Thermalization in open classical systems with finite heat baths

We discuss thermalization of a test particle schematized as a harmonic oscillator and coupled to a Boltzmann heat bath of finite size and with a finite bandwidth for the frequencies of its particles. We find that complete thermalization only occurs when the test particle frequency is within a certain range of the bath particle frequencies, and for a certain range of mass ratios between the test particle and the bath particles. These results have implications for the study of classical and quantum behaviour of high-frequency nanomechanical resonators. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 200805.40.Jc Brownian motion, 05.70.Ln Nonequilibrium and irreversible thermodynamics, 62.25.-g Mechanical properties of nanoscale systems, 83.10.Rs Computer simulation of molecular and particle dynamics,