  It was shown by Jacobson in 1995 that the Einstein equation can be derived as
a local constitutive equation for an equilibrium spacetime thermodynamics. With
the aim to understand if such thermodynamical description is an intrinsic
property of gravitation, many attempts have been done so far to generalise this
treatment to a broader class of gravitational theories. Here we consider the
case of the Einstein-Cartan theory as a prototype of theories with
non-propagating torsion. In doing so, we study the properties of Killing
horizons in the presence of torsion, establish the notion of local causal
horizon in Riemann-Cartan spacetimes, and derive the generalised Raychaudhuri
equation for this kind of geometries. Then, starting with the entropy that can
be associated to these local causal horizons, we derive the Einstein-Cartan
equation by implementing the Clausius equation. We outline two ways of
proceeding with the derivation depending on whether we take torsion as a
geometric field or as a matter field. In both cases we need to add internal
entropy production terms to the Clausius equation as the shear and twist cannot
be taken to be zero a priori for our setup. This fact implies the necessity of
a non-equilibrium thermodynamics treatment for the local causal horizon.
Furthermore, it implies that a non-zero twist at the horizon will in general
contribute to the Hartle-Hawking tidal heating for black holes with possible
implications for future observations.
