Second law of thermodynamics. The second law of thermodynamics states that every process occurring in nature proceeds in the sense in which the sum of the entropies of all bodies taking part in the process is increased. In the limit, i.e. for reversible processes, the sum of the entropies remains unchanged.[1][2][3] The second law is an empirical finding that has been accepted as an axiom of thermodynamic theory. Statistical thermodynamics, classical or quantum, explains the law. The second law has been expressed in many ways. Its first formulation is credited to the French scientist Sadi Carnot in 1824 (see Timeline of thermodynamics). Introduction[edit] The first law of thermodynamics provides the basic definition of thermodynamic energy, also called internal energy, associated with all thermodynamic systems, but unknown in classical mechanics, and states the rule of conservation of energy in nature.[4][5] For mathematical analysis of processes, entropy is introduced as follows.
Various statements of the law[edit] Thus, [cs/0406015] Zipf's law and the creation of musical context. Zipf's law. Zipf's law /ˈzɪf/, an empirical law formulated using mathematical statistics, refers to the fact that many types of data studied in the physical and social sciences can be approximated with a Zipfian distribution, one of a family of related discrete power law probability distributions. The law is named after the American linguist George Kingsley Zipf (1902–1950), who first proposed it (Zipf 1935, 1949), though the French stenographer Jean-Baptiste Estoup (1868–1950) appears to have noticed the regularity before Zipf.[1] It was also noted in 1913 by German physicist Felix Auerbach[2] (1856–1933). Motivation[edit] Zipf's law states that given some corpus of natural language utterances, the frequency of any word is inversely proportional to its rank in the frequency table.
Thus the most frequent word will occur approximately twice as often as the second most frequent word, three times as often as the third most frequent word, etc. Theoretical review[edit] Formally, let: Related laws[edit] Isaac Newton. Sir Isaac Newton PRS MP (/ˈnjuːtən/;[8] 25 December 1642 – 20 March 1726/7[1]) was an English physicist and mathematician (described in his own day as a "natural philosopher") who is widely recognised as one of the most influential scientists of all time and as a key figure in the scientific revolution. His book Philosophiæ Naturalis Principia Mathematica ("Mathematical Principles of Natural Philosophy"), first published in 1687, laid the foundations for classical mechanics. Newton made seminal contributions to optics, and he shares credit with Gottfried Leibniz for the development of calculus. Newton built the first practical reflecting telescope and developed a theory of colour based on the observation that a prism decomposes white light into the many colours of the visible spectrum.
He formulated an empirical law of cooling, studied the speed of sound, and introduced the notion of a Newtonian fluid. Life Early life Isaac Newton (Bolton, Sarah K. Middle years Mathematics Optics. Occam's razor. The sun, moon and other solar system planets can be described as revolving around the Earth. However that explanation's ideological and complex assumptions are completely unfounded compared to the modern consensus that all solar system planets revolve around the Sun. Ockham's razor (also written as Occam's razor and in Latin lex parsimoniae) is a principle of parsimony, economy, or succinctness used in problem-solving devised by William of Ockham (c. 1287 - 1347).
It states that among competing hypotheses, the one with the fewest assumptions should be selected. Other, more complicated solutions may ultimately prove correct, but—in the absence of certainty—the fewer assumptions that are made, the better. Solomonoff's theory of inductive inference is a mathematically formalized Occam's Razor:[2][3][4][5][6][7] shorter computable theories have more weight when calculating the probability of the next observation, using all computable theories which perfectly describe previous observations.