  We study by molecular dynamics simulations the thermodynamics of an anomalous
fluid confined in a slit pore with one wall structured and attractive and
another unstructured and repulsive. We find that the phase diagram of the
homogeneous part of the confined fluid is shifted to higher temperatures,
densities and pressures with respect to the bulk, but it can be rescaled on the
bulk case. We calculate a moderate increase of mobility of the homogeneous
confined fluid that we interpret as a consequence of the layering due to
confinement and the collective modes due to long-range correlations. We show
that, as in bulk, the confined fluid has structural, diffusion and density
anomalies, that order in the water-like hierarchy, and a liquid-liquid critical
point (LLCP). The overall anomalous region moves to higher temperatures,
densities and pressure and the LLCP displaces to higher temperature compared to
bulk. Motivated by experiments, we calculate also the phase diagram not just
for the homogeneous part of the confined fluid but for the entire fluid in the
pore and show that it is shifted towards higher pressures but preserves the
thermodynamics, including the LLCP. Because our model has water-like
properties, we argue that in experiments with supercooled water confined in
slit pores with a width of > 3 nm if hydrophilic, and of > 1.5 nm if
hydrophobic, the existence of the LLCP could be easier to test than in bulk,
where it is not directly accessible.
