Two refreshing views of Fluctuation Theorems through Kinematics Elements and Exponential Martingale

In the context of Markov evolution, we present two original approaches to obtain Generalized Fluctuation-Dissipation Theorems (GFDT), by using the language of stochastic derivatives and by using a family of exponential martingales functionals. We show that GFDT are perturbative versions of relations verified by these exponential martingales. Along the way, we prove GFDT and Fluctuation Relations (FR) for general Markov processes, beyond the usual proof for diffusion and pure jump processes. Finally, we relate the FR to a family of backward and forward exponential martingales.Comment: 41 pages, 7 figures; version2: 45 pages, 7 figures, minor revisions, new results in Section

Asymptotic expansions at any time for scalar fractional SDEs with Hurst index H> 1/2

We study the asymptotic expansions with respect to h of E[∆hf(Xt)], E[∆hf(Xt)|F X t] and E[∆hf(Xt)|Xt], where ∆hf(Xt) = f(Xt+h) − f(Xt), when f:R → R is a smooth real function, t ≥ 0 is a fixed time, X is the solution of a one-dimensional stochastic differential equation driven by a fractional Brownian motion with Hurst index H> 1/2 and F X is its natural filtration

Tandem catalysis: access to ketones from aldehydes and arylboronic acids via rhodium-catalyzed addition/oxidation.

International audienc

Tandem catalysis: access to ketones from aldehydes and arylboronic acids via rhodium-catalyzed addition/oxidation.

International audienc