Table of Contents

Abstract: We review recent progress in understanding the entanglement entropy of gravitational configurations for anti-de Sitter gravity in two and three spacetime dimensions using the AdS/CFT correspondence. We derive simple expressions for the entanglement entropy of two- and three-dimensional black holes. In both cases, the leading term of the entanglement entropy in the large black hole mass expansion reproduces exactly the Bekenstein-Hawking entropy, whereas the subleading term behaves logarithmically. In particular, for the BTZ black hole the leading term of the entanglement entropy can be obtained from the large temperature expansion of the partition function of a broad class of 2D CFTs on the torus.

Abstract: Numerical simulation of quantum systems is crucial to further our understanding of natural phenomena. Many systems of key interest and importance, in areas such as superconducting materials and quantum chemistry, are thought to be described by models which we cannot solve with sufficient accuracy, neither analytically nor numerically with classical computers. Using a quantum computer to simulate such quantum systems has been viewed as a key application of quantum computation from the very beginning of the field in the 1980s. Moreover, useful results beyond the reach of classical computation are expected to be accessible with fewer than a hundred qubits, making quantum simulation potentially one of the earliest practical applications of quantum computers. In this paper we survey the theoretical and experimental development of quantum simulation using quantum computers, from the first ideas to the intense research efforts currently underway.

Abstract: The design of autonomously moving objects that resemble living matter is an excellent research topic that may develop into various applications of functional motion. Autonomous motion can demonstrate numerous significant characteristics such as transduction of chemical potential into work without heat, chemosensitive motion, chemotactic and phototactic motions, and pulse-like motion with periodicities responding to the chemical environment. Sustainable motion can be realized with an open system that exchanges heat and matter across its interface. Hence the autonomously moving object has a colloidal scale with a large specific area. This article reviews several examples of systems with such characteristics that have been studied, focusing on chemical systems containing amphiphilic molecules.

Abstract: The principle of least action provides a holistic worldview in which Nature in its entirety and every detail is described in terms of actions. Each and every action is ultimately composed of one or multiple of the most elementary actions which relates to Planck’s constant. Elements of space are closed actions, known as fermions, whereas elements of time are open actions, known as bosons. The actions span an energy landscape, the Universe, which evolves irreversibly according to the 2nd law of thermodynamics by diminishing energy density differences in least time. During evolution densely-curled actions unfold step-by-step when opening up and expelling one or multiple elementary actions to their surrounding sparser space. The energy landscape will process from one symmetry group to another until the equivalence to its dual, i.e., the surrounding density has been attained. The scale-free physical portrayal of nature in terms of actions does not recognize any fundamental difference between fundamental particles and fundamental forces. Instead a plethora of particles and a diaspora of forces are perceived merely as diverse manifestations of a natural selection for various mechanisms and ways to decrease free energy in the least time.