Energy Balance of a Boson Gas at Zero Temperature in Curved Spacetime

TL;DR

This paper presents a unified thermodynamic and information-theoretic framework for zero-temperature boson gases in curved spacetime, applicable to models like boson stars and scalar dark matter.

Contribution

It introduces a dual formulation separating energy transport from information conservation, linking quantum effects with spacetime fluctuations in a relativistic setting.

Findings

Established an energy balance equation from a spacetime perspective.

Connected Fisher entropy to boson density evolution.

Validated the framework in Minkowski and Schwarzschild spacetimes.

Abstract

We develop a comprehensive thermodynamic description for a zero-temperature boson gas in curved spacetime, integrating energy conservation with information-theoretic principles. Using the hydrodynamic Madelung representation within the ADM 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 dual formulation clearly separates energy transport from information conservation while revealing how quantum 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.