Thermodynamics and mechanical laws of causal-diamond horizons

We develop a unified thermodynamic and mechanical framework for causal-diamond horizons in Minkowski spacetime. Euclidean regularity fixes the temperature T_D=1/(πα), where 2α is the temporal extent of the diamond. The regulated Gibbons--Hawking--York contribution gives I_D^E=-A_0/(4G), with A_0 the area of the horizon bifurcation surface, and the vanishing equilibrium geometric energy then yields the entropy--area relation S_D=A_0/(4G). For weak matter perturbations crossing a localized portion of the future horizon, a Raychaudhuri analysis relates the associated Killing-energy flux to the area response, yielding a local physical-process first law at leading order near the bifurcation surface and, for classical matter satisfying the null energy condition, a local second law. Uniform conformal surface gravity establishes the zeroth law, while zero temperature is approached only in the limit αtoinfty, in which the finite causal horizon disappears. These results show that a coherent horizon-law structure can arise within a causal diamond, a fundamental building block of the causal structure of Minkowski spacetime. The derivation is explicit in (2+1) dimensions, while the physical results retain the same form for spherical causal diamonds in dgeq3.