Relativistic diffusing particles, entropy and varying cosmological constants
Abstract
We discuss Einstein equations with a non-conserved energy-momentum Tμν. The energy-momentum tensor T̃μν on the right hand side of Einstein equations is expressed in the form 8πGTμν−gμνΛ+Σμν where G is the Newton constant, Λ is the cosmological term and Tμν is the energy-momentum of an ideal fluid. The remaining part Σμν describes the viscosity and a heat flow. We discuss space-time-dependent Newton ``constant" G and the cosmological term Λ. The covariant conservation law for T̃μν imposes a relation between the energy-momentum (non)conservation and the variation of G and Λ. The covariant derivative ∇μTμν can be related to the first law of thermodynamics and expressed by the temperature T and the entropy S. The energy-momentum non-conservation in our models is a consequence of a diffusion of its constituting particles. We describe a gas of diffusing massive particles in a homogeneous isotropic space-time as a system with a time-dependent linear barotropic equation of state Pt=wtρt with 0<wt≤ 1/3. The gas of massive diffusing particles in an expanding universe tends in a limit of infinite time to the gas of diffusing massless particles. We obtain results on the energy density, entropy and phase space dstribution in a soluble model of massless relativistic particles in a spatially flat expanding universe.
Versions
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BibTeX
@misc{haba2026relativistic,
title = {{Relativistic diffusing particles, entropy and varying cosmological constants}},
author = {Z. Haba},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.34341},
eprint = {2610.34341},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.34341},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Relativistic diffusing particles, entropy and varying cosmological constants
AU - Z. Haba
PY - 2026
DA - 2026/10/25
PB - arXiv
DO - 10.48550/arxiv.2610.34341
UR - https://arxiv.org/abs/2610.34341
AB - We discuss Einstein equations with a non-conserved energy-momentum T^μν. The energy-momentum tensor T̃^μν on the right hand side of Einstein equations is expressed in the form 8πGT^μν−g^μνΛ+Σ^μν where G is the Newton constant, Λ is the cosmological term and T^μν is the energy-momentum of an ideal fluid. The remaining part Σ^μν describes the viscosity and a heat flow. We discuss space-time-dependent Newton ``constant" G and the cosmological term Λ. The covariant conservation law for T̃^μν imposes a relation between the energy-momentum (non)conservation and the variation of G and Λ. The covariant derivative ∇_μT^μν can be related to the first law of thermodynamics and expressed by the temperature T and the entropy S. The energy-momentum non-conservation in our models is a consequence of a diffusion of its constituting particles. We describe a gas of diffusing massive particles in a homogeneous isotropic space-time as a system with a time-dependent linear barotropic equation of state P_t=w_tρ_t with 0<w_t≤ 1/3. The gas of massive diffusing particles in an expanding universe tends in a limit of infinite time to the gas of diffusing massless particles. We obtain results on the energy density, entropy and phase space dstribution in a soluble model of massless relativistic particles in a spatially flat expanding universe.
ER -