  The black hole entropy formula applied to local Rindler horizon at each
spacetime point has been used in the literature to derive the Einstein field
equation as an equation of state of a thermodynamical system of spacetime. In
the present paper we argue that due to the key role of causal structure and
discrete spacetime in this approach the natural framework is unimodular
relativity rather than general relativity. It is shown that the equation of
state is trace free unimodular relativity field equation that uniquely
determines only the traceless stress tensor. Recent generalization to
nonequilibrium thermodynamics is shown to be equivalent to the conformally
related spacetime metrics, and energy-momentum conservation is satisfied
without invoking entropy production. We suggest that the cosmological constant
should possess thermodynamical fluctuations, and at a deeper level the metric
may have statistical origin.
