Entropy (arrow of time)
Entropy is the only quantity in the physical sciences (apart from certain rare interactions in particle physics; see below) that requires a particular direction for time, sometimes called an arrow of time. As one goes "forward" in time, the second law of thermodynamics says, the entropy of an isolated system can increase, but not decrease. Hence, from one perspective, entropy measurement is a way of distinguishing the past from the future. However in thermodynamic systems that are not closed, entropy can decrease with time: many systems, including living systems, reduce local entropy at the expense of an environmental increase, resulting in a net increase in entropy. Examples of such systems and phenomena include the formation of typical crystals, the workings of a refrigerator and living organisms.
Entropy, like temperature, is an abstract concept, yet, like temperature, everyone has an intuitive sense of the effects of entropy. Watching a movie, it is usually easy to determine whether it is being run forward or in reverse. When run in reverse, broken glasses spontaneously reassemble, smoke goes down a chimney, wood "unburns", cooling the environment and ice "unmelts" warming the environment. No physical laws are broken in the reverse movie except the second law of thermodynamics, which reflects the time-asymmetry of entropy. An intuitive understanding of the irreversibility of certain physical phenomena (and subsequent creation of entropy) allows one to make this determination.
Entropy (1977 board game)
Entropy is an abstract strategy board game for two players designed by Eric Solomon in 1977. The game is "based on the eternal conflict in the universe between order and chaos [...] One player is Order, the other Chaos. Order is trying to make patterns vertically and horizontally. Chaos is trying to prevent this."
The game originally employed a 5×5 gameboard, but in 2000 a 7x7 board was introduced to allow deeper strategies.Entropy was awarded a rare 6 out of 6 by Games & Puzzles Magazine in 1981.David Pritchard called the game "a modern classic". It is sold commercially under the names Hyle (a 5×5 board) and Hyle7 (a 7×7 board).
Rules
The gameboard is a square grid of 7×7 cells. A game consists of two rounds. Each round starts with the board empty, and a bag containing 49 chips in seven colours.
The first player to move ("Chaos") draws coloured chips at random from the bag and places each one on the board in an empty cell. For each chip that is placed, the second player ("Order") may slide any chip horizontally or vertically any distance through empty cells, to rest in a currently empty cell. When the board becomes full, the round is finished, and Order scores 1 point for each chip in any palindromic pattern of chip colors (e.g. red–green–blue–green–red scores 3 + 5 = 8 points; red–red–red scores 2 + 2 + 3 = 7 points) occurring either horizontally or vertically. The players reverse roles and play a second round. The player with the higher score wins the game.
Entropy (information theory)
In information theory, systems are modeled by a transmitter, channel, and receiver. The transmitter produces messages that are sent through the channel. The channel modifies the message in some way. The receiver attempts to infer which message was sent. In this context, entropy (more specifically, Shannon entropy) is the expected value (average) of the information contained in each message. 'Messages' can be modeled by any flow of information.
In a more technical sense, there are reasons (explained below) to define information as the negative of the logarithm of the probability distribution. The probability distribution of the events, coupled with the information amount of every event, forms a random variable whose expected value is the average amount of information, or entropy, generated by this distribution. Units of entropy are the shannon, nat, or hartley, depending on the base of the logarithm used to define it, though the shannon is commonly referred to as a bit.
Entropy (astrophysics)
In astrophysics, what is referred to as "entropy" is actually the adiabatic constant derived as follows.
Using the first law of thermodynamics for a quasi-static, infinitesimal process for a hydrostatic system
For an ideal gas in this special case, the internal energy, U, is only a function of the temperature T; therefore the partial derivative of heat capacity with respect to T is identically the same as the full derivative, yielding through some manipulation
Further manipulation using the differential version of the ideal gas law, the previous equation, and assuming constant pressure, one finds
For an adiabatic process 
and recalling 
, one finds
One can solve this simple differential equation to find
This equation is known as an expression for the adiabatic constant, K, also called the adiabat. From the ideal gas equation one also knows
where 
is Boltzmann's constant.
Substituting this into the above equation along with ![V=[grams]/\rho\,](http://assets.wn.com/wiki/en/9/56/385eb969ce38828861671-197251.png)
and 
for an ideal monatomic gas one finds
where 
is the mean molecular weight of the gas or plasma; and 
is the mass of the Hydrogen atom, which is extremely close to the mass of the proton, 
, the quantity more often used in astrophysical theory of galaxy clusters.
This is what astrophysicists refer to as "entropy" and has units of [keV cm2]. This quantity relates to the thermodynamic entropy as
Arrow
An arrow is a shafted projectile that is shot with a bow. It predates recorded history and is common to most cultures. An arrow usually consists of a shaft with an arrowhead attached to the front end, with fletchings and a nock at the other.
History
The oldest evidence of stone-tipped projectiles, which may or may not have been propelled by a bow (c.f. atlatl), dating to c. 64,000 years ago, were found in Sibudu Cave, South Africa. The oldest evidence of the use of bows to shoot arrows dates to about 10,000 years ago; it is based on pinewood arrows found in the Ahrensburg valley north of Hamburg. They had shallow grooves on the base, indicating that they were shot from a bow. The oldest bow so far recovered is about 8,000 years old, found in the Holmegård swamp in Denmark. Archery seems to have arrived in the Americas with the Arctic small tool tradition, about 4,500 years ago.
Size
Arrow sizes vary greatly across cultures, ranging from eighteen inches to five feet (45 cm to 150 cm). However, most modern arrows are 75 centimetres (30 in) to 96 centimetres (38 in); most war arrows from an English ship sunk in 1545 were 76 centimetres (30 in). Very short arrows have been used, shot through a guide attached either to the bow (an "overdraw") or to the archer's wrist (the Turkish "siper"). These may fly farther than heavier arrows, and an enemy without suitable equipment may find himself unable to return them.
Arrow (train)
The Arrow was a passenger train operated by the Chicago, Milwaukee, St. Paul and Pacific Railroad (the "Milwaukee Road") between Chicago, Illinois and Omaha, Nebraska. It operated from 1926 until 1967. The Arrow provided overnight service between the two cities and included through cars for other destinations in Iowa.
History
The Milwaukee Road introduced the Arrow in August of 1926, replacing two previous services: the Omaha Limited (Chicago–Omaha) and Sioux City Limited (Chicago–Sioux City). The new train served both Omaha and Sioux City (for Sioux Falls, South Dakota), splitting in Manilla, Iowa. Through connections with other trains the Arrow also carried Chicago–Des Moines, Iowa and Milwaukee, Wisconsin–Omaha sleeping cars (via the Southwest Limited). The train made the run between Chicago and Omaha in 13 hours and 20 minutes. In 1934 the Milwaukee Road extended the Arrow over the Big Sioux River to Sioux Falls.
The Omaha sleeping car ended in early 1955, was reinstated later that year when the Milwaukee Road began handling the Union Pacific Railroad's Overland Route trains, and ended for good in 1958. Between 1956–1959 the Arrow carried a Chicago–Los Angeles coach which it exchanged in Omaha. The Sioux Falls section, including the train's last sleeping cars, ended on September 17, 1965. All that remained of the Arrow was a Chicago–Omaha coach train, which the Milwaukee Road discontinued on October 5, 1967.
Arrow (Israeli missile)
The Arrow or Hetz (Hebrew: חֵץ, pronounced [ˈχet͡s]) is a family of anti-ballistic missiles designed to fulfill an Israeli requirement for a theater missile defense system that would be more effective against ballistic missiles than the MIM-104 Patriot surface-to-air missile. Jointly funded and produced by Israel and the United States, development of the system began in 1986 and has continued since, drawing some contested criticism. Undertaken by Israel Aerospace Industries (IAI) and Boeing, it is overseen by the Israeli Ministry of Defense's "Homa" (Hebrew: חומה, pronounced [χoma], "rampart") administration and the U.S. Missile Defense Agency.
The Arrow system consists of the joint production hypersonic Arrow anti-missile interceptor, the Elta EL/M-2080 "Green Pine" early-warning AESA radar, the Elisra "Golden Citron" ("Citron Tree") C3I center, and the Israel Aerospace Industries "Brown Hazelnut" ("Hazelnut Tree") launch control center. The system is transportable, as it can be moved to other prepared sites.
