2017/10/15 by Thibaut Demaerel, Christian Maes, Karel Netočný
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Amplitude #Classical mechanics #Computer science #Fixed point #Geometry #Materials science #Mathematical analysis #Mathematics #Mechanics #Micro and Nano Robotics #Non-equilibrium thermodynamics #Optics #Physics #Quantum Electrodynamics and Casimir Effect #Range (aeronautics) #Restoring force #Rotation (mathematics) #Stability (learning theory) #Stiffness #Thermodynamics #cond-mat.soft #cond-mat.stat-mech #math.PR
paper · pdf · open access · doi:10.1007/s00023-018-0697-z
published in Annales Henri Poincaré 19(9), 2673-2699 (Birkhäuser) · 32 pages
arxiv created 2017/10/15 · openalex publication_date 2018/06/29 · arxiv updated 2018/10/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We consider the systematic force on a heavy probe induced by interaction with an overdamped diffusive medium where particles undergo a rotating force around a fixed center. The stiffness matrix summarizes the stability of the probe around that center, where the induced force vanishes. We prove that the introduction of the rotational force in general enhances the stability of that point (and may turn it from unstable to stable!), starting at second-order in the nonequilibrium amplitude. When the driving is further enhanced the stabilization occurs for a wide range of rotation profiles and the induced stiffness converges to a universal expression proportional to the average mechanical stiffness. The model thus provides a rigorous example of stabilization of a fixed point due to contact with a nonequilibrium medium and beyond linear order around equilibrium.