Kernel moments and thermodynamic stability in nonlocal Nambu--Jona-Lasinio models
Abstract
We study thermodynamic consistency and stability in a covariant two-flavor nonlocal Nambu--Jona-Lasinio model at zero chemical potential in the homogeneous quark mean-field approximation. A controlled large-source expansion gives a sufficient entropy-sign criterion directly from Euclidean kernel moments, without locating propagator poles. At fixed couplings and kernel, every admissible positive Gaussian mixture develops negative total entropy at sufficiently large source mass for each fixed positive temperature. In a separate light-source fit to pion observables and a subtracted condensate, one quartic-exponent kernel has positive entropy and heat capacity for all T>0, while dP/dε=s/CV exceeds unity on a finite interval. This constructive example separates thermal positivity from the static EOS slope test. Numerical refits show that the enhancement weakens with the condensate input, and a certified counterexample excludes uniform thermal positivity over the adopted matching domain. The results provide diagnostics of the mean-field functional, rather than a preferred phenomenological kernel. Omitted thermal mesons can change the low-temperature slope test, and the static derivative does not determine a real-time front velocity.
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BibTeX
@misc{yu2026kernel,
title = {{Kernel moments and thermodynamic stability in nonlocal Nambu--Jona-Lasinio models}},
author = {Xiaozhu Yu and Xinyang Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.17622},
eprint = {2610.17622},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.17622},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Kernel moments and thermodynamic stability in nonlocal Nambu--Jona-Lasinio models
AU - Xiaozhu Yu
AU - Xinyang Wang
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.17622
UR - https://arxiv.org/abs/2610.17622
AB - We study thermodynamic consistency and stability in a covariant two-flavor nonlocal Nambu--Jona-Lasinio model at zero chemical potential in the homogeneous quark mean-field approximation. A controlled large-source expansion gives a sufficient entropy-sign criterion directly from Euclidean kernel moments, without locating propagator poles. At fixed couplings and kernel, every admissible positive Gaussian mixture develops negative total entropy at sufficiently large source mass for each fixed positive temperature. In a separate light-source fit to pion observables and a subtracted condensate, one quartic-exponent kernel has positive entropy and heat capacity for all T>0, while dP/dε=s/C_V exceeds unity on a finite interval. This constructive example separates thermal positivity from the static EOS slope test. Numerical refits show that the enhancement weakens with the condensate input, and a certified counterexample excludes uniform thermal positivity over the adopted matching domain. The results provide diagnostics of the mean-field functional, rather than a preferred phenomenological kernel. Omitted thermal mesons can change the low-temperature slope test, and the static derivative does not determine a real-time front velocity.
ER -