Thermodynamics and mechanical laws of causal-diamond horizons
Abstract
We develop a unified thermodynamic and mechanical framework for causal-diamond horizons in Minkowski spacetime. Euclidean regularity fixes the temperature TD=1/(πα), where 2α is the temporal extent of the diamond. The regulated Gibbons-Hawking-York contribution gives IDE=−A0/(4G), with A0 the area of the horizon bifurcation surface, and the vanishing equilibrium geometric energy then yields the entropy-area relation SD=A0/(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 α→∞, 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 d≥3.
Versions
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BibTeX
@misc{ordonez2026thermodynamics,
title = {{Thermodynamics and mechanical laws of causal-diamond horizons}},
author = {Carlos R. Ordóñez and Gustavo Valdivia-Mera},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.07746},
eprint = {2610.07746},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.07746},
}
RIS
TY - UNPB
TI - Thermodynamics and mechanical laws of causal-diamond horizons
AU - Carlos R. Ordóñez
AU - Gustavo Valdivia-Mera
PY - 2026
DA - 2026/10/25
PB - arXiv
DO - 10.48550/arxiv.2610.07746
UR - https://arxiv.org/abs/2610.07746
AB - 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 α→∞, 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 d≥3.
ER -