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The second law of thermodynamics is an expression of the universal law of increasing entropy. In simple terms, it is an expression of the fact that over time, differences in temperature, pressure, and density tend to even out in a physical system which is isolated from the outside world. Entropy is a measure of how far along this evening-out process has progressed.

The origin of the second law can be traced to French physicist `There was an error working with the wiki: Code[18]`

's 1824 paper Reflections on the Motive Power of Fire, which presented the view that motive power (work) is due to the flow of caloric (heat) from a hot to cold body (working substance). In simple terms, the second law is an expression of the fact that over time, ignoring the effects of self-gravity, differences in temperature, pressure, and density tend to even out in a physical system that is isolated from the outside world. Entropy is a measure of how much this evening-out process has progressed.

There are many versions of the second law, but they all have the same effect, which is to explain the phenomenon of irreversibility in nature.

A mathematical representation of the second law is:

\int \frac{\delta Q}{T} \ge 0

where {\delta Q} is the heat energy added to the system and T is the temperature.

There are many ways of stating the second law of thermodynamics, but all are equivalent in the sense that each form of the second law logically implies every other form.`There was an error working with the wiki: Code[1]`

Thus, the theorems of thermodynamics can be proved using any form of the second law and third law.

The formulation of the second law that refers to entropy directly is as follows:

In a `There was an error working with the wiki: Code[37]`

, a process that occurs will tend to increase the total entropy of the universe.

Thus, while a system can undergo some physical process that decreases its own entropy, the entropy of the universe (which includes the system and its surroundings) must increase overall. (An exception to this rule is a reversible or "isentropic" process, such as frictionless adiabatic compression.) Processes that decrease the total entropy of the universe are impossible. If a system is at equilibrium, by definition no spontaneous processes occur, and therefore the system is at maximum entropy.

Also, due to `There was an error working with the wiki: Code[38]`

, is the simplest formulation of the second law, the heat formulation or Clausius statement:

Heat generally cannot flow from a material spontaneously at lower temperature to a material at higher temperature.

Informally, "Heat doesn't flow from cold to hot (without work input)", which is true obviously from ordinary experience. For example in a refrigerator, heat flows from cold to hot, but only when aided by an external agent (i.e. the compressor). Note that from the mathematical definition of Entropy, a process in which heat flows from cold to hot has decreasing entropy. This can happen in a non-isolated system if entropy is created elsewhere, such that the total entropy is constant or increasing, as required by the second law. For example, the electrical energy going into a refrigerator is converted to heat and goes out the back, representing a net increase in entropy.

The exception to this is for statistically unlikely events where hot particles will "steal" the energy of cold particles enough that the cold side gets colder and the hot side gets hotter, for an instant. Such events have been observed at a small enough scale where the likelihood of such a thing happening is significant.G.M. Wang, E.M. Sevick, E. Mittag, D.J. Searles & Denis J. Evans (2002). "Experimental demonstration of violations of the Second Law of Thermodynamics for small systems and short time scales". Physical Review Letters 89: 050601/1–050601/4. doi:10.1103/PhysRevLett.89.050601 The mathematics involved in such an event are described by `There was an error working with the wiki: Code[39]`

.

A third formulation of the second law, by `There was an error working with the wiki: Code[19]`

, is the heat engine formulation, or Kelvin statement:

It is impossible to convert heat completely into `There was an error working with the wiki: Code[20]`

in a cyclic process.

That is, it is impossible to extract energy by heat from a high-temperature energy source and then convert all of the energy into work. At least some of the energy must be passed on to heat a low-temperature energy sink. Thus, a heat engine with 100% efficiency is thermodynamically impossible.

Thermodynamics is a theory of macroscopic systems and therefore the second law applies only to macroscopic systems with well-defined temperatures. For example, in a system of two molecules, there is a non-trivial probability that the slower-moving ("cold") molecule transfers energy to the faster-moving ("hot") molecule. Such tiny systems are not part of classical thermodynamics, but they can be investigated by quantum thermodynamics by using `There was an error working with the wiki: Code[21]`

, probabilities of observing a decrease in entropy approach zero.`There was an error working with the wiki: Code[2]`

The second law of Thermodynamics is an axiom of thermodynamics concerning heat, entropy, and the direction in which thermodynamic processes can occur. For example, the second law implies that heat does not flow spontaneously from a cold material to a hot material, but it allows heat to flow from a hot material to a cold material. Roughly speaking, the second law says that in an isolated system, concentrated energy disperses over time, and consequently less concentrated energy is available to do useful work. Energy dispersal also means that differences in temperature, pressure, and density even out. Again roughly speaking, thermodynamic Entropy is a measure of energy dispersal, and so the second law is closely connected with the concept of entropy.

In a general sense, the second law is that temperature differences between systems in contact with each other tend to equalize and that `There was an error working with the wiki: Code[22]`

can be obtained from these non-equilibrium differences, but that loss of heat occurs, in the form of entropy, when work is done.`There was an error working with the wiki: Code[3]`

Pressure differences, density differences, and particularly temperature differences, all tend to equalize if given the opportunity. This means that an `There was an error working with the wiki: Code[40]`

will eventually have a uniform temperature. A Heat engine is a mechanical device that provides useful work from the difference in temperature of two bodies:

`There was an error working with the wiki: Code[17]`

During the 19th century, the second law was synthesized, essentially, by studying the dynamics of the `There was an error working with the wiki: Code[41]`

in coordination with James Joule's `There was an error working with the wiki: Code[42]`

experiments. Since any thermodynamic engine requires such a temperature difference, it follows that useful work cannot be derived from an `There was an error working with the wiki: Code[43]`

in equilibrium there must always be an external energy source and a cold sink. By definition, Perpetual motion machines of the second kind would have to violate the second law to function.

`There was an error working with the wiki: Code[4]`

The first theory of the conversion of heat into mechanical work is due to `There was an error working with the wiki: Code[44]`

in 1824. He was the first to realize correctly that the efficiency of this conversion depends on the difference of temperature between an engine and its environment.

Recognizing the significance of `There was an error working with the wiki: Code[45]`

's work on the conservation of energy, `There was an error working with the wiki: Code[46]`

was the first to formulate the second law during 1850, in this form: heat does not flow spontaneously from cold to hot bodies. While common knowledge now, this was contrary to the `There was an error working with the wiki: Code[47]`

of heat popular at the time, which considered heat as a fluid. From there he was able to infer the principle of Sadi Carnot and the definition of entropy (1865).

Established during the 19th century, the `There was an error working with the wiki: Code[23]`

to receive heat from a single `There was an error working with the wiki: Code[24]`

and produce a net amount of work." This was shown to be equivalent to the statement of Clausius.

The `There was an error working with the wiki: Code[48]`

is also important for the `There was an error working with the wiki: Code[49]`

approach. It says that, over long periods of time, the time spent in some region of the phase space of microstates with the same energy is proportional to the volume of this region, i.e. that all accessible microstates are equally probable over long period of time. Equivalently, it says that time average and average over the statistical ensemble are the same.

It has been shown that not only classical systems but also Quantum mechanics ones tend to maximize their entropy over time. Thus the second law follows, given initial conditions with low entropy. More precisely, it has been shown that the local `There was an error working with the wiki: Code[50]`

is at its maximum value with an extremely great probability.{{Citation

| last1 = Gemmer | first1 = Jochen

| last2 = Otte | first2 = Alexander

| last3 = Mahler | first3 = Günter

| title = Quantum Approach to a Derivation of the Second Law of Thermodynamics

| journal = Phys. Rev. Lett.

| volume = 86

| issue = 10

| pages = 1927–1930

| year = 2001

| url = http://prola.aps.org/abstract/PRL/v86/i10/p1927_1

| doi = 10.1103/PhysRevLett.86.1927}} The result is valid for a large class of isolated quantum systems (e.g. a gas in a container). While the full system is pure and therefore does not have any entropy, the `There was an error working with the wiki: Code[51]`

between gas and container gives rise to an increase of the local entropy of the gas. This result is one of the most important achievements of `There was an error working with the wiki: Code[52]`

`There was an error working with the wiki: Code[5]`

.

Today, much effort in the field is to understand why the initial conditions early in the universe were those of low entropyDoes Inflation Provide Natural Initial Conditions for the Universe?, Carrol SM, Chen J, Gen.Rel.Grav. 37 (2005) 1671-1674 Int.J.Mod.Phys. D14 (2005) 2335-2340, arXiv:gr-qc/0505037v1The arrow of time and the initial conditions of the universe, Wald RM, Studies In History and Philosophy of Science Part B, Volume 37, Issue 3, September 2006, Pages 394-398 , as this is seen as the origin of the second law (see below).

The second law can be stated in various succinct ways, including:

It is impossible to produce work in the surroundings using a cyclic process connected to a single heat reservoir (`There was an error working with the wiki: Code[25]`

, 1851).

It is impossible to carry out a cyclic process using an engine connected to two heat reservoirs that will have as its only effect the transfer of a quantity of heat from the low-temperature reservoir to the high-temperature reservoir (`There was an error working with the wiki: Code[26]`

, 1854).

If thermodynamic `There was an error working with the wiki: Code[27]`

is to be done at a finite rate, `There was an error working with the wiki: Code[28]`

must be expended.Stoner, C.D. (2000). Inquiries into the Nature of Free Energy and Entropy – in Biochemical Thermodynamics. Entropy, Vol 2.

In 1856, the German physicist `There was an error working with the wiki: Code[53]`

stated what he called the "second fundamental theorem in the `There was an error working with the wiki: Code[54]`

" in the following form:Clausius, R. (1865). The Mechanical Theory of Heat – with its Applications to the Steam Engine and to Physical Properties of Bodies. London: John van Voorst, 1 Paternoster Row. MDCCCLXVII.

:\int \frac{\delta Q}{T} = -N

where Q is heat, T is temperature and N is the "equivalence-value" of all uncompensated transformations involved in a cyclical process. Later, in 1865, Clausius would come to define "equivalence-value" as entropy. On the heels of this definition, that same year, the most famous version of the second law was read in a presentation at the Philosophical Society of Zurich on April 24, in which, in the end of his presentation, Clausius concludes:

The entropy of the universe tends to a maximum.

This statement is the best-known phrasing of the second law. Moreover, owing to the general broadness of the terminology used here, e.g. `There was an error working with the wiki: Code[55]`

, as well as lack of specific conditions, e.g. open, closed, or isolated, to which this statement applies, many people take this simple statement to mean that the second law of thermodynamics applies virtually to every subject imaginable. This, of course, is not true this statement is only a simplified version of a more complex description.

In terms of time variation, the mathematical statement of the second law for an `There was an error working with the wiki: Code[56]`

undergoing an arbitrary transformation is:

:\frac{dS}{dt} \ge 0

where

:S is the entropy and

:t is `There was an error working with the wiki: Code[57]`

.

It should be noted that `There was an error working with the wiki: Code[29]`

of the system and because of the constant motion, the system is constantly changing its microstate. Statistical mechanics postulates that, in equilibrium, each microstate that the system might be in is equally likely to occur, and when this assumption is made, it leads directly to the conclusion that the second law must hold in a statistical sense. That is, the second law will hold on average, with a statistical variation on the order of 1/?N where N is the number of particles in the system. For everyday (macroscopic) situations, the probability that the second law will be violated is practically zero. However, for systems with a small number of particles, thermodynamic parameters, including the entropy, may show significant statistical deviations from that predicted by the second law. Classical thermodynamic theory does not deal with these statistical variations.

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An important and revealing idealized special case is to consider applying the Second Law to the scenario of an isolated system (called the total system or universe), made up of two parts: a sub-system of interest, and the sub-system's surroundings. These surroundings are imagined to be so large that they can be considered as an unlimited heat reservoir at temperature TR and pressure PR — so that no matter how much heat is transferred to (or from) the sub-system, the temperature of the surroundings will remain TR and no matter how much the volume of the sub-system expands (or contracts), the pressure of the surroundings will remain PR.

Whatever changes dS and dSR occur in the entropies of the sub-system and the surroundings individually, according to the Second Law the entropy Stot of the isolated total system must not decrease:

: dS_{\mathrm{tot}}= dS + dS_R \ge 0

According to the First law of thermodynamics, the change dU in the internal energy of the sub-system is the sum of the heat ?q added to the sub-system, less any work ?w done by the sub-system, plus any net chemical energy entering the sub-system d ??iRNi, so that:

: dU = \delta q - \delta w + d(\sum \mu_{iR}N_i) \,

where ?iR are the `There was an error working with the wiki: Code[58]`

s of chemical species in the external surroundings.

Now the heat leaving the reservoir and entering the sub-system is

: \delta q = T_R (-dS_R) \le T_R dS

where we have first used the definition of entropy in classical thermodynamics (alternatively, the definition of temperature in statistical thermodynamics) and then the Second Law inequality from above.

It therefore follows that any net work ?w done by the sub-system must obey

: \delta w \le - dU + T_R dS + \sum \mu_{iR} dN_i \,

It is useful to separate the work ?w done by the subsystem into the useful work ?wu that can be done by the sub-system, over and beyond the work pR dV done merely by the sub-system expanding against the surrounding external pressure, giving the following relation for the useful work that can be done:

: \delta w_u \le -d (U - T_R S + p_R V - \sum \mu_{iR} N_i )\,

It is convenient to define the right-hand-side as the exact derivative of a thermodynamic potential, called the availability or `There was an error working with the wiki: Code[59]`

X of the subsystem,

: X = U - T_R S + p_R V - \sum \mu_{iR} N_i

The Second Law therefore implies that for any process which can be considered as divided simply into a subsystem, and an unlimited temperature and pressure reservoir with which it is in contact,

: d X + \delta w_u \le 0 \,

i.e. the change in the subsystem's exergy plus the useful work done by the subsystem (or, the change in the subsystem's exergy less any work, additional to that done by the pressure reservoir, done on the system) must be less than or equal to zero.

When no useful work is being extracted from the sub-system, it follows that

: d X \le 0 \,

with the `There was an error working with the wiki: Code[60]`

X reaching a minimum at equilibrium, when dX=0.

If no chemical species can enter or leave the sub-system, then the term ? ?iR Ni can be ignored. If furthermore the temperature of the sub-system is such that T is always equal to TR, then this gives:

:X = U - TS + p_R V + \mathrm{const.} \,

If the volume V is constrained to be constant, then

:X = U - TS + \mathrm{const.'} = A + \mathrm{const.'}\,

where A is the thermodynamic potential called `There was an error working with the wiki: Code[61]`

, A=U?TS. Under constant-volume conditions therefore, dA ? 0 if a process is to go forward and dA=0 is the condition for equilibrium.

Alternatively, if the sub-system pressure p is constrained to be equal to the external reservoir pressure pR, then

:X = U - TS + pV + \mathrm{const.} = G + \mathrm{const.}\,

where G is the `There was an error working with the wiki: Code[62]`

, G=U?TS+PV. Therefore under constant-pressure conditions, if dG ? 0, then the process can occur spontaneously, because the change in system energy exceeds the energy lost to entropy. dG=0 is the condition for equilibrium. This is also commonly written in terms of `There was an error working with the wiki: Code[63]`

, where H=U+PV.

In sum, if a proper infinite-reservoir-like reference state is chosen as the system surroundings in the real world, then the Second Law predicts a decrease in X for an irreversible process and no change for a reversible process.

:dS_{tot} \ge 0 is equivalent to dX + \delta W_u \le 0

This expression together with the associated reference state permits a `There was an error working with the wiki: Code[30]`

.)

This approach to the Second Law is widely utilized in `There was an error working with the wiki: Code[64]`

practice, `There was an error working with the wiki: Code[65]`

, `There was an error working with the wiki: Code[66]`

, and other disciplines.

Owing to the somewhat ambiguous nature of the formulation of the second law, i.e. the postulate that the quantity `There was an error working with the wiki: Code[31]`

increases in spontaneous natural processes, it has occasionally been subject to criticism as well as attempts to dispute or disprove it. Clausius himself even noted the abstract nature of the second law. In his 1862 memoir, for example, after mathematically stating the second law by saying that integral of the differential of a quantity of heat divided by temperature must be less than or equal to zero for every cyclical process which is in any way possible: (Clausius Inequality)

:\oint \frac{\delta Q}{T} \le 0,

Clausius then stated:

Although the necessity of this theorem admits of strict mathematical proof if we start from the fundamental proposition above quoted it thereby nevertheless retains an abstract form, in which it is with difficulty embraced by the mind, and we feel compelled to seek for the precise physical cause, of which this theorem is a consequence.

Recall that Heat and Temperature are statistical, macroscopic quantities that become somewhat ambiguous when dealing with a small number of atoms.

Before 1850, Heat was regarded as an indestructible particle of matter. This was called the “material hypothesis”, as based principally on the views of Isaac Newton. It was on these views, partially, that in 1824 Sadi Carnot formulated the initial version of the second law. It soon was realized, however, that if the heat particle was conserved, and as such not changed in the cycle of an engine, that it would be possible to send the heat particle cyclically through the working fluid of the engine and use it to push the piston and then return the particle, unchanged, to its original state. In this manner Perpetual motion could be created and used as an unlimited energy source. Thus, historically, people have always been attempting to create a perpetual motion machine so to disprove the second law.

Non-equilibrium chips could avoid overheating laptops - Researchers are re-examining the Second Law of Thermodynamics in a bid to manage heat from laptops and other miniaturised electronics. [Hence the mainstream is forced, by a very practical difficulty - heat dissipation in laptops - to investigate reversing entropy.] (IT News Oct. 2, 2008)

`There was an error working with the wiki: Code[7]`

In 1871, `There was an error working with the wiki: Code[67]`

proposed a `There was an error working with the wiki: Code[68]`

, now called `There was an error working with the wiki: Code[69]`

, which challenged the second law. This experiment reveals the importance of observability in discussing the second law. In other words, it requires a certain amount of energy to collect the information necessary for the demon to "know" the whereabouts of all the particles in the system. This energy requirement thus negates the challenge to the second law. This apparent paradox can also be reconciled from another perspective, by resorting to a use of `There was an error working with the wiki: Code[70]`

.

`There was an error working with the wiki: Code[8]`

The second law is a law about macroscopic irreversibility, and so may appear to violate the principle of `There was an error working with the wiki: Code[71]`

. `There was an error working with the wiki: Code[72]`

first investigated the link with microscopic reversibility. In his `There was an error working with the wiki: Code[73]`

he gave an explanation, by means of `There was an error working with the wiki: Code[74]`

, for dilute gases in the zero density limit where the `There was an error working with the wiki: Code[75]`

equation of state holds. He derived the second law of thermodynamics not from mechanics alone, but also from the probability arguments. His idea was to write an equation of motion for the probability that a single particle has a particular position and momentum at a particular time. One of the terms in this equation accounts for how the single particle distribution changes through collisions of pairs of particles. This rate depends on the probability of pairs of particles. Boltzmann introduced the assumption of `There was an error working with the wiki: Code[76]`

to reduce this pair probability to a product of single particle probabilities. From the resulting `There was an error working with the wiki: Code[77]`

he derived his famous `There was an error working with the wiki: Code[73]`

, which implies that on average the entropy of an ideal gas can only increase.

The assumption of molecular chaos in fact violates time reversal symmetry. It assumes that particle momenta are uncorrelated before collisions. If you replace this assumption with "anti-molecular chaos," namely that particle momenta are uncorrelated after collision, then you can derive an anti-Boltzmann equation and an anti-H-Theorem which implies entropy decreases on average. Thus we see that in reality Boltzmann did not succeed in solving `There was an error working with the wiki: Code[79]`

. The molecular chaos assumption is the key element that introduces the `There was an error working with the wiki: Code[80]`

.

The origin of the arrow of time is today usually thought to be the smooth, uncorrelated (and hence low entropy) initial conditions that existed in the very early universe.The Thermodynamic Arrow: Puzzles and Pseudo-Puzzles, Price H., Proceedings of Time and Matter, Venice, 2002 `There was an error working with the wiki: Code[9]`

Arrow of time in cosmology, Hawking S.W., Phys. Rev. D 32, 2489 - 2495 (1985)scholarpedia: Time's arrow and Boltzmann's entropy

`There was an error working with the wiki: Code[10]`

The second law of thermodynamics has been proven mathematically for thermodynamic systems, where entropy is defined in terms of Heat divided by the `There was an error working with the wiki: Code[81]`

. The second law is often applied to other situations, such as the complexity of `There was an error working with the wiki: Code[82]`

, or orderliness.

`There was an error working with the wiki: Code[11]`

However it is incorrect to apply the closed-system expression of the second law of thermodynamics to any one sub-system connected by mass-energy flows to another ("open system"). In sciences such as `There was an error working with the wiki: Code[83]`

and `There was an error working with the wiki: Code[84]`

the application of thermodynamics is well-established, e.g. `There was an error working with the wiki: Code[85]`

. The general viewpoint on this subject is summarized well by biological thermodynamicist Donald Haynie as he states: "Any theory claiming to describe how organisms originate and continue to exist by natural causes must be compatible with the first and second laws of thermodynamics."`There was an error working with the wiki: Code[12]`

This is very different, however, from the claim made by many `There was an error working with the wiki: Code[86]`

that `There was an error working with the wiki: Code[87]`

violates the second law of thermodynamics. Evidence indicates that biological systems and evolution of those systems conform to the second law, since although biological systems may become more ordered, the net change in entropy for the entire universe is still positive as a result of evolution.Five Major Misconceptions about Evolution Additionally, the process of natural selection responsible for such local increase in order may be mathematically derived from the expression of the second law equation for non-equilibrium connected open systems,doi:10.1098/rspa.2008.0178 "Natural selection for least action", Ville R. I. Kaila and Arto Annila Proceedings of the Royal Society A. arguably making the Theory of Evolution itself an expression of the Second Law.

Furthermore, the second law is only true of closed systems. It is easy to decrease entropy, with an energy source. For example, a refrigerator separates warm and cold air, but only when it is plugged in. Since all biology requires an external energy source, the Sun, there's nothing unusual (thermodynamically) with it growing more complex with time.

It is occasionally claimed that the second law is incompatible with autonomous `There was an error working with the wiki: Code[88]`

, or even the coming into existence of complex systems. This is a common creationist argument against evolution.{{Harvard reference

|last =Rennie

|first= John

|year= 2002

|title= 15 Answers to Creationist Nonsense

|journal= Scientific American

|volume= 287 (1)

|pages = 78–85

|url=http://www.sciam.com/article.cfm?articleID=000D4FEC-7D5B-1D07-8E49809EC588EEDF

}} page 82, accessed `There was an error working with the wiki: Code[32]`

explains how this claim is a misconception. In fact, as hot systems cool down in accordance with the second law, it is not unusual for them to undergo `There was an error working with the wiki: Code[89]`

, i.e. for structure to spontaneously appear as the temperature drops below a critical threshold. Complex structures, such as `There was an error working with the wiki: Code[90]`

, also spontaneously appear where there is a steady flow of energy from a high temperature input source to a low temperature external sink.

Furthermore, a system that energy flows into and out of may decrease its local entropy provided the increase of the entropy to its surrounding that this process causes is greater than or equal to the local decrease in entropy. A good example of this is `There was an error working with the wiki: Code[91]`

. As a liquid cools, crystals begin to form inside it. While these crystals are more ordered than the liquid they originated from, in order for them to form they must release a great deal of heat, known as the latent heat of fusion. This heat flows out of the system and increases the entropy of its surroundings to a greater extent than the decrease of energy that the liquid undergoes in the formation of crystals.

An interesting situation to consider is that of a supercooled liquid perfectly isolated thermodynamically, into which a grain of dust is dropped. Here even though the system cannot export energy to its surroundings, it will still crystallize. Now however the release of latent heat will contribute to raising its own temperature. If this release of heat causes the temperature to reach the melting point before it has fully crystallized, then it shall remain a mixture of liquid and solid if not, then it will be a solid at a significantly higher temperature than it previously was as a liquid. In both cases entropy from its disordered structure is converted into entropy of disordered motion.`There was an error working with the wiki: Code[13]`

`There was an error working with the wiki: Code[14]`

"The law that entropy always increases holds, I think, the supreme position among the `There was an error working with the wiki: Code[92]`

. If someone points out to you that your pet theory of the `There was an error working with the wiki: Code[93]`

is in disagreement with `There was an error working with the wiki: Code[94]`

— then so much the worse for Maxwell's equations. If it is found to be contradicted by observation — well, these experimentalists do bungle things sometimes. But if your theory is found to be against the second law of thermodynamics I can give you no hope there is nothing for it but to collapse in deepest humiliation." — Sir `There was an error working with the wiki: Code[95]`

, The Nature of the Physical World (1927)

The tendency for entropy to increase in isolated systems is expressed in the second law of thermodynamics — perhaps the most pessimistic and amoral formulation in all human thought. — `There was an error working with the wiki: Code[33]`

and `There was an error working with the wiki: Code[96]`

, `There was an error working with the wiki: Code[97]`

(1965)

There are almost as many formulations of the second law as there have been discussions of it. — Philosopher / Physicist `There was an error working with the wiki: Code[34]`

, (1941)

`There was an error working with the wiki: Code[15]`

`There was an error working with the wiki: Code[98]`

produced a setting of a statement of the Second Law of Thermodynamics to music, called "First and Second Law".

The economist `There was an error working with the wiki: Code[99]`

showed the significance of the Entropy Law in the field of economics (see his work The Entropy Law and the Economic Process (1971), Harvard University Press).

Creationist `There was an error working with the wiki: Code[100]`

incorrectly used the Second Law of Thermodynamics to argue that evolution was impossible, although stand-up comedian `There was an error working with the wiki: Code[101]`

has pointed out that Gish misunderstood the definition of a closed system.

`There was an error working with the wiki: Code[102]`

, a science fiction short story by Isaac Asimov, is centered around the question of how to reverse the Second Law of Thermodynamics, or entropy.

One of acclaimed comic writer `There was an error working with the wiki: Code[103]`

's short stories, chronicled in a collection called Wild Worlds, depicts indestructible and/or immortal characters facing down the unstoppable entropy at the end of the universe.

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Goldstein, Martin, and Inge F., 1993. The Refrigerator and the Universe. Harvard Univ. Press. Chpts. 4-9 contain an introduction to the Second Law, one a bit less technical than this entry. ISBN 978-0674753242

Leff, Harvey S., and Rex, Andrew F. (eds.) 2003. Maxwell's Demon 2 : Entropy, classical and quantum information, computing. Bristol UK Philadelphia PA: Institute of Physics. ISBN 978-0585492377

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(technical).

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: "Philosophy of Statistical Mechanics" -- by Lawrence Sklar.

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, 1988, "The evolution of Carnot's principle," in G. J. Erickson and C. R. Smith (eds.) Maximum-Entropy and Bayesian Methods in Science and Engineering, Vol 1, p. 267.

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