Dictionary Definition
entropy
Noun
1 (communication theory) a numerical measure of
the uncertainty of an outcome; "the signal contained thousands of
bits of information" [syn: information, selective
information]
2 (thermodynamics) a thermodynamic quantity
representing the amount of energy in a system that is no longer
available for doing mechanical work; "entropy increases as matter
and energy in the universe degrade to an ultimate state of inert
uniformity" [syn: randomness, S]
User Contributed Dictionary
English
Pronunciation
Etymology
First attested in 1868. From German Entropie (first coined 1865 by Rudolph Clausius), from ἐντροπία < ἐν + τροπή.Noun
 In the context of "thermodynamicscountable":
 strictly thermodynamic entropy. A measure of the amount of energy in a physical system which cannot be used to do mechanical work.
 A measure of the disorder present in a system (now becoming obsolete in chemistry http://www.entropysite.com/).
 The capacity factor for thermal energy that is hidden with respect to temperature http://arxiv.org/pdf/physics/0004055.
 The dispersal of energy; how much energy is spread out in a process, or how widely spread out it becomes, at a specific temperature. http://www.entropysite.com/students_approach.html
 In the context of "statisticsinformation theorycountable": A measure of the amount of information and noise present in a signal.
 The tendency of a system that is left to itself to descend into chaos.
Derived terms
Translations
term in thermodynamics
 Czech: entropie
 Finnish: entropia
 German: Entropie
 Russian: энтропия
measure of the amount of information in a signal
 German: Entropie
 Russian: энтропия
tendency of a system to descend into chaos
 Finnish: entropia
 German: Entropie
 Russian: энтропия
Extensive Definition
In thermodynamics (a branch
of physics), entropy is
a measure of the unavailability of a system’s
energy to do work.
It is a measure of the randomness of molecules in
a system and is central to the
second law of thermodynamics and the
fundamental thermodynamic relation, which deal with physical
processes and whether they occur spontaneously. Spontaneous
changes, in isolated
systems, occur with an increase in entropy. Spontaneous changes
tend to smooth out differences in temperature, pressure, density, and chemical
potential that may exist in a system, and entropy is thus a
measure of how far this smoothingout process has progressed.
The word "entropy" is derived from the Greek
εντροπία "a turning toward" (εν "in" + τροπή "a turning"), and is
symbolized by S in physics.
Explanation
When a system's energy is defined as the sum of its "useful" energy, (e.g. that used to push a piston), and its "useless energy", i.e. that energy which cannot be used for external work, then entropy may be (most concretely) visualized as the "scrap" or "useless" energy whose energetic prevalence over the total energy of a system is directly proportional to the absolute temperature of the considered system. (Note the product "TS" in the Gibbs free energy or Helmholtz free energy relations).Entropy is a function of a quantity of heat which
shows the possibility of conversion of that heat into work. The
increase in entropy is small when heat is added at high temperature
and is greater when heat is added at lower temperature. Thus for
maximum entropy there is minimum availability for conversion into
work and for minimum entropy there is maximum availability for
conversion into work.
Quantitatively, entropy is defined by the
differential quantity dS = \delta Q/T, where \delta Q is the amount
of heat absorbed in an
isothermal and
reversible process in which the system goes from one state
to another, and T is the absolute
temperature at which the process is occurring. Entropy is one
of the factors that determines the free
energy of the system. This thermodynamic definition of entropy
is only valid for a system in equilibrium (because temperature is
defined only for a system in equilibrium), while the statistical
definition of entropy (see below) applies to any system. Thus the
statistical definition is usually considered the fundamental
definition of entropy.
Entropy increase has often been defined as a
change to a more disordered
state at a molecular level. In recent years, entropy has been
interpreted in terms of the "dispersal"
of energy. Entropy is an extensive
state
function that accounts for the effects of irreversibility in
thermodynamic
systems.
In terms of statistical
mechanics, the entropy describes the number of the possible
microscopic configurations of the system. The statistical
definition of entropy is the more fundamental definition, from
which all other definitions and all properties of entropy
follow.
Origin of concept
The first law of thermodynamics, formalized through the heatfriction experiments of James Joule in 1843, deals with the concept of energy, which is conserved in all processes; the first law, however, lacks in its ability to quantify the effects of friction and dissipation.The concept of entropy was developed in the 1850s
by German
physicist Rudolf
Clausius who described it as the transformationcontent, i.e.
dissipative energy use,
of a thermodynamic
system or working body
of chemical
species during a change of state.
History
The history of entropy begins with the work of French mathematician Lazare Carnot who in his 1803 paper Fundamental Principles of Equilibrium and Movement proposed that in any machine the accelerations and shocks of the moving parts all represent losses of moment of activity. In other words, in any natural process there exists an inherent tendency towards the dissipation of useful energy. Building on this work, in 1824 Lazare's son Sadi Carnot published Reflections on the Motive Power of Fire in which he set forth the view that in all heatengines whenever "caloric", or what is now known as heat, falls through a temperature difference, that work or motive power can be produced from the actions of the "fall of caloric" between a hot and cold body. This was an early insight into the second law of thermodynamics.Carnot based his views of heat partially on the
early 18th century "Newtonian hypothesis" that both heat and light
were types of indestructible forms of matter, which are attracted
and repelled by other matter, and partially on the contemporary
views of Count
Rumford who showed in 1789 that heat could be created by
friction as when cannon bores are machined. Accordingly, Carnot
reasoned that if the body of the working substance, such as a body
of steam, is brought back to its original state (temperature and
pressure) at the end of a complete engine
cycle, that "no change occurs in the condition of the working
body." This latter comment was amended in his foot notes, and it
was this comment that led to the development of entropy.
In the 1850s and 60s, German physicist Rudolf
Clausius gravely objected to this latter supposition, i.e. that
no change occurs in the working body, and gave this "change" a
mathematical interpretation by questioning the nature of the
inherent loss of usable heat when work is done, e.g. heat produced
by friction. This was in contrast to earlier views, based on the
theories of Isaac
Newton, that heat was an indestructible particle that had mass.
Later, scientists such as Ludwig
Boltzmann, Josiah
Willard Gibbs, and James
Clerk Maxwell gave entropy a statistical basis. Carathéodory
linked entropy with a mathematical definition of irreversibility,
in terms of trajectories and integrability.
Definitions and descriptions
In science, the term "entropy" is generally interpreted in three distinct, but semirelated, ways, i.e. from macroscopic viewpoint (classical thermodynamics), a microscopic viewpoint (statistical thermodynamics), and an information viewpoint (information theory).The statistical definition of entropy (see below)
is the fundamental definition because the other two can be
mathematically derived from it, but not vice versa. All properties
of entropy (including
second law of thermodynamics) follow from this
definition.
Macroscopic viewpoint (classical thermodynamics)
In a thermodynamic system, a "universe" consisting of "surroundings" and "systems" and made up of quantities of matter, its pressure differences, density differences, and temperature differences all tend to equalize over time  simply because equilibrium state has higher probability (more possible combinations of microstates) than any other  see statistical mechanics. In the ice melting example, the difference in temperature between a warm room (the surroundings) and cold glass of ice and water (the system and not part of the room), begins to be equalized as portions of the heat energy from the warm surroundings spread out to the cooler system of ice and water. Over time the temperature of the glass and its contents and the temperature of the room become equal. The entropy of the room has decreased as some of its energy has been dispersed to the ice and water. However, as calculated in the example, the entropy of the system of ice and water has increased more than the entropy of the surrounding room has decreased. In an isolated system such as the room and ice water taken together, the dispersal of energy from warmer to cooler always results in a net increase in entropy. Thus, when the 'universe' of the room and ice water system has reached a temperature equilibrium, the entropy change from the initial state is at a maximum. The entropy of the thermodynamic system is a measure of how far the equalization has progressed.A special case of entropy increase, the entropy
of mixing, occurs when two or more different substances are
mixed. If the substances are at the same temperature and pressure,
there will be no net exchange of heat or work  the entropy
increase will be entirely due to the mixing of the different
substances.
From a macroscopic perspective, in classical
thermodynamics the entropy is interpreted simply as a state
function of a thermodynamic
system: that is, a property depending only on the current state
of the system, independent of how that state came to be achieved.
The state function has the important property that, when multiplied
by a reference temperature, it can be understood as a measure of
the amount of energy in a
physical system that cannot be used to do thermodynamic
work; i.e., work mediated by thermal energy. More precisely, in
any process where the system gives up energy ΔE, and its entropy
falls by ΔS, a quantity at least TR ΔS of that energy must be given
up to the system's surroundings as unusable heat (TR is the temperature of the
system's external surroundings). Otherwise the process will not go
forward.
In 1862, Clausius stated what he calls the
“theorem respecting the equivalencevalues of the transformations”
or what is now known as the
second law of thermodynamics, as such:
 The algebraic sum of all the transformations occurring in a cyclical process can only be positive, or, as an extreme case, equal to nothing.
Quantitatively, Clausius states the mathematical
expression for this theorem is as follows. Let δQ be an element of
the heat given up by the body to any reservoir of heat during its
own changes, heat which it may absorb from a reservoir being here
reckoned as negative, and T the absolute
temperature of the body at the moment of giving up this heat,
then the equation:
 \int \frac = 0
 \int \frac \ge 0
must hold good for every cyclical process which
is in any way possible. This is the essential formulation of the
second law and one of the original forms of the concept of entropy.
It can be seen that the dimensions of entropy are energy divided by
temperature, which is the same as the dimensions of Boltzmann's
constant (kB) and heat
capacity. The SI unit of entropy is
"joule per kelvin" (J·K−1). In this manner,
the quantity "ΔS" is utilized as a type of internal energy, which
accounts for the effects of irreversibility, in the
energy balance equation for any given system. In the Gibbs
free energy equation, i.e. ΔG = ΔH  TΔS, for example, which is
a formula commonly utilized to determine if chemical
reactions will occur, the energy related to entropy changes TΔS
is subtracted from the "total" system energy ΔH to give the "free"
energy ΔG of the system, as during a chemical
process or as when a system changes state.
Microscopic definition of entropy (statistical mechanics)
In statistical thermodynamics the entropy is defined as (proportional to) the logarithm of the number of microscopic configurations that result in the observed macroscopic description of the thermodynamic system: S = k_B \ln \Omega \!
 kB is Boltzmann's constant 1.38066×10−23 J K−1 and
 \Omega \! is the number of microstates corresponding to the observed thermodynamic macrostate.
This definition is considered to be the
fundamental definition of entropy (as all other definitions can be
mathematically derived from it, but not vice versa). In Boltzmann's
1896 Lectures on Gas Theory, he showed that this expression gives a
measure of entropy for systems of atoms and molecules in the gas
phase, thus providing a measure for the entropy of classical
thermodynamics.
In 1877, Boltzmann visualized a probabilistic way
to measure the entropy of an ensemble of ideal gas
particles, in which he defined entropy to be proportional to the
logarithm of the number of microstates such a gas could occupy.
Henceforth, the essential problem in statistical
thermodynamics, i.e. according to Erwin
Schrödinger, has been to determine the distribution of a given
amount of energy E over N identical systems.
Statistical
mechanics explains entropy as the amount of uncertainty (or
"mixedupness" in the phrase of Gibbs)
which remains about a system, after its observable macroscopic
properties have been taken into account. For a given set of
macroscopic variables, like temperature and volume, the entropy
measures the degree to which the probability of the system is
spread out over different possible quantum states. The more states
available to the system with higher probability, the greater the
entropy. More specifically, entropy is a logarithmic
measure of the density
of states. In essence, the most general interpretation of
entropy is as a measure of our uncertainty about a system. The
equilibrium
state of a system maximizes the entropy because we have lost
all information about the initial conditions except for the
conserved variables; maximizing the entropy maximizes our ignorance
about the details of the system. This uncertainty is not of the
everyday subjective kind, but rather the uncertainty inherent to
the experimental method and interpretative model.
On the molecular scale, the two definitions match
up because adding heat to a system, which increases its classical
thermodynamic entropy, also increases the system's thermal fluctuations, so
giving an increased lack of information about the exact microscopic
state of the system, i.e. an increased statistical mechanical
entropy.
The interpretative model has a central role in
determining entropy. The qualifier "for a given set of macroscopic
variables" above has very deep implications: if two observers use
different sets of macroscopic variables, then they will observe
different entropies. For example, if observer A uses the variables
U, V and W, and observer B uses U, V, W, X, then, by changing X,
observer B can cause an effect that looks like a violation of the
second law of thermodynamics to observer A. In other words: the set
of macroscopic variables one chooses must include everything that
may change in the experiment, otherwise one might see decreasing
entropy!
Entropy in chemical thermodynamics
Thermodynamic entropy is central in chemical thermodynamics, enabling changes to be quantified and the outcome of reactions predicted. The second law of thermodynamics states that entropy in the combination of a system and its surroundings (or in an isolated system by itself) increases during all spontaneous chemical and physical processes. Spontaneity in chemistry means “by itself, or without any outside influence”, and has nothing to do with speed. The Clausius equation of δqrev/T = ΔS introduces the measurement of entropy change, ΔS. Entropy change describes the direction and quantitates the magnitude of simple changes such as heat transfer between systems – always from hotter to cooler spontaneously. Thus, when a mole of substance at 0 K is warmed by its surroundings to 298 K, the sum of the incremental values of qrev/T constitute each element's or compound's standard molar entropy, a fundamental physical property and an indicator of the amount of energy stored by a substance at 298 K. Entropy change also measures the mixing of substances as a summation of their relative quantities in the final mixture.Entropy is equally essential in predicting the
extent of complex chemical reactions, i.e. whether a process will
go as written or proceed in the opposite direction. For such
applications, ΔS must be incorporated in an expression that
includes both the system and its surroundings, ΔSuniverse =
ΔSsurroundings + ΔS system. This expression becomes, via some
steps, the Gibbs
free energy equation for reactants and products in the system:
ΔG [the Gibbs
free energy change of the system] = ΔH [the enthalpy change] −T ΔS [the
entropy change].
 \frac = \sum_^K \dot_k \hat_k + \frac + \dot_
where
 \sum_^K \dot_k \hat_k = the net rate of entropy flow due to the flows of mass into and out of the system (where \hat = entropy per unit mass).
 \frac = the rate of entropy flow due to the flow of heat across the system boundary.
 \dot_ = the rate of internal generation of entropy within the system.
Note, also, that if there are multiple heat
flows, the term \dot/T is to be replaced by \sum \dot_j/T_j, where
\dot_j is the heat flow and T_j is the temperature at the jth heat
flow port into the system.
Entropy in quantum mechanics (von Neumann entropy)
main article von
Neumann entropy
In
quantum statistical mechanics, the concept of entropy was
developed by John von
Neumann and is generally referred to as "von
Neumann entropy". Von Neumann established a rigorous
mathematical framework for quantum mechanics with his work
Mathematische Grundlagen der Quantenmechanik. He provided in this
work a theory of measurement, where the usual notion of wave
collapse is described as an irreversible process (the so called von
Neumann or projective measurement). Using this concept, in
conjunction with the density
matrix he extended the classical concept of entropy into the
quantum domain.
It is well known that a Shannon based definition
of information entropy leads in the classical case to the Boltzmann
entropy. It is tempting to regard the Von Neumann entropy as the
corresponding quantum mechanical definition. But the latter is
problematic from quantum information point of view. Consequently
Stotland, Pomeransky, Bachmat and Cohen have introduced a new
definition of entropy that reflects the inherent uncertainty of
quantum mechanical states. This definition allows to distinguish
between the minimum uncertainty entropy of pure states, and the
excess statistical entropy of mixtures.
Entropy in 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
quasistatic, infinitesimal process for a hydrostatic system
 dQ = dUdW.
For an ideal gas in this special case, the
internal energy, U, is only a function of T; therefore the partial
derivative of heat capacity with respect to T is identically the
same as the full derivative, yielding through some manipulation dQ
= C_ dT+P dV.
Further manipulation using the differential
version of the ideal gas law, the previous equation, and assuming
constant pressure, one finds dQ = C_ dTV dP.
For an adiabatic process dQ=0 and recalling
\gamma = \frac, one finds
One can solve this simple differential equation
to find PV^ = constant = K
This equation is known as an expression for the
adiabatic constant, K,
also called the adiabat. From the ideal gas equation one also knows
P=\frac,
where k_ is Boltzmann's constant. Substituting
this into the above equation along with V=[grams]/\rho and \gamma =
5/3 for an ideal monoatomic gas one finds K = \frac,
where \mu is the mean molecular weight of the gas
or plasma; and m_ is the mass of the Hydrogen atom, which is
extremely close to the mass of the proton, m_, 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 S = k_\, ln \Omega +
S_
where \Omega, the density of states in
statistical theory, takes on the value of K as defined above.
Standard textbook definitions
The following is a list of definitions of entropy from a collection of textbooks. Note that textbook definitions are not always the most helpful definitions, but they are an important aspect of the culture surrounding the concept of entropy. Entropy – energy broken down in irretrievable heat.
 Boltzmann's constant times the logarithm of a multiplicity; where the multiplicity of a macrostate is the number of microstates that correspond to the macrostate.
 the number of ways of arranging things in a system (times the Boltzmann's constant).
 a nonconserved thermodynamic state function, measured in terms of the number of microstates a system can assume, which corresponds to a degradation in usable energy.
 a direct measure of the randomness of a system.
 a measure of energy dispersal at a specific temperature.
 a measure of the partial loss of the ability of a system to perform work due to the effects of irreversibility.
 an index of the tendency of a system towards spontaneous change.
 a measure of the unavailability of a system’s energy to do work; also a measure of disorder; the higher the entropy the greater the disorder.
 a parameter representing the state of disorder of a system at the atomic, ionic, or molecular level.
 a measure of disorder in the universe or of the availability of the energy in a system to do work.
Approaches to understanding entropy
Order and disorder
Entropy, historically, has often been associated with the amount of order, disorder, and/or chaos in a thermodynamic system. The traditional definition of entropy is that it refers to changes in the status quo of the system and is a measure of "molecular disorder" and the amount of wasted energy in a dynamical energy transformation from one state or form to another. In this direction, a number of authors, in recent years, have derived exact entropy formulas to account for and measure disorder and order in atomic and molecular assemblies. One of the simpler entropy order/disorder formulas is that derived in 1984 by thermodynamic physicist Peter Landsberg, which is based on a combination of thermodynamics and information theory arguments. Landsberg argues that when constraints operate on a system, such that it is prevented from entering one or more of its possible or permitted states, as contrasted with its forbidden states, the measure of the total amount of “disorder” in the system is given by the following expression: Similar terms have been in use from early in the history of classical thermodynamics, and with the development of statistical thermodynamics and quantum theory, entropy changes have been described in terms of the mixing or "spreading" of the total energy of each constituent of a system over its particular quantized energy levels.Ambiguities in the terms disorder and chaos,
which usually have meanings directly opposed to equilibrium,
contribute to widespread confusion and hamper comprehension of
entropy for most students. As the
second law of thermodynamics shows, in an isolated
system internal portions at different temperatures will tend to
adjust to a single uniform temperature and thus produce
equilibrium. A recently developed educational approach avoids
ambiguous terms and describes such spreading out of energy as
dispersal, which leads to loss of the differentials required for
work even though the total energy remains constant in accordance
with the
first law of thermodynamics. Physical chemist Peter
Atkins, for example, who previously wrote of dispersal leading
to a disordered state, now writes that "spontaneous changes are
always accompanied by a dispersal of energy", and has discarded
'disorder' as a description. Shannon
entropy is a broad and general concept which finds applications
in information
theory as well as
thermodynamics. It was originally devised by Claude
Shannon in 1948 to study the amount of information in a
transmitted message. The definition of the information entropy is,
however, quite general, and is expressed in terms of a discrete set
of probabilities p_i. In the case of transmitted messages, these
probabilities were the probabilities that a particular message was
actually transmitted, and the entropy of the message system was a
measure of how much information was in the message. For the case of
equal probabilities (i.e. each message is equally probable), the
Shannon entropy (in bits) is just the number of yes/no questions
needed to determine the content of the message.
The question of the link between information
entropy and thermodynamic entropy is a hotly debated topic. Some
authors argue that there is a link between the two, while others
will argue that they have absolutely nothing to do with each
other.
The expressions for the two entropies are very
similar. The information entropy H for equal probabilities p_i=p
is:
 H=K\ln(1/p)\,
where K is a constant which determines the units
of entropy. For example, if the units are bits, then K=1/ln(2). The
thermodynamic entropy S , from a statistical mechanical
point of view was first expressed by Boltzmann:
 S=k\ln(1/p)\,
where p is the probability of a system
being in a particular microstate, given that it is in a particular
macrostate, and k is Boltzmann's constant. It can be seen
that one may think of the thermodynamic entropy as Boltzmann's
constant, divided by ln(2), times the number of yes/no questions
that must be asked in order to determine the microstate of the
system, given that we know the macrostate. The link between
thermodynamic and information entropy was developed in a series of
papers by Edwin Jaynes
beginning in 1957.
The problem with linking thermodynamic entropy to
information entropy is that in information entropy the entire body
of thermodynamics which deals with the physical nature of entropy
is missing. The second law of thermodynamics which governs the
behavior of thermodynamic systems in equilibrium, and the first law
which expresses heat energy as the product of temperature and
entropy are physical concepts rather than informational concepts.
If thermodynamic entropy is seen as including all of the physical
dynamics of entropy as well as the equilibrium statistical aspects,
then information entropy gives only part of the description of
thermodynamic entropy. Some authors, like Tom Schneider, argue for
dropping the word entropy for the H function of information theory
and using Shannon's other term "uncertainty" instead.
Ice melting example
The illustration for this article is a classic example in which entropy increases in a small 'universe', a thermodynamic system consisting of the 'surroundings' (the warm room) and 'system' (glass, ice, cold water). In this universe, some heat energy δQ from the warmer room surroundings (at 298 K or 25 °C) will spread out to the cooler system of ice and water at its constant temperature T of 273 K (0 °C), the melting temperature of ice. The entropy of the system will change by the amount dS = δQ/T, in this example δQ/273 K. (The heat δQ for this process is the energy required to change water from the solid state to the liquid state, and is called the enthalpy of fusion, i.e. the ΔH for ice fusion.) The entropy of the surroundings will change by an amount dS = −δQ/298 K. So in this example, the entropy of the system increases, whereas the entropy of the surroundings decreases.It is important to realize that the decrease in
the entropy of the surrounding room is less than the increase in
the entropy of the ice and water: the room temperature of 298 K is
larger than 273 K and therefore the ratio, (entropy change), of
δQ/298 K for the surroundings is smaller than the ratio (entropy
change), of δQ/273 K for the ice+water system. To find the entropy
change of our "universe", we add up the entropy changes for its
constituents: the surrounding room, and the ice+water. The total
entropy change is positive; this is always true in spontaneous
events in a thermodynamic
system and it shows the predictive importance of entropy: the
final net entropy after such an event is always greater than was
the initial entropy.
As the temperature of the cool water rises to
that of the room and the room further cools imperceptibly, the sum
of the δQ/T over the continuous range, at many increments, in the
initially cool to finally warm water can be found by calculus. The
entire miniature "universe", i.e. this thermodynamic system, has
increased in entropy. Energy has spontaneously become more
dispersed and spread out in that "universe" than when the glass of
ice water was introduced and became a "system" within it.
Topics in entropy
Entropy and life
For over a century and a half, beginning with Clausius' 1863 memoir "On the Concentration of Rays of Heat and Light, and on the Limits of its Action", much writing and research has been devoted to the relationship between thermodynamic entropy and the evolution of life. The argument that life feeds on negative entropy or negentropy as put forth in the 1944 book What is Life? by physicist Erwin Schrödinger served as a further stimulus to this research. Recent writings have utilized the concept of Gibbs free energy to elaborate on this issue. Tangentially, some creationists have argued that entropy rules out evolution.In the popular 1982 textbook Principles of
Biochemistry by noted American biochemist Albert
Lehninger, for example, it is argued that the order produced
within cells as they grow and divide is more than compensated for
by the disorder they create in their surroundings in the course of
growth and division. In short, according to Lehninger, "living
organisms preserve their internal order by taking from their
surroundings free
energy, in the form of nutrients or sunlight, and returning to
their surroundings an equal amount of energy as heat and entropy."
Evolution related definitions:
 Negentropy  a shorthand colloquial phrase for negative entropy.
 Ectropy  a measure of the tendency of a dynamical system to do useful work and grow more organized.
 Syntropy  a tendency towards order and symmetrical combinations and designs of ever more advantageous and orderly patterns.
 Extropy – a metaphorical term defining the extent of a living or organizational system's intelligence, functional order, vitality, energy, life, experience, and capacity and drive for improvement and growth.
 Ecological entropy  a measure of biodiversity in the study of biological ecology.
The arrow of time
Entropy is the only quantity in the physical sciences that "picks" a particular direction for time, sometimes called an arrow of time. As we go "forward" in time, the Second Law of Thermodynamics tells us that the entropy of an isolated system can only increase or remain the same; it cannot decrease. Hence, from one perspective, entropy measurement is thought of as a kind of clock.Entropy and cosmology
As a finite universe may be considered an isolated system, it may be subject to the Second Law of Thermodynamics, so that its total entropy is constantly increasing. It has been speculated that the universe is fated to a heat death in which all the energy ends up as a homogeneous distribution of thermal energy, so that no more work can be extracted from any source.If the universe can be considered to have
generally increasing entropy, then  as Roger
Penrose has pointed out  gravity plays an important role
in the increase because gravity causes dispersed matter to
accumulate into stars, which collapse eventually into black holes.
Jacob
Bekenstein and Stephen
Hawking have shown that black holes have the maximum possible
entropy of any object of equal size. This makes them likely end
points of all entropyincreasing processes, if they are totally
effective matter and energy traps. Hawking has, however, recently
changed his stance on this aspect.
The role of entropy in cosmology remains a
controversial subject. Recent work has cast extensive doubt on the
heat death hypothesis and the applicability of any simple
thermodynamic model to the universe in general. Although entropy
does increase in the model of an expanding universe, the maximum
possible entropy rises much more rapidly  thus entropy density is
decreasing with time. This results in an "entropy gap" pushing the
system further away from equilibrium. Other complicating factors,
such as the energy density of the vacuum and macroscopic quantum
effects, are difficult to reconcile with thermodynamical models,
making any predictions of largescale thermodynamics extremely
difficult.
Miscellaneous definitions
 Entropy unit  a nonS.I. unit of thermodynamic entropy, usually denoted "e.u." and equal to one calorie per kelvin
 Gibbs entropy  the usual statistical mechanical entropy of a thermodynamic system.
 Boltzmann entropy  a type of Gibbs entropy, which neglects internal statistical correlations in the overall particle distribution.
 Tsallis entropy  a generalization of the standard BoltzmannGibbs entropy.
 Standard molar entropy  is the entropy content of one mole of substance, under conditions of standard temperature and pressure.
 Black hole entropy  is the entropy carried by a black hole, which is proportional to the surface area of the black hole's event horizon.
 Residual entropy  the entropy present after a substance is cooled arbitrarily close to absolute zero.
 Entropy of mixing  the change in the entropy when two different chemical substances or components are mixed.
 Loop entropy  is the entropy lost upon bringing together two residues of a polymer within a prescribed distance.
 Conformational entropy  is the entropy associated with the physical arrangement of a polymer chain that assumes a compact or globular state in solution.
 Entropic force  a microscopic force or reaction tendency related to system organization changes, molecular frictional considerations, and statistical variations.
 Free entropy  an entropic thermodynamic potential analogous to the free energy.
 Entropic explosion – an explosion in which the reactants undergo a large change in volume without releasing a large amount of heat.
 Entropy change – a change in entropy dS between two equilibrium states is given by the heat transferred dQrev divided by the absolute temperature T of the system in this interval.
 SackurTetrode entropy  the entropy of a monatomic classical ideal gas determined via quantum considerations.
Other relations
Other mathematical definitions
 KolmogorovSinai entropy  a mathematical type of entropy in dynamical systems related to measures of partitions.
 Topological entropy  a way of defining entropy in an iterated function map in ergodic theory.
 Relative entropy  is a natural distance measure from a "true" probability distribution P to an arbitrary probability distribution Q.
 Rényi entropy  a generalized entropy measure for fractal systems.
Sociological definitions
The concept of entropy has also entered the domain of sociology, generally as a metaphor for chaos, disorder or dissipation of energy, rather than as a direct measure of thermodynamic or information entropy: Entropology – the study or discussion of entropy or the name sometimes given to thermodynamics without differential equations.
 Psychological entropy  the distribution of energy in the psyche, which tends to seek equilibrium or balance among all the structures of the psyche.
 Economic entropy – a semiquantitative measure of the irrevocable dissipation and degradation of natural materials and available energy with respect to economic activity.
 Social entropy – a measure of social system structure, having both theoretical and statistical interpretations, i.e. society (macrosocietal variables) measured in terms of how the individual functions in society (microsocietal variables); also related to social equilibrium.
 Corporate entropy  energy waste as red tape and business team inefficiency, i.e. energy lost to waste. (This definition is comparable to von Clausewitz's concept of friction in war.)
Quotes














 Willard Gibbs, Graphical Methods in the Thermodynamics of Fluids (1873)



























 Conversation between Claude Shannon and John von Neumann regarding what name to give to the “measure of uncertainty” or attenuation in phoneline signals (1949)













See also
 Arrow of time
 Autocatalytic reactions and order creation
 Brownian ratchet
 Chaos theory
 Configuration entropy
 Departure function
 Enthalpy
 Entropy: A New World View (book)
 Entropy rate
 Geometrically frustrated magnet
 Introduction to entropy
 Maxwell's demon
 Multiplicity function
 Statistical mechanics
 Stirling's formula
 Thermodynamic databases for pure substances
 Thermodynamic potential
 Entropy for beginners
References
 P. Pluch Quantum Probability Theory, PhD Thesis, University of Klagenfurt (2006)
Further reading
 The Refrigerator and the Universe
 Maxwell's Demon: Why Warmth Disperses and Time Passes
External links
 Entropy  A Basic Understanding A primer for entropy from a chemical perspective
 Max Jammer (1973). Dictionary of the History of Ideas: Entropy
 Frank L. Lambert; entropysite.com – links to articles including simple introductions to entropy for chemistry students and for general readers.
 Thermodynamics  a chapter from an online textbook
 Entropy on Project PHYSNET
 Entropy Journal  a free journal on Entropy
entropy in Arabic: إنتروبية (تحريك حراري)
entropy in Bengali: এনট্রপি
entropy in Belarusian: Энтрапія
entropy in Bosnian: Entropija
entropy in Breton: Entropiezh
entropy in Bulgarian: Ентропия
entropy in Catalan: Entropia
entropy in Czech: Entropie
entropy in Danish: Entropi
entropy in German: Entropie
entropy in Estonian: Entroopia
entropy in Modern Greek (1453): Εντροπία
entropy in Spanish: Entropía
(termodinámica)
entropy in Esperanto: Entropio
entropy in Persian: انتروپی
entropy in French: Entropie
entropy in Galician: Entropía
entropy in Korean: 엔트로피
entropy in Hindi: उत्क्रम
entropy in Croatian: Entropija
entropy in Interlingua (International Auxiliary
Language Association): Entropia
entropy in Italian: Entropia
(termodinamica)
entropy in Hebrew: אנטרופיה
entropy in Latvian: Entropija
entropy in Lithuanian: Entropija
entropy in Hungarian: Entrópia
entropy in Dutch: Entropie
entropy in Japanese: エントロピー
entropy in Norwegian: Entropi
entropy in Norwegian Nynorsk: Entropi
entropy in Polish: Entropia
entropy in Portuguese: Entropia
entropy in Romanian: Entropie
entropy in Russian: Термодинамическая
энтропия
entropy in Sardinian: Entropia
entropy in Slovak: Entropia
entropy in Slovenian: Entropija
entropy in Serbian: Ентропија
entropy in SerboCroatian: Entropija
entropy in Finnish: Entropia
entropy in Swedish: Entropi
entropy in Thai: เอนโทรปี
entropy in Vietnamese: Entropy
entropy in Turkish: Entropi
entropy in Ukrainian: Термодинамічна
ентропія
entropy in Chinese: 熵 (熱力學)
Synonyms, Antonyms and Related Words
EDP,
abeyance, aloofness, amorphia, amorphism, amorphousness, anarchy, apathy, bit, blurriness, catalepsy, catatonia, channel, chaos, communication explosion,
communication theory, confusion, data retrieval,
data storage, deadliness, deathliness, decoding, derangement, diffusion, disarrangement, disarray, disarticulation,
discomfiture,
discomposure,
disconcertedness,
discontinuity,
discreteness,
disharmony, dishevelment, disintegration, disjunction, dislocation, disorder, disorderliness, disorganization,
dispersal, dispersion, disproportion, disruption, dissolution, disturbance, dormancy, electronic data
processing, encoding,
formlessness,
fuzziness, haphazardness, haziness, incoherence, inconsistency, indecisiveness, indefiniteness, indeterminateness,
indifference,
indiscriminateness,
indolence, inertia, inertness, information
explosion, information theory, inharmonious harmony, irregularity, languor, latency, lotuseating, messiness, mistiness, most admired
disorder, noise, nonadhesion, noncohesion, nonsymmetry, nonuniformity, obscurity, orderlessness, passiveness, passivity, perturbation, promiscuity, promiscuousness,
randomness, redundancy, scattering, separateness, shapelessness, signal, stagnancy, stagnation, stasis, suspense, torpor, turbulence, unadherence, unadhesiveness, unclearness, unsymmetry, untenacity, ununiformity, upset, vagueness, vegetation, vis
inertiae