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Von Neumann-Landauer Limit
Landauer's principle is a physical principle pertaining to a lower theoretical limit of energy consumption of computation. It holds that an irreversible change in information stored in a computer, such as merging two computational paths, dissipates a minimum amount of heat to its surroundings.. It is hypothesized that energy consumption below this lower bound would require the development of reversible computing. The principle was first proposed by Rolf Landauer in 1961. Statement Landauer's principle states that the minimum energy needed to erase one bit of information is proportional to the temperature at which the system is operating. Specifically, the energy needed for this computational task is given by :E \geq k_\text T \ln 2, where k_\text is the Boltzmann constant and T is the temperature in Kelvin. At room temperature, the Landauer limit represents an energy of approximately . , modern computers use about a billion times as much energy per operation. History Rolf Landau ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Principle
A principle may relate to a fundamental truth or proposition that serves as the foundation for a system of beliefs or behavior or a chain of reasoning. They provide a guide for behavior or evaluation. A principle can make values explicit, so they are expressed in the form of rules and standards. Principles unpack the values underlying them more concretely so that the values can be more easily operationalized in policy statements and actions. In law, higher order, overarching principles establish rules to be followed, modified by sentencing guidelines relating to context and proportionality. In science and nature, a principle may define the essential characteristics of the system, or reflect the system's designed purpose. The effective operation would be impossible if any one of the principles was to be ignored. A system may be explicitly based on and implemented from a document of principles as was done in IBM's 360/370 ''Principles of Operation''. It is important to differe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Kaiserslautern
The University of Kaiserslautern-Landau (German: ''Rheinland-Pfälzische Technische Universität Kaiserslautern-Landau'', also known as RPTU) is a public research university in Kaiserslautern and Landau in der Pfalz, Germany. The university was formed by the merger of the Technical University of Kaiserslautern and the Landau campus of the University of Koblenz and Landau on January 1, 2023. There are numerous institutes around the university, including two Fraunhofer Institutes ( and ITWM), the Max Planck Institute for Software Systems (MPI-SWS), the German Research Center for Artificial Intelligence (DFKI), the Institute for Composite Materials (IVW) and the Institute for Surface and Thin Film Analysis (IFOS), all of which cooperate closely with the university. RPTU is organized into 16 faculties. About 17,000 students are enrolled at the moment. RPTU is part of the Software-Cluster along with the Technische Universität Darmstadt, the Karlsruhe Institute of Technology ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Entropy In Thermodynamics And Information Theory
Because the mathematical expressions for information theory developed by Claude Shannon and Ralph Hartley in the 1940s are similar to the mathematics of statistical thermodynamics worked out by Ludwig Boltzmann and J. Willard Gibbs in the 1870s, in which the concept of entropy is central, Shannon was persuaded to employ the same term 'entropy' for his measure of uncertainty. Information entropy is often presumed to be equivalent to physical (thermodynamic) entropy. Equivalence of form of the defining expressions The defining expression for entropy in the theory of statistical mechanics established by Ludwig Boltzmann and J. Willard Gibbs in the 1870s, is of the form: : S = - k_\text \sum_i p_i \ln p_i , where p_i is the probability of the microstate ''i'' taken from an equilibrium ensemble, and k_B is the Boltzmann constant. The defining expression for entropy in the theory of information established by Claude E. Shannon in 1948 is of the form: : H = - \sum_i p_i \log_b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kolmogorov Complexity
In algorithmic information theory (a subfield of computer science and mathematics), the Kolmogorov complexity of an object, such as a piece of text, is the length of a shortest computer program (in a predetermined programming language) that produces the object as output. It is a measure of the computational resources needed to specify the object, and is also known as algorithmic complexity, Solomonoff–Kolmogorov–Chaitin complexity, program-size complexity, descriptive complexity, or algorithmic entropy. It is named after Andrey Kolmogorov, who first published on the subject in 1963 and is a generalization of classical information theory. The notion of Kolmogorov complexity can be used to state and prove impossibility results akin to Cantor's diagonal argument, Gödel's incompleteness theorem, and Turing's halting problem. In particular, no program ''P'' computing a lower bound for each text's Kolmogorov complexity can return a value essentially larger than ''P'''s own len ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bekenstein Bound
In physics, the Bekenstein bound (named after Jacob Bekenstein) is an upper limit on the thermodynamic entropy ''S'', or Shannon entropy ''H'', that can be contained within a given finite region of space which has a finite amount of energy—or conversely, the maximum amount of information that is required to perfectly describe a given physical system down to the quantum level. It implies that the information of a physical system, or the information necessary to perfectly describe that system, must be finite if the region of space and the energy are finite. Equations The universal form of the bound was originally found by Jacob Bekenstein in 1981 as the inequality S \leq \frac, where ''S'' is the entropy, ''k'' is the Boltzmann constant, ''R'' is the radius of a sphere that can enclose the given system, ''E'' is the total mass–energy including any rest masses, ''ħ'' is the reduced Planck constant, and ''c'' is the speed of light. Note that while gravity plays a significant ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bremermann's Limit
Bremermann's limit, named after Hans-Joachim Bremermann, is a theoretical limit on the maximum rate of computation that can be achieved in a self-contained system in the material universe. It is derived from Einstein's mass–energy equivalency and the Heisenberg uncertainty principle, and is ''c''2/ ''h'' ≈ 1.3563925 × 1050 bits per second per kilogram. This value establishes an asymptotic bound on adversarial resources when designing cryptographic algorithms, as it can be used to determine the minimum size of encryption keys or hash values required to create an algorithm that could never be cracked by a brute-force search. For example, a computer with the mass of the entire Earth operating at Bremermann's limit could perform approximately 1075 mathematical computations per second. If one assumes that a cryptographic key can be tested with only one operation, then a typical 128-bit key could be cracked in under 10−36 seconds. However, a 256-bit key (which is alrea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Speed Limit
In quantum mechanics, a quantum speed limit (QSL) is a limitation on the minimum time for a quantum system to evolve between two distinguishable (orthogonal) states. QSL theorems are closely related to time-energy uncertainty relations. In 1945, Leonid Mandelstam and Igor Tamm derived a time-energy uncertainty relation that bounds the speed of evolution in terms of the energy dispersion. Reprinted as Over half a century later, Norman Margolus and Lev Levitin showed that the speed of evolution cannot exceed the mean energy, a result known as the Margolus–Levitin theorem. Realistic physical systems in contact with an environment are known as open quantum systems and their evolution is also subject to QSL. Quite remarkably it was shown that environmental effects, such as non-Markovian dynamics can speed up quantum processes, which was verified in a cavity QED experiment. QSL have been used to explore the limits of computation and complexity. In 2017, QSLs were studied in a quantum ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Perugia
The University of Perugia ( Italian ''Università degli Studi di Perugia'') is a public university in Perugia, Italy. It was founded in 1308, as attested by the Bull issued by Pope Clement V certifying the birth of the Studium Generale. The official seal of the university depicts Saint Herculan, one of the patron saints, and the rampant crowned griffin, which is the city symbol; they represent the ecclesiastical and civil powers, respectively, which gave rise to the university in the Middle Ages. History One of the "free" universities of Italy, it was elevated into a ''studium generale'' on September 8, 1308, by the Bull "Super specula" of Clement V. A school of arts existed by about 1200, in which medicine and law were soon taught, with a strong commitment expressed by official documents of the City Council of Perugia. Before 1300 there were several ''universitates scholiarum''. Jacobus de Belviso, a famous civil jurist, taught here from 1316 to 1321. By Bull on August 1, 131 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Circular Reasoning
Circular reasoning (, "circle in proving"; also known as circular logic) is a fallacy, logical fallacy in which the reasoner begins with what they are trying to end with. Circular reasoning is not a formal logical fallacy, but a pragmatic defect in an argument whereby the premises are just as much in need of proof or evidence as the conclusion. As a consequence, the argument becomes a matter of faith and fails to persuade those who do not already accept it. Other ways to express this are that there is no reason to accept the premises unless one already believes the conclusion, or that the premises provide no independent ground or evidence for the conclusion. Circular reasoning is closely related to begging the question, and in modern usage the two generally refer to the same thing. Circular reasoning is often of the form: "A is true because B is true; B is true because A is true." Circularity can be difficult to detect if it involves a longer chain of propositions. An example of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Physical Law
Scientific laws or laws of science are statements, based on repeated experiments or observations, that describe or predict a range of natural phenomena. The term ''law'' has diverse usage in many cases (approximate, accurate, broad, or narrow) across all fields of natural science (physics, chemistry, astronomy, geoscience, biology). Laws are developed from data and can be further developed through mathematics; in all cases they are directly or indirectly based on empirical evidence. It is generally understood that they implicitly reflect, though they do not explicitly assert, causal relationships fundamental to reality, and are discovered rather than invented. Scientific laws summarize the results of experiments or observations, usually within a certain range of application. In general, the accuracy of a law does not change when a new theory of the relevant phenomenon is worked out, but rather the scope of the law's application, since the mathematics or statement representing ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Single-molecule Magnet
A single-molecule magnet (SMM) is a metal-organic compound that has superparamagnetic behavior below a certain blocking temperature at the molecular scale. In this temperature range, an SMM exhibits magnetic hysteresis of purely molecular origin.Introduction to Molecular Magnetism by Dr. Joris van Slageren. In contrast to conventional bulk s and molecule-based magnets, collective long-range magnetic ordering of s is not necessary ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spin (physics)
Spin is an Intrinsic and extrinsic properties, intrinsic form of angular momentum carried by elementary particles, and thus by List of particles#Composite particles, composite particles such as hadrons, atomic nucleus, atomic nuclei, and atoms. Spin is quantized, and accurate models for the interaction with spin require relativistic quantum mechanics or quantum field theory. The existence of electron spin angular momentum is inferred from experiments, such as the Stern–Gerlach experiment, in which silver atoms were observed to possess two possible discrete angular momenta despite having no orbital angular momentum. The relativistic spin–statistics theorem connects electron spin quantization to the Pauli exclusion principle: observations of exclusion imply half-integer spin, and observations of half-integer spin imply exclusion. Spin is described mathematically as a vector for some particles such as photons, and as a spinor or bispinor for other particles such as electrons. Sp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
