\textquoteright}s thought experiment. Under a quasilinearity assumption we establish exponential entropic turnpike estimates for the corresponding Schr{\"o}dinger bridges and exponentially fast convergence of the entropic cost to the sum of the marginal entropies in the long-time regime, which provides as a corollary an entropic Talagrand inequality. In order to do so, we benefit from recent advances in the understanding of classical Schr{\"o}dinger bridges and adaptations of Bakry–{\'E}mery formalism to the kinetic setting. Our quantitative results are complemented by basic structural results such as dual representation of the entropic cost and the existence of Schr{\"o}dinger potentials.",
keywords = "Langevin dynamics, Schr{\"o}dinger problem, gamma calculus, long-time behavior of entropic cost, turnpike estimates",
author = "Alberto Chiarini and Giovanni Conforti and Giacomo Greco and Zhenjie Ren",
year = "2022",
doi = "10.1214/22-EJP850",
language = "English",
volume = "27",
journal = "Electronic Journal of Probability",
issn = "1083-6489",
publisher = "Institute of Mathematical Statistics",
}