We suggest a certain statistical interpretation for the entropy produced in driven thermodynamic processes. The exponential function of the irreversible entropy re-weights the probability of the standard Ornstein-Uhlenbeck-type thermodynamic fluctuations. ∗E-mail: [email protected]

We prove that the passive scalar field in the Ornstein-Uhlenbeck velocity field with wave-number dependent correlation times converges, in the white-noise limit, to that of Kraichnan’s model with higher spatial regularity.

We review and extend recent developments on the statistical properties of Active Ornstein Uhlenbeck particles (AOUPs). In this simplest models, Gaussian white noise overdamped Brownian colloids is replaced by a colored noise. This suffice to grant system hallmark active matter, while still allowing for analytical progress. first detail perturbative derivation steady state AOUPs in small persist...

We study the Dyson–Ornstein–Uhlenbeck diffusion process, an evolving gas of interacting particles. Its invariant law is beta Hermite ensemble random matrix theory, a non-product log-concave distribution. explore convergence to equilibrium this process for various distances or divergences, including total variation, relative entropy, and transportation cost. When number particles sent infinity, ...