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Reversible Computation
Reversible computing is any model of computation where the computational process, to some extent, is time-reversible. In a model of computation that uses deterministic transitions from one state of the abstract machine to another, a necessary condition for reversibility is that the relation of the mapping from states to their successors must be one-to-one. Reversible computing is a form of unconventional computing. Due to the unitarity of quantum mechanics, quantum circuits are reversible, as long as they do not "collapse" the quantum states they operate on. Reversibility There are two major, closely related types of reversibility that are of particular interest for this purpose: physical reversibility and logical reversibility. A process is said to be ''physically reversible'' if it results in no increase in physical entropy; it is isentropic. There is a style of circuit design ideally exhibiting this property that is referred to as charge recovery logic, adiabatic circui ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Model Of Computation
In computer science, and more specifically in computability theory and computational complexity theory, a model of computation is a model which describes how an output of a mathematical function is computed given an input. A model describes how units of computations, memories, and communications are organized. The computational complexity of an algorithm can be measured given a model of computation. Using a model allows studying the performance of algorithms independently of the variations that are specific to particular implementations and specific technology. Models Models of computation can be classified into three categories: sequential models, functional models, and concurrent models. Sequential models Sequential models include: * Finite state machines * Post machines (Post–Turing machines and tag machines). * Pushdown automata * Register machines ** Random-access machines * Turing machines * Decision tree model Functional models Functional models include: * Abstract re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Isentropic
In thermodynamics, an isentropic process is an idealized thermodynamic process that is both adiabatic and reversible. The work transfers of the system are frictionless, and there is no net transfer of heat or matter. Such an idealized process is useful in engineering as a model of and basis of comparison for real processes. This process is idealized because reversible processes do not occur in reality; thinking of a process as both adiabatic and reversible would show that the initial and final entropies are the same, thus, the reason it is called isentropic (entropy does not change). Thermodynamic processes are named based on the effect they would have on the system (ex. isovolumetric: constant volume, isenthalpic: constant enthalpy). Even though in reality it is not necessarily possible to carry out an isentropic process, some may be approximated as such. The word "isentropic" can be interpreted in another way, since its meaning is deducible from its etymology. It means a pr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
CPT Symmetry
Charge, parity, and time reversal symmetry is a fundamental symmetry of physical laws under the simultaneous transformations of charge conjugation (C), parity transformation (P), and time reversal (T). CPT is the only combination of C, P, and T that is observed to be an exact symmetry of nature at the fundamental level. The CPT theorem says that CPT symmetry holds for all physical phenomena, or more precisely, that any Lorentz invariant local quantum field theory with a Hermitian Hamiltonian must have CPT symmetry. History The CPT theorem appeared for the first time, implicitly, in the work of Julian Schwinger in 1951 to prove the connection between spin and statistics. In 1954, Gerhart Lüders and Wolfgang Pauli derived more explicit proofs, so this theorem is sometimes known as the Lüders–Pauli theorem. At about the same time, and independently, this theorem was also proved by John Stewart Bell. These proofs are based on the principle of Lorentz invariance and the princ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logical Consequence
Logical consequence (also entailment) is a fundamental concept in logic, which describes the relationship between statements that hold true when one statement logically ''follows from'' one or more statements. A valid logical argument is one in which the conclusion is entailed by the premises, because the conclusion is the consequence of the premises. The philosophical analysis of logical consequence involves the questions: In what sense does a conclusion follow from its premises? and What does it mean for a conclusion to be a consequence of premises?Beall, JC and Restall, Greg, Logical Consequence' The Stanford Encyclopedia of Philosophy (Fall 2009 Edition), Edward N. Zalta (ed.). All of philosophical logic is meant to provide accounts of the nature of logical consequence and the nature of logical truth. Logical consequence is necessary and formal, by way of examples that explain with formal proof and models of interpretation. A sentence is said to be a logical conse ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Second Law Of Thermodynamics
The second law of thermodynamics is a physical law based on universal experience concerning heat and Energy transformation, energy interconversions. One simple statement of the law is that heat always moves from hotter objects to colder objects (or "downhill"), unless energy in some form is supplied to reverse the direction of heat flow. Another definition is: "Not all heat energy can be converted into Work (thermodynamics), work in a cyclic process."Young, H. D; Freedman, R. A. (2004). ''University Physics'', 11th edition. Pearson. p. 764. The second law of thermodynamics in other versions establishes the concept of entropy as a physical property of a thermodynamic system. It can be used to predict whether processes are forbidden despite obeying the requirement of conservation of energy as expressed in the first law of thermodynamics and provides necessary criteria for spontaneous processes. The second law may be formulated by the observation that the entropy of isolated systems ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Single-valued Function
In mathematics, a multivalued function, also called multifunction, many-valued function, set-valued function, is similar to a function, but may associate several values to each input. More precisely, a multivalued function from a domain to a codomain associates each in to one or more values in ; it is thus a serial binary relation. Some authors allow a multivalued function to have no value for some inputs (in this case a multivalued function is simply a binary relation). However, in some contexts such as in complex analysis (''X'' = ''Y'' = C), authors prefer to mimic function theory as they extend concepts of the ordinary (single-valued) functions. In this context, an ordinary function is often called a single-valued function to avoid confusion. The term ''multivalued function'' originated in complex analysis, from analytic continuation. It often occurs that one knows the value of a complex analytic function f(z) in some neighbourhood of a point z=a. This is the case fo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
One-to-one Function
In mathematics, an injective function (also known as injection, or one-to-one function) is a function that maps distinct elements of its domain to distinct elements; that is, implies . (Equivalently, implies in the equivalent contrapositive statement.) In other words, every element of the function's codomain is the image of one element of its domain. The term must not be confused with that refers to bijective functions, which are functions such that each element in the codomain is an image of exactly one element in the domain. A homomorphism between algebraic structures is a function that is compatible with the operations of the structures. For all common algebraic structures, and, in particular for vector spaces, an is also called a . However, in the more general context of category theory, the definition of a monomorphism differs from that of an injective homomorphism. This is thus a theorem that they are equivalent for algebraic structures; see for more details. A ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Landauer's Principle
Landauer's principle is a physical principle pertaining to the lower theoretical limit of energy consumption of computation. It holds that "any logically irreversible manipulation of information, such as the erasure of a bit or the merging of two computation paths, must be accompanied by a corresponding entropy increase in non-information-bearing degrees of freedom of the information-processing apparatus or its environment".. Another way of phrasing Landauer's principle is that if an observer loses information about a physical system, heat is generated and the observer loses the ability to extract useful work from that system. A so-called logically reversible computation, in which no information is erased, may in principle be carried out without releasing any heat. This has led to considerable interest in the study of reversible computing. Indeed, without reversible computing, increases in the number of computations per joule of energy dissipated must eventually come to a halt. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rolf Landauer
Rolf William Landauer (February 4, 1927 – April 27, 1999) was a German-American physicist who made important contributions in diverse areas of the thermodynamics of information processing, condensed matter physics, and the conductivity of disordered media. In 1961 he discovered Landauer's principle, that in any logically irreversible operation that manipulates information, such as erasing a bit of memory, entropy increases and an associated amount of energy is dissipated as heat. This principle is relevant to reversible computing, quantum information and quantum computing. He also is responsible for the Landauer formula relating the electrical resistance of a conductor to its scattering properties. He won the Stuart Ballantine Medal of the Franklin Institute, the Oliver Buckley Prize of the American Physical Society and the IEEE Edison Medal, among many other honors. Biography Landauer was born on February 4, 1927, in Stuttgart, Germany. He emigrated to the United States in 1 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bit Operation
In computer programming, a bitwise operation operates on a bit string, a bit array or a binary numeral (considered as a bit string) at the level of its individual bits. It is a fast and simple action, basic to the higher-level arithmetic operations and directly supported by the processor. Most bitwise operations are presented as two-operand instructions where the result replaces one of the input operands. On simple low-cost processors, typically, bitwise operations are substantially faster than division, several times faster than multiplication, and sometimes significantly faster than addition. While modern processors usually perform addition and multiplication just as fast as bitwise operations due to their longer instruction pipelines and other architectural design choices, bitwise operations do commonly use less power because of the reduced use of resources. Bitwise operators In the explanations below, any indication of a bit's position is counted from the right (least signi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
KT (energy)
{, class="wikitable" style="float: right;" ! Approximate values of ''kT'' at 298 K ! Units , - , ''kT'' = , , J , - , ''kT'' = , , pN⋅nm , - , ''kT'' = , , cal , - , ''kT'' = , , meV , - , ''kT'' = {{val, kT=-174 , , dBm/Hz , - ! colspan=2, {{center, Related quantities (also at 298 K) , - , ''kT/hc'' ≈ {{val, 207 {{cite web , title=Google Unit Converter , url=https://www.google.ca/search?ei=VzDnW4mbLOfMjwS694DYCw&q=k*298Kelvin%2Fh%2Fc+in+cm%5E-1&oq=k*298Kelvin%2Fh%2Fc+in+cm%5E-1&gs_l=psy-ab.3...2293.2598.0.3103.2.2.0.0.0.0.125.214.1j1.2.0....0...1.1.64.psy-ab..0.0.0....0.gYQvcs3LZis , accessdate=10 November 2018 , , cm−1 , - , ''kT''/''e'' = 25.7 , , mV , - , ''RT'' = ''kT'' ⋅ ''N''A = {{val, 2.479 , , kJ⋅mol−1 , - , ''RT'' = 0.593 , , kcal⋅mol−1 , - , ''h''/''kT'' = 0.16 , , ps ''kT'' (also written as ''k''B''T'') is the product of the Boltzmann constant, ''k'' (or ''k''B), and the temperature, ''T''. This product is used in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Von Neumann-Landauer Limit
Landauer's principle is a physical principle pertaining to the lower theoretical limit of energy consumption of computation. It holds that "any logically irreversible manipulation of information, such as the erasure of a bit or the merging of two computation paths, must be accompanied by a corresponding entropy increase in non-information-bearing degrees of freedom of the information-processing apparatus or its environment".. Another way of phrasing Landauer's principle is that if an observer loses information about a physical system, heat is generated and the observer loses the ability to extract useful work from that system. A so-called logically reversible computation, in which no information is erased, may in principle be carried out without releasing any heat. This has led to considerable interest in the study of reversible computing. Indeed, without reversible computing, increases in the number of computations per joule of energy dissipated must eventually come to a halt. I ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
