Related papers: Ultimate Intelligence Part II: Physical Measure an…
The ultimate limits of computation are not just logical, but physical. We investigate the physical resources -- time, energy, entropy, and free energy -- required to perform computational work. We apply the resulting measures of physical…
One quantum characterization of a black hole motivated by (local) holography and thermodynamics is that it maximizes thermodynamic entropy for a given surface area. In the context of quantum gravity, this could be more fundamental than the…
The finiteness of black hole entropy suggest that spacetime is fundamentally discrete, and hints at an underlying relationship between geometry and "information". The foundation of this relationship is yet to be uncovered, but should…
The rapid scaling of artificial intelligence models has revealed a fundamental tension between model capacity (storage) and inference efficiency (computation). While classical information theory focuses on transmission and storage limits,…
We show that the concept of entropy and the dynamics of gravitation provide the linchpin in a unified scheme to understand the physics of black hole computers, space-time foam, dark energy, dark matter and the phenomenon of turbulence. We…
We propose a rigorous derivation of the Bekenstein upper limit for the entropy/information that can be contained by a physical system in a given finite region of space with given finite energy. The starting point is the observation that the…
It is shown that for any ensemble, whether classical or quantum, continuous or discrete, there is only one measure of the "volume" of the ensemble that is compatible with several basic geometric postulates. This volume measure is thus a…
We study entropy-bounded computational geometry, that is, geometric algorithms whose running times depend on a given measure of the input entropy. Specifically, we introduce a measure that we call range-partition entropy, which unifies and…
The paper describes an approach to measuring convergence of an algorithm to its result in terms of an entropy-like function of partitions of its inputs of a given length. The goal is to look at the algorithmic data processing from the…
Black hole entropy is studied for an exactly solvable model of two-dimensional gravity\cite{rst1}, using recently developed Noether charge techniques\cite{wald1}. This latter approach is extended to accomodate the non-local form of the…
Based on the AdS/CFT correspondence, we study how to reconstruct bulk spacetime metrics by various quantum information measures on the boundary field theories, which include entanglement entropy, mutual information, entanglement of…
Information-theoretic (IT) measures are ubiquitous in artificial intelligence: entropy drives decision-tree splits and uncertainty quantification, cross-entropy is the default classification loss, mutual information underpins representation…
Analytic continuation of numerical data obtained in imaginary time or frequency has become an essential part of many branches of quantum computational physics. It is, however, an ill-conditioned procedure and thus a hard numerical problem.…
The two apparently distinct phenomena of dark energy (or late-time cosmic acceleration) and quantum gravity dominate physics on extremely low, and extremely high energies, but do not seem to have any apparent empirical connection.…
This paper describes an entropy equation, but one that should be used for measuring energy and not information. In relation to the human brain therefore, both of these quantities can be used to represent the stored information. The human…
In this paper we estimate the size of a measurable inclusion in terms of power measurements for a single applied boundary current. This problem arises in medical imaging for the screening of organs. For this kind of problem one has to deal…
These lectures deal with the problem of inductive inference, that is, the problem of reasoning under conditions of incomplete information. Is there a general method for handling uncertainty? Or, at least, are there rules that could in…
We present a mathematical framework for quantifying energy efficiency in intelligent systems by linking energy consumption to information-processing capacity. We introduce a watts-per-intelligence metric that integrates algorithmic…
We establish a version of the Momentum/Complexity (PC) duality between the rate of operator complexity growth and a radial component of bulk momentum for a test system falling into a black hole. In systems of finite entropy, our map remains…
This work demonstrates how the concept of the entropic potential of events -- a parameter quantifying the influence of discrete events on the expected future entropy of a system -- can enhance uncertainty quantification, decision-making,…