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Classical-like formulas are given in order to evaluate thermal averages ofobservables belonging to a quantum nonlinear system with dissipation describedby the Caldeira-Leggett model [Phys. Rev. Lett. 46, 211 (1981); Ann. Phys.(N.Y.) 149, 374 (1983)]. The underlying scheme is the pure-quantumself-consistent harmonic approximation, which leads to expressions with aBoltzmann factor involving an effective potential and with a Gaussian average.The latter describes the effect of the fluctuations of purely quantum origin.As an illustration we calculate the coordinate probability distribution for adouble-well potential in the presence of various degrees of Ohmic dissipation.Comment: 4 pages, 3 figures included by psfig (minor corrections in revised  version

Thermodynamics of dissipative quantum systems by effective potential