# Entropy

Entropy is a thermodynamic quantity whose value depends on the physical state or condition of a system. It is useful in physics as a means of expressing the Second Law of Thermodynamics. That is, while the law may be stated in terms of it being impossible to extract heat from a reservoir and convert it totally to usable work, in terms of entropy the law states that any changes occurring in a system that is thermally isolated from its surroundings are such that its entropy never decreases.

This behavior corresponds to the fact that entropy is a measure of the disorder of a system. On average all of nature proceeds to a greater state of disorder. Examples of irreversible progression to disorder are pervasive in the world and in everyday experience. Bread crumbs will never gather back into the loaf. Helium atoms that escape from a balloon never return. A drop of ink placed in a glass of water will uniformly color the entire glass and never assemble into its original shape.

Entropy as a measure of disorder can be shown to depend on the probability that the particles of a system are in a given state of order. The tendency for entropy to increase occurs because the number of possible states of disorder that a system can assume is greater than the number of more ordered states, making a state of disorder more probable. For example, the entropy of the ordered state of the water molecules in ice crystal is less than it is when the crystal is melted to liquid water. The entropy difference involved corresponds to the transfer of heat to the crystal in order to melt it.

It may appear that there are exceptions to the general rule of ultimate progression to disorder; the growth of crystals, plants, animals, and humans are all remarkable examples of order or organization. However, these are open systems that exchange matter and energy with their surroundings for their growth and sustenance. If a composite of the system plus its environment is considered, then it can always be shown that its entropy will never decrease, as long as the composite system is isolated.

Entropy is defined in physics as the ratio of the heat absorbed by a system to its absolute temperature (i.e., temperature based on the Kelvin scale). When a certain amount of heat passes to a system from one at a higher temperature, the entropy of the two systems combined increases. This is an irreversible process characterizing the general tendency of matter to seek temperature equilibrium, a state of maximum entropy or disorder.

This progressive tendency of nature toward disorder has been considered by many scholars as one of the primal natural processes that serve as a gauge for the irreversible nature of time. Accordingly, a considerable number have identified the relentless increase of entropy with what they term the thermodynamic arrow of time. In addition, the degradation associated with the increase of entropy has been discussed by some scholars of science and religion as a meaningful metaphor for evil.

See also Disorder; Thermodynamics, Second Law of

## Bibliography

feynman, richard p. the feynman lectures on physics, vol. 1. reading, mass.: addison-wesley, 1963.

coveney, peter, and highfield, roger. the arrow of time: a voyage through science to solve time's greatest mystery. new york: ballantine, 1990.

russell, john robert. "entropy and evil." zygon: journal of science and religion 19 (1984): 449468.

sears, francis w. thermodynamics. reading, mass.: addison-wesley, 1953.

zemansky, mark w., and dittman, richard h. heat and thermodynamics, 6th edition. new york: mcgraw-hill, 1979.

lawrence w. fagg

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## entropy

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

entropy Symbol S. A measure of the unavailability of a system's energy to do work; an increase in entropy is accompanied by a decrease in energy availability. When a system undergoes a reversible change the entropy (S) changes by an amount equal to the energy (Q) absorbed by the system divided by the thermodynamic temperature (T) at which the energy is absorbed, i.e. ΔS = ΔQ/T. However, all real processes are to a certain extent irreversible changes and in any closed system an irreversible change is always accompanied by an increase in entropy.

In a wider sense entropy can be interpreted as a measure of a system's disorder; the higher the entropy the greater the disorder. As any real change to a closed system tends towards higher entropy, and therefore higher disorder, it follows that the entropy of the universe (if it can be considered a closed system) is increasing and its available energy is decreasing. This increase in the entropy of the universe is one way of stating the second law of thermodynamics.

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## entropy

entropy A measure of the amount of information that is output by a source, or throughput by a channel, or received by an observer (per symbol or per second). Following Shannon (1948) and later writers, the entropy of a discrete memoryless source with alphabet A = {ai} of size n, and output X at time t is

where p(xi) = Prob {Xt = ai}

The logarithmic base b is chosen to give a convenient scale factor. Usually,

b = 2

b = e = 2.71828…

or

b = 10

Entropy is then measured in bits, in natural units or nats, or in Hartleys, respectively. When the source has memory, account has to be taken of the dependence between successive symbols output by the source.

The term arises by analogy with entropy in thermodynamics, where the defining expression has the same form but with a physical scale factor k (Boltzmann constant) and with the sign changed. The word negentropy is therefore sometimes used for the measure of information, as is uncertainty or simply “information”.

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## entropy

en·tro·py / ˈentrəpē/ • n. Physics a thermodynamic quantity representing the unavailability of a system's thermal energy for conversion into mechanical work, often interpreted as the degree of disorder or randomness in the system. (Symbol: S) ∎ fig. lack of order or predictability; gradual decline into disorder: a marketplace where entropy reigns supreme. ∎  (in information theory) a logarithmic measure of the rate of transfer of information in a particular message or language. DERIVATIVES: en·tro·pic / enˈträpik/ adj. en·tro·pi·cal·ly adv.

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## entropy

entropy Quantity that specifies the disorder of a physical system; the greater the disorder, the greater the entropy. In thermodynamics, it expresses the degree to which thermal energy is available for work – the less available it is, the greater the entropy. According to the second law of thermodynamics, a system's change in entropy is either zero or positive in any process.

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## entropy

entropy
1. Measure of disorder or unavailable energy in a thermodynamic system; the measure of increasing disorganization of the universe.

2. See LEAST-WORK PRINCIPLE; and LEAST-WORK PROFILE.

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## entropy

entropy
1. A measure of disorder or unavailable energy in a thermodynamic system; the measure of increasing disorganization of the universe.

2. See least-work principle and least-work profile.

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## entropy

entropy XIX. — G. entropie, f. Gr. en EN-2 + tropḗ transformation (see TROPE), after energy; see -Y3.

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## entropy

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