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We investigate the interaction of a particle with a finite-size bath represented by a set of independent linear oscillators with frequencies that fall within a finite bandwidth. We discover that when the oscillators have particular frequency distributions, the finite-size bath behaves much as an infinite-size bath exhibiting dissipation properties and thus allowing irreversible energy absorption from a particle immersed in it. We also present a reinterpretation of the Langevin equation using a perturbation approach in which the small parameter represents the inverse of the number of oscillators in the bath, elucidating the relationship between finite-size and infinite-size bath responses. [ABSTRACT FROM AUTHOR]

This 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. [ABSTRACT FROM AUTHOR]