Related papers: Ultimate Intelligence Part II: Physical Measure an…
A unified thermodynamic formalism describing the efficiency of learning is proposed. First, we derive an inequality, which is more strength than Clausius's inequality, revealing the lower bound of the entropy-production rate of a subsystem.…
Rapidly developing experiments across multiple platforms now aim to realise small quantum codes, and so demonstrate a memory within which a logical qubit can be protected from noise. There is a need to benchmark the achievements in these…
By analyzing the key properties of black holes from the point of view of quantum information, we derive a model-independent picture of black hole quantum computing. It has been noticed that this picture exhibits striking similarities with…
Motivated by the doubly special relativity theories and noncommutative spacetime structures, thermodynamical properties of the photon gas in a phase space with compact spatial momentum space is studied. At the high temperature limit, the…
Combining deeper insight of Einstein's equations with sophisticated numerical techniques promises the ability to construct accurate numerical implementations of these equations. We illustrate this in two examples, the numerical evolution of…
An new ensemble - the angular velocity ensemble - is derived using Jaynes' method of maximising entropy subject to prior information constraints. The relevance of the ensemble to black holes is motivated by a discussion of external…
Estimating the intrinsic dimensionality (ID) of data is a fundamental problem in machine learning and computer vision, providing insight into the true degrees of freedom underlying high-dimensional observations. Existing methods often rely…
The objectivity of black hole entropy is discussed in the particular case of a Schwarzchild black hole. Using Jaynes' maximum entropy formalism and Euclidean path integral evaluation of partition function, it is argued that in the…
We first propose and study a quantum toy model of black hole dynamics. The model is unitary, displays quantum thermalization, and the Hamiltonian couples every oscillator with every other, a feature intended to emulate the color sector…
Optimization results are one method for understanding neural computation from Nature's perspective and for defining the physical limits on neuron-like engineering. Earlier work looks at individual properties or performance criteria and…
Using a unified approach we study the entropy of extremal black holes through the entropy of an electrically charged thin shell. We encounter three cases in which a shell can be taken to its own gravitational or horizon radius and become an…
The Cauchy problem for the complete Euler system is in general ill posed in the class of admissible (entropy producing) weak solutions. This suggests there might be sequences of approximate solutions that develop fine scale oscillations.…
We give arguments for the existence of a thermodynamics of quantum complexity that includes a "Second Law of Complexity". To guide us, we derive a correspondence between the computational (circuit) complexity of a quantum system of $K$…
We have derived an analytical formulation for estimating the volume of geometries enclosed by implicitly defined surfaces. The novelty of this work is due to two aspects. First we provide a general analytical formulation for all…
Entropy is useful in statistical problems as a measure of irreversibility, randomness, mixing, dispersion, and number of microstates. However, there remains ambiguity over the precise mathematical formulation of entropy, generalized beyond…
The measurement postulate of quantum theory stands in conflict with the laws of thermodynamics and has evoked debate regarding what actually constitutes a measurement. With the help of modern quantum statistical mechanics, we take the first…
It is shown for classical and quantum ensembles that there is a unique quantity which has the properties of a "volume". This quantity is a function of the ensemble entropy, and hence provides a geometric interpretation for the latter. It…
Artificial Intelligence (AI) techniques continue to broaden across governmental and public sectors, such as power and energy - which serve as critical infrastructures for most societal operations. However, due to the requirements of…
We define the analytic continuation of the number of black hole microstates in Loop Quantum Gravity to complex values of the Barbero-Immirzi parameter $\gamma$. This construction deeply relies on the link between black holes and…
By a simple physical consideration and uncertain principle, we derive that temperature is proportional to the surface gravity and entropy is proportional to the surface area of the black hole. We apply the same consideration to de Sitter…