Photoionisation is one of the main processes that shape the gaseous environment of
bright astrophysical sources, including Active Galactic Nuclei, Gamma-Ray Bursts and
compact sources. Many information on the gas physics, chemistry and kinematics, as well
as on the ionising source itself, can be gathered through optical to X-ray spectroscopy.
Several time equilibrium photoionisation codes are publicly available and can be used to
compute the gas ionisation and compare its spectroscopic imprint with the
observations. However, as most (if not all) bright, accretion-powered sources are
intrinsically variable, such codes are only able to offer an average description of the
gas properties and, in extreme cases, can lead to erroneous diagnostics of its density,
physics and geometry. In all these cases, time-evolving photoionisation is necessary to
properly analyse the observations and consistently derive the gas properties.

In this talk I will present the Time-Evolving Photo-Ionisation Device (TEPID;
Luminari+23), a new code that self-consistently solves time-evolving photoionisation
equations (with both thermal and ionisation balance) and accurately follows the response
of the gas to changes in the ionising source. TEPID produces time-resolved gas
absorption spectra that can be directly fitted to observations, from the optical up to
the X-ray band. Along with the usual properties (ionisation, column density, velocity)
time-evolving ionisation offers a unique channel to directly constrain the gas number
density, which is a totally degenerate quantity at equilibrium. Such time-evolving codes
are especially needed in the light of the recently-launched XRISM satellite, whose
microcalorimeter Resolve will perform unprecedented high-resolution spectroscopy through
the entire X-ray band, making equilibrium codes obsolete.

Finally, I will present the applications of TEPID to two dramatically different
environments (AGN ionised absorbers and circumburst environments of Gamma-Ray Bursts) to
offer a glimpse of the unique capabilities offered by time-evolving photoionisation.