Energy balance of a boson gas at zero temperature in curved spacetime
Phys. Rev. D 113, 124048 – Published 15 June, 2026
DOI: https://doi.org/10.1103/xyy5-69fx
Abstract
We develop a comprehensive thermodynamic description for a zero-temperature boson gas in a fixed, classical curved spacetime, integrating energy conservation with information-theoretic principles. Using the hydrodynamic Madelung representation within the Arnowitt-Deser-Misner formalism, we establish two fundamental relationships: an energy balance equation representing the first law of thermodynamics from a spacetime perspective, and an information-theoretic constraint connecting Fisher entropy to the dynamical evolution of the boson density. This formulation clearly separates energy transport from the conservation of quantum information encoded in the boson gas, while revealing how such information is preserved in curved backgrounds. The introduction of a stochastic velocity provides a bridge between quantum potential effects and underlying spacetime fluctuations. We demonstrate the consistency of our framework through detailed analyses of quantum systems in both Minkowski and Schwarzschild spacetimes. This work provides a unified foundation for studying relativistic bosonic systems, with direct relevance to boson stars and scalar field dark matter models.
