  Recently, non-perturbative approximate solutions were presented that go
beyond the well-known mean-field resummation. In this work, these
non-perturbative approximations are used to calculate finite temperature
equilibrium properties for scalar $\phi^4$ theory in two dimensions such as the
pressure, entropy density and speed of sound. Unlike traditional approaches, it
is found that results are well-behaved for arbitrary temperature/coupling
strength, are independent of the choice of the renormalization scale
$\bar\mu^2$, and are apparently converging as the resummation level is
increased. Results also suggest the presence of a possible analytic cross-over
from the high-temperature to the low-temperature regime based on the change in
the thermal entropy density.
