  We report on the possibility of studying the properties of cosmic diffuse
baryons by studying self-gravitating clumps and filaments connected to galaxy
clusters. While filaments are challenging to detect with X-ray observations,
the higher density of clumps make them visible and a viable tracer to study the
thermodynamical properties of baryons undergoing accretion along cosmic web
filaments onto galaxy clusters. We developed new algorithms to identify these
structures in a set of non-radiative high-resolution simulations of galaxy
clusters, cosmological simulations of galaxy clusters. We show that the density
and temperature of clumps are independent of the mass of the cluster where they
reside. We detected a positive correlation between the filament temperature and
the host cluster mass. Density and Temperature of clumps and filaments tend to
correlate. Both decrease moving outward. We observe that clumps are hotter,
more massive and more luminous if identified closer to the cluster center.
Clumps and filaments contribute to ~17 (1) per cent of the gas mass (volume)
outside R500,c, with clumps contributing a factor of 2 more. Especially in the
outermost cluster regions (~3*R500,c or beyond) X-ray observations might
already have the chance of locating filaments based on the distribution of
clumps, and by studying the thermodynamics of diffuse baryons before they are
processed by the dynamical interaction with the host intracluster medium.
