Pressure-Energy Equations of State of the Nucleon
Abstract
The pressure-energy equations of state in the nucleon are derived from the gravitational form factors, which parametrize matrix elements of the energy-momentum tensor (EMT), together with EMT conservation. The pressure and energy densities naturally separate into two distinct components. The static pressure distribution, arising from the Lorentz trace part of the EMT, as manifested in the spatial stress 1/3 Tii, is equal to minus the corresponding trace part of the energy density. This relation may be interpreted as a consequence of the full or partial depletion of the gluon and quark condensates through the pressure-volume relation. The resulting trace anomaly- and sigma term-induced pressure is shown, through its volume scaling, to play a pivotal role in QCD confinement. In contrast, the dynamic pressure distribution, associated with the traceless part of the stress tensor equals 1/d of the corresponding traceless part of the energy density, where d is the spatial dimension. These static and dynamic components together satisfy the pressure-balance condition in the nucleon. We further show that the same pressure-energy equations of state hold for vortices in type-II superconductors, where the static pressure-energy relation originates from the depletion of the Cooper-pair condensate. Moreover, these equations of state are identical to those of the ΛCDM cosmological model, where the static pressure-energy relation is generated by the cosmological constant.
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BibTeX
@misc{liu2026pressureenergy,
title = {{Pressure-Energy Equations of State of the Nucleon}},
author = {Keh-Fei Liu},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2605.04163},
eprint = {2605.04163},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.04163},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Pressure-Energy Equations of State of the Nucleon
AU - Keh-Fei Liu
PY - 2026
DA - 2026/08/31
PB - arXiv
DO - 10.48550/arxiv.2605.04163
UR - https://arxiv.org/abs/2605.04163
AB - The pressure-energy equations of state in the nucleon are derived from the gravitational form factors, which parametrize matrix elements of the energy-momentum tensor (EMT), together with EMT conservation. The pressure and energy densities naturally separate into two distinct components. The static pressure distribution, arising from the Lorentz trace part of the EMT, as manifested in the spatial stress 1/3 T^ii, is equal to minus the corresponding trace part of the energy density. This relation may be interpreted as a consequence of the full or partial depletion of the gluon and quark condensates through the pressure-volume relation. The resulting trace anomaly- and sigma term-induced pressure is shown, through its volume scaling, to play a pivotal role in QCD confinement. In contrast, the dynamic pressure distribution, associated with the traceless part of the stress tensor equals 1/d of the corresponding traceless part of the energy density, where d is the spatial dimension. These static and dynamic components together satisfy the pressure-balance condition in the nucleon. We further show that the same pressure-energy equations of state hold for vortices in type-II superconductors, where the static pressure-energy relation originates from the depletion of the Cooper-pair condensate. Moreover, these equations of state are identical to those of the ΛCDM cosmological model, where the static pressure-energy relation is generated by the cosmological constant.
ER -