  We study the physical conditions in DLAs, using a sample of 33 systems toward
26 QSOs acquired for a recently completed survey of H_2 by Ledoux et al.
(2003). We use the column densities of H_2 in different rotational levels,
together with those of C I, C I*, C I**, C II* and singly ionized atomic
species to discuss the kinetic temperature, the density of hydrogen and the
electronic density in the gas together with the ambient UV radiation field.
Detailed comparisons are made between the observed properties in DLAs, the
interstellar medium (ISM) of the Galaxy, LMC and SMC. The mean kinetic
temperature of the gas corresponding to DLA subcomponents in which H_2
absorption line is detected, derived from the ortho-to-para ratio (153+/-78 K),
is higher than that measured in the ISM (77+/-17 K) and the Magellanic clouds
(82+/-21 K). Typical pressure in these components (corresponding to T = 100-300
K and n = 10-200 cm^-3), measured using C I fine-structure excitation, are
higher than what is measured along ISM sightlines. This is consistent with the
corresponding higher values for N(H_2,J=2)/N(H_2,J=0) seen in DLAs. From the
column densities of the high-J rotational levels, we derive that the typical
radiation field in the H_2 bearing components is of the order of or slightly
higher than the mean UV field in the Galactic ISM. Determination of electron
density in the gas with H_2 and C I show the ionization rate is similar to that
of a cold neutral medium (CNM) in a moderate radiation field. This, together
with the fact that we see H_2 in 13-20% of the DLAs, can be used to conclude
that DLAs at z>1.9 could contribute as much as 50% star formation rate density
seen in Lyman break galaxies (LBGs). (Abridged)
