Carcaterra, A.Akay, A.2018-04-122018-04-1220162470-0045http://hdl.handle.net/11693/36540This paper expands a recent proposal by the authors to rederive the Langevin equation for a test particle in a finite-size thermal bath using a perturbation approach that yields a cascade of Langevin-type equations. Such an approach produces a different viewpoint for the fluctuation-dissipation duality by expressing them on similar scales. General properties of energy sharing between the test particle and the bath are outlined, investigating the resonant and nonresonant conditions. © 2016 American Physical Society.EnglishDifferential equationsEnergy propertyEnergy sharingsFluctuation dissipationLangevin equationLangevin type equationsPerturbation approachTest particlesThermal bathKinetic theoryArticle10.1103/PhysRevE.93.032142