  Topological phase transitions are found in a variety of systems and were
shown to be deeply related with a thermodynamic description through scaling
relations. Here, we investigate the entanglement entropy, which is a quantity
that captures the central charge of a critical model and the thermodynamics of
the non-reciprocal Su-Schrieffer-Heeger (SSH) model. Although this model has
been widely studied, the thermodynamic properties reveal interesting physics
not explored so far. In order to analyze the boundary effects of the model, we
use Hill's thermodynamics to split the grand potential in two contributions:
the extensive one, related to the bulk, and the subdivision one, related to the
boundaries. Then, we derive the thermodynamic entropy for both, the edges and
the bulk and the heat capacity for the bulk at the topological phase
transitions. The latter is related to the central charge when the underlying
theory is a conformal field theory, whereas the first reveals the resilience of
the topological edge states to finite temperatures. The phase transition
between phases that are adiabatically connected with the Hermitian SSH model
display the well-known behaviour of systems within the Dirac universality
class, but the transition between phases with complex energies shows an
unexpected critical behavior, which signals the emergence of an imaginary time
crystal.
