Stochastic Dynamics Out of Equilibrium

Explore advanced concepts in non-equilibrium statistical mechanics through this comprehensive lecture series from Institut Henri Poincaré's 2017 trimester program. Delve into stochastic dynamics that operate outside equilibrium conditions, examining non-reversible dynamics and their unique features that require novel analytical methods. Study three key domains including transport phenomena in non-equilibrium statistical mechanics, efficient simulation methodologies, and applications in life sciences. Investigate synchronization theory across multiple lectures, learn about stochastic resetting processes, and examine hydrodynamics for symmetric exclusion processes in contact with reservoirs. Analyze the emergence of noise-like behavior in deterministic dynamical systems and explore scalar conservation laws with their Markovian solutions. Discover connections between Hamilton-Jacobi partial differential equations, Hamiltonian ordinary differential equations, and Mather theory. Examine the role of topology and compactness in large deviation theory, and study balanced chemical reaction networks and reaction-diffusion systems. Gain insights into numerical simulations for long-time dynamics spanning from atomic to stellar scales, explore mathematical approaches in plant biology, and understand probability theory's relationship with irreversibility and chaos propagation. This interdisciplinary program brings together perspectives from physics, mathematics, computer science, and biology to address challenging open questions in non-equilibrium dynamics.