In molecular simulation and fluid mechanics, the coupling of a particle
    domain with a continuum representation of its embedding environment is an
    ongoing challenge. In this work, we show a novel approach where the latest
    version of the adaptive resolution scheme (AdResS), with non-interacting
    tracers as particles reservoir, is combined with a fluctuating hydrodynamics
    (FHD) solver. The resulting algorithm, supported by a solid mathematical model,
    allows for a physically consistent exchange of matter and energy between the
    particle domain and its fluctuating continuum reservoir. Numerical tests are
    performed to show the validity of the algorithm. Differently from previous
    algorithms of the same kind, the current approach allows for simulations where,
    in addition to density fluctuations, also thermal fluctuations can be accounted
    for, thus large complex molecular systems, as for example hydrated biological
    membranes in a thermal field, can now be efficiently treated.

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