Entropy Bound And Holographic Principle

Since Hawking radiation was discovered in 1975, the thermodynamics of black holes and the quantum gravitational mechanism behind it have gained a lot of interest. Especially, illuminated by the area law of black hole entropy,'t Hooft and Susskind subsequently de-veloped the concept of holographic principle, which states that the information capacity of a system will not exceed its boundary area in Planck units. Later, the holographic principle was realized by the famous ADS/CFT dual, which soon turns holographic principle to be a central topic in the research of quantum gravity.In this thesis, we introduce the fundamental lore in the area of entropy bounds and holographic principle. Starting from the study of entropy bounds, we have investigated several questions related to holographic principle.First, we investigate the entropy bound for local quantum field theory under gravita-tional constraint. We strictly proved that bosonic and fermionic fields conform to the same entropy bound A3/4lp-3/2, where A is the boundary area of the system, lp=1.616×10-35m is Planck length. The results have supported the qualitative analysis given by't Hooft some years ago, and rectified the incorrect viewpoint that local quantum field theory could satu-rate the holographic entropy.Second, we investigate the thermodynamical and statistical entropy bound for quan-tum Boltzmann fields which obey infinite statistics. We find infinite statistics complies with the holographic entropy bound Alp-2 very well. In general cases, the entropy bound comes back to the Bekenstein bound El/(hc), where E and l are respectively the energy and size of the system. Our results have improved the understanding of the gap between the entropy bound of local quantum field theory and the holographic entropy, that is, from A3/4lp-3/2 to Alp-2, the corresponding degrees of freedom of which are very obscure before our work. Our results also suggest a close relationship between infinite statistics and quantum gravity.Finally, starting from a quantum computational perspective, combining quantum and gravitational principles, we derived a new space-time uncertainty relation, which can be used to facilitate the discussion of several profound questions, such as computational ca-pacity and thermodynamic properties of the universe. This uncertainty relation can be viewed as an extension of holographic principle. Holographic principle only limits the information of a system, while from our relation one can obtain some other important properties of the system such as its capacity of information processing.