Entropy Bounds, Holographic Principle and Uncertainty Relation

TL;DR

This paper explores the entropy bounds in physics, discussing the holographic principle and uncertainty relations, and compares different derivations of entropy limits within the context of black hole thermodynamics and general relativity.

Contribution

It provides a simple derivation of entropy bounds and discusses the connection between kinematical and dynamical holographic principles.

Findings

Estimated the number of quantum states using uncertainty relations.

Compared the entropy bound with the Bekenstein formula.

Argued for the derivation of the holographic principle from dynamical principles.

Abstract

A simple derivation of the bound on entropy is given and the holographic principle is discussed. We estimate the number of quantum states inside space region on the base of uncertainty relation. The result is compared with the Bekenstein formula for entropy bound, which was initially derived from the generalized second law of thermodynamics for black holes. The holographic principle states that the entropy inside a region is bounded by the area of the boundary of that region. This principle can be called the kinematical holographic principle. We argue that it can be derived from the dynamical holographic principle which states that the dynamics of a system in a region should be described by a system which lives on the boundary of the region. This last principle can be valid in general relativity because the ADM hamiltonian reduces to the surface term.