  We explore a generalised unified dark energy model that incorporates a
non-minimal interaction between a tachyonic fluid and an additional scalar
field. Specifically, we require that the second field possesses a vacuum
energy, introducing an ineliminable offset due to a symmetry-breaking
mechanism. After the transition (occurring as due to the symmetry-breaking
mechanism of the second field), the corresponding equation of state (EoS) takes
the form of a combination between a generalised Chaplygin gas (GCG) component
and a cosmological constant contribution. We reinterpret this outcome by
drawing parallels to the so-called Murnaghan EoS, widely-employed in the realm
of solid-state physics to characterise fluids that, under external pressure,
counteract the pressure's effect. We examine the dynamic behaviour of this
model and highlight its key distinctions compared to the GCG model. We
establish parameter bounds that clarifies the model's evolution across cosmic
expansion history, showing that it, precisely, exhibits behaviour akin to a
logotropic fluid that eventually converges to the $\Lambda$CDM model in the
early universe, while behaving as a logotropic or Chaplygin gas at intermediate
and late times respectively. We explain our findings from a thermodynamic
perspective, and determine the small perturbations in the linear regime. At
very early times, the growth factor flattens as expected while the main
departures occur at late times, where the Murnagham EoS results in a more
efficient growth of perturbations. We discuss this deviation in view of current
observations and conclude that our model is a suitable alternative to the
standard cosmological paradigm, introducing the concept of a matter-like field
with non-zero pressure.
