  With non-equilibrium applications in mind we present in this paper a
self-contained calculation of the hydrostatic pressure of the O(N)\lambda
\phi^4 theory at finite temperature. By combining the Keldysh-Schwinger
closed-time path formalism with thermal Dyson-Schwinger equations we compute in
the large N limit the hydrostatic pressure in a fully resumed form. We also
calculate the high-temperature expansion for the pressure (in D=4) using the
Mellin transform technique. The result obtained extends the results found by
Drummond et al. [hep-ph/9708426] and Amelino-Camelia and Pi [hep-ph/9211211].
The latter are reproduced in the limits m_r(0)\to 0, T \to \infty and T \to
\infty, respectively. Important issues of renormalizibility of composite
operators at finite temperature are addressed and the improved energy-momentum
tensor is constructed. The utility of the hydrostatic pressure in the
non-equilibrium quantum systems is discussed.
