Boltzmann Entropy, the Holographic Bound and Newtonian Cosmology

Proceedings

Pedro Fernández De Córdoba¹  Jose Maria Isidro San Juan¹ 

[1] Instituto Universitario de Matemática Pura y Aplicada, Universidad Politécnica de Valencia, 46022 Valencia, Spain;

关键词: gravitational entropy;    holographic principle;    emergent spacetime;   

DOI  :  10.3390/ecea-4-05008

来源: DOAJ

【 摘 要 】

The holographic principle sets an upper bound on the total (Boltzmann) entropy content of the Universe at around10 123 k B(k B being Boltzmann’s constant). In this work we point out the existence of a remarkable duality between nonrelativistic quantum mechanics on the one hand, and Newtonian cosmology on the other. Specifically, nonrelativistic quantum mechanics has a quantum probability fluid that exactly mimics the behaviour of the cosmological fluid, the latter considered in the Newtonian approximation. One proves that the equations governing the cosmological fluid (the Euler equation and the continuity equation) become the very equations that govern the quantum probability fluid after applying the Madelung transformation to the Schroedinger wavefunction. Under the assumption that gravitational equipotential surfaces can be identified with isoentropic surfaces, this model allows for a simple computation of the gravitational entropy of a Newtonian Universe.

【 授权许可】

Unknown