entropy (redirected from Disorder(thermodynamics))

entropy (ĕn`trəpē), quantity specifying the amount of disorder or randomness in a system bearing energy or information. Originally defined in thermodynamics in terms of heat and temperature, entropy indicates the degree to which a given quantity of thermal energy is available for doing useful work—the greater the entropy, the less available the energy. For example, consider a system composed of a hot body and a cold body; this system is ordered because the faster, more energetic molecules of the hot body are separated from the less energetic molecules of the cold body. If the bodies are placed in contact, heat will flow from the hot body to the cold one. This heat flow can be utilized by a heat engine (device which turns thermal energy into mechanical energy, or work), but once the two bodies have reached the same temperature, no more work can be done. Furthermore, the combined lukewarm bodies cannot unmix themselves into hot and cold parts in order to repeat the process. Although no energy has been lost by the heat transfer, the energy can no longer be used to do work. Thus the entropy of the system has increased. According to the second law of thermodynamics, during any process the change in entropy of a system and its surroundings is either zero or positive. In other words the entropy of the universe as a whole tends toward a maximum. This means that although energy cannot vanish because of the law of conservation of energy (see conservation laws), it tends to be degraded from useful forms to useless ones. It should be noted that the second law of thermodynamics is statistical rather than exact; thus there is nothing to prevent the faster molecules from separating from the slow ones. However, such an occurrence is so improbable as to be impossible from a practical point of view. In information theory the term entropy is used to represent the sum of the predicted values of the data in a message.

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entropy

Measure of a system's energy that is unavailable for work, or of the degree of a system's disorder. When heat is added to a system held at constant temperature, the change in entropy is related to the change in energy, the pressure, the temperature, and the change in volume. Its magnitude varies from zero to the total amount of energy in a system. The concept, first proposed in 1850 by the German physicist Rudolf Clausius (1822–1888), is sometimes presented as the second law of thermodynamics, which states that entropy increases during irreversible processes such as spontaneous mixing of hot and cold gases, uncontrolled expansion of a gas into a vacuum, and combustion of fuel. In popular, nontechnical use, entropy is regarded as a measure of the chaos or randomness of a system.

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entropy

Disorder or randomness. In data compression, it is a measure of the amount of non-redundant and non-compressible data in an object (the amount that is not similar). In encryption, it is the amount of disorder or randomness that is added. In software, it is the disorder and jumble of its logic, which occurs after the program has been modified over and over. See encryption algorithm.

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entropy

1. a thermodynamic quantity that changes in a reversible process by an amount equal to the heat absorbed or emitted divided by the thermodynamic temperature. It is measured in joules per kelvin.

2. a statistical measure of the disorder of a closed system expressed by S = klog P + c where P is the probability that a particular state of the system exists, k is the Boltzmann constant, and c is another constant - PLEASE CHECK FORMULA

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entropy [′en·trə·pē]

(communications)

A measure of the absence of information about a situation, or, equivalently, the uncertainty associated with the nature of a situation.

(mathematics)

In a mathematical context, this concept is attached to dynamical systems, transformations between measure spaces, or systems of events with probabilities; it expresses the amount of disorder inherent or produced.

(statistical mechanics)

Measure of the disorder of a system, equal to the Boltzmann constant times the natural logarithm of the number of microscopic states corresponding to the thermodynamic state of the system; this statistical-mechanical definition can be shown to be equivalent to the thermodynamic definition.

(thermodynamics)

Function of the state of a thermodynamic system whose change in any differential reversible process is equal to the heat absorbed by the system from its surroundings divided by the absolute temperature of the system. Also known as thermal charge.

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Entropy

A function first introduced in classical thermodynamics to provide a quantitative basis for the common observation that naturally occurring processes have a particular direction. Subsequently, in statistical thermodynamics, entropy was shown to be a measure of the number of microstates a system could assume. Finally, in communication theory, entropy is a measure of information. Each of these aspects will be considered in turn. Before the entropy function is introduced, it is necessary to discuss reversible processes.

Reversible processes

Any system under constant external conditions is observed to change in such a way as to approach a particularly simple final state called an equilibrium state. For example, two bodies initially at different temperatures are connected by a metal wire. Heat flows from the hot to the cold body until the temperatures of both bodies are the same. It is common experience that the reverse processes never occur if the systems are left to themselves; that is, heat is never observed to flow from the cold to the hot body. Max Planck classified all elementary processes into three categories: natural, unnatural, and reversible. Natural processes do occur, and proceed in a direction toward equilibrium. Unnatural processes move away from equilibrium and never occur. A reversible process is an idealized natural process that passes through a continuous sequence of equilibrium states.

Entropy function

The state function entropy S puts the foregoing discussion on a quantitative basis. Entropy is related to q, the heat flowing into the system from its surroundings, and to T, the absolute temperature of the system. The important properties for this discussion are:

1. dS > q/T for a natural change.

dS = q/T for a reversible change.

2. The entropy of the system S is made up of the sum of all the parts of the system so that . See Heat, Temperature

Nonconservation

In his study of the first law of thermodynamics, J. P. Joule caused work to be expended by rubbing metal blocks together in a large mass of water. By this and similar experiments, he established numerical relationships between heat and work. When the experiment was completed, the apparatus remained unchanged except for a slight increase in the water temperature. Work (W) had been converted into heat (Q) with 100% efficiency. Provided the process was carried out slowly, the temperature difference between the blocks and the water would be small, and heat transfer could be considered a reversible process. The entropy increase of the water at its temperature T is ΔS = Q/T = W/T. Since everything but the water is unchanged, this equation also represents the total entropy increase. The entropy has been created from the work input, and this process could be continued indefinitely, creating more and more entropy. Unlike energy, entropy is not conserved. See Conservation of energy, Thermodynamic processes

Degradation of energy

Energy is never destroyed. But in the Joule friction experiment and in heat transfer between bodies, as in any natural process, something is lost. In the Joule experiment, the energy expended in work now resides in the water bath. But if this energy is reused, less useful work is obtained than was originally put in. The original energy input has been degraded to a less useful form. The energy transferred from a high-temperature body to a lower-temperature body is also in a less useful form. If another system is used to restore this degraded energy to its original form, it is found that the restoring system has degraded the energy even more than the original system had. Thus, every process occurring in the world results in an overall increase in entropy and a corresponding degradation in energy.

Measure of information

The probability characteristic of entropy leads to its use in communication theory as a measure of information. The absence of information about a situation is equivalent to an uncertainty associated with the nature of the situation. This uncertainty is the entropy of the information about the particular situation.

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(theory)

entropy - A measure of the disorder of a system. Systems tend to go from a state of order (low entropy) to a state of maximum disorder (high entropy). The entropy of a system is related to the amount of information it contains. A highly ordered system can be described using fewer bits of information than a disordered one. For example, a string containing one million "0"s can be described using run-length encoding as [("0", 1000000)] whereas a string of random symbols (e.g. bits, or characters) will be much harder, if not impossible, to compress in this way. Shannon's formula gives the entropy H(M) of a message M in bits: H(M) = -log2 p(M) Where p(M) is the probability of message M.