  A semiclassical theory of dissipative Henon-Heiles system is proposed. Based
on $\hbar$-scaling of an equation for evolution of Wigner quasiprobability
distribution function in presence of dissipation and thermal diffusion, we
derive a semiclassical equation for quantum fluctuations, governed by the
dissipation and the curvature of the classical potential. We show how the
initial quantum noise gets amplified by classical chaotic diffusion which is
expressible in terms of correlation of stochastic fluctuations of the curvature
of the potential due to classical chaos and ultimately settles down to
equilibrium under the influence of dissipation. We also establish that there
exists a critical limit to the expansion of phase space. The limit is set by
chaotic diffusion and dissipation. Our semiclassical analysis is corroborated
by numerical simulation of quantum operator master equation.

Chaotic Dynamics;Statistical Mechanics;Chaotic Dynamics