  We show how to write a set of brackets for the Langevin equation, describing
the dissipative motion of a classical particle, subject to external random
forces. The method does not rely on an action principle, and is based solely on
the phenomenological description of the dissipative dynamics as given by the
Langevin equation. The general expression for the brackets satisfied by the
coordinates, as well as by the external random forces, at different times, is
determined, and it turns out that they all satisfy the Jacobi identity. Upon
quantization, these classical brackets are found to coincide with the
commutation rules for the quantum Langevin equation, that have been obtained in
the past, by appealing to microscopic conservative quantum models for the
friction mechanism.
