Why does your desk always get dirty, you ask? Entropy is a tendency for systems to move towards disorder and a quantification of that disorder. The reason a deck of cards doesn't reorganize itself when you drop it is because it's naturally easier for it to remain unordered. Think about the energy that it takes to arrange cards by value and suit: you've got to look at a card, compare it to others, classify it and then arrange it. You've got to repeat this process over and over until all 52 of the cards have been compared and arranged, and that demands a lot of energy.

In fact, the cards fall to the floor in the first place because they would naturally rather go with gravity than oppose it. Imagine if you dropped your cards and they went flying at the ceiling -- that just doesn't make any sense. A long time ago scientists or one in particular, Rudolf Clausis began to recognize this natural trend towards lower energy and sought to quantify it, sparking the idea of entropy. Entropy explained why heat flowed from warm objects to cold ones. It explained why balloons popped when filled with too much air at least qualitatively and it paved the way towards a more sophisticated understanding of everything from balancing a needle upright to describing why proteins fold the very specific ways they do.

Entropy gave all of science's processes a veritable direction. Today's modern understanding of entropy is twofold. On one hand, it's a macroscopic idea that describes things like falling leaves. On the microscopic level, however, entropy is highly statistical and is rooted in the principles of uncertainty. Gaseous substances, for instance, have atoms or molecules that zoom around freely in whatever space they occupy. If you could see gas in a box, you'd observe tiny atoms bouncing erratically from wall to wall, occasionally colliding with each other and changing direction accordingly. If you record the temperature and pressure of this system you have thus also effectively measured its macroscopic entropy - if the gas's temperature is very high, its molecules are zooming around so chaotically that its entropy, which quantifies this chaos, would be extremely high as well.

Our single box of gas might contain more than five hundred million tiny particles, though. So while it's great that we can say something about the average of the gas's observable properties, there is something important for scientists to gain from speculating how the microscopic states of the molecules are connected to these macroscopic observations.

This bridge has called for a somewhat finer but more absolute definition of entropy from which all other mathematical expressions involving the term can be defined. Depending on the type of gas you have whizzing around in your box, the energy it contains can be distributed in different ways. For example, lots of the molecules could be spinning rapidly but moving at a very slow speed.

On the other hand, the molecules could be vibrating intensely and moving faster than an airplane without any rotational momentum. Statistically, this variance in the distribution of energy in our gas can be captured in the concept of a microstate. In one microstate most of the energy will be rotational, while in another it might be all in the velocity of the molecules.

Thermodynamics usually makes the assumption that the probability of the gas being in any one of these microstates is equal, the so-called a priori probability postulate. This leads to the following equation:. As the number of microstates increases the information we know about energy distribution decreases, meaning that the system's entropy, its chaos, skyrockets. This is the most fundamental and absolute definition of entropy. When you shuffle a deck of cards you are basically maximizing the entropy of that system, since you know absolutely nothing about the order of the numbers or the suits.

Each possibility is a microstate in this case, and each ordering of the 52 cards has an equal probability of occurring. When you arrange the deck by number and suit, you lower the entropy of the system by increasing the amount of information you know about it.

## The intuition behind Shannon’s Entropy

The second law of thermodynamics qualitatively explains nature's tendency to move towards lower energy. Ice cubes don't just form from a glass of hot water; broken eggs don't spontaneously regenerate into whole eggs; your office desk isn't going to clean itself. The mathematical idea of entropy can be extracted from this principle. If you put an ice cube into a piping hot bowl of water, what happens? The ice melts, of course. But in a deeper sense, ice is a very ordered solid object, which means that as a whole it has very low entropy.

By absorbing the heat from the hot water, the molecules inside the ice cube break loose and are able to move more freely as a liquid - their randomness increases, and so does their entropy.

## Introduction to entropy

Heat flows from hot objects to colder ones because of this idea of equilibrium. All things in nature tend towards higher entropy, which suggests that the entropy of the universe must also be continuously increasing. Quantum thermodynamics attempts to link micro-scale states to macroscopic observations and is ultimately able to deduce a statistical description of entropy from this marriage.

The guiding idea here is that molecular motion is responsible for major thermodynamic occurrences. When a substance heats up, its molecules move faster and faster, and that movement is all the more randomized at high speeds. When a substance cools down, its molecules move very slowly and are unnaturally constrained.

## Urban Dictionary: entropy

Entropy is intimately related to temperature for this reason - and temperature is one of the most basic thermodynamic properties. As it turns out, pressure - a very important thermodynamic concept as well - is also a result of molecular motion. A statistical approach to thermodynamics allows us to figure out very delicate information about systems, especially ones that involve chemicals. In contrast, a block of ice placed in an ice-water bath will either thaw a little more or freeze a little more, depending on whether a small amount of heat is added to or subtracted from the system.

Such a process is reversible because only an infinitesimal amount of heat is needed to change its direction from progressive freezing to progressive thawing. Similarly, compressed gas confined in a cylinder could either expand freely into the atmosphere if a valve were opened an irreversible process , or it could do useful work by pushing a moveable piston against the force needed to confine the gas.

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The latter process is reversible because only a slight increase in the restraining force could reverse the direction of the process from expansion to compression. For reversible processes the system is in equilibrium with its environment , while for irreversible processes it is not. To provide a quantitative measure for the direction of spontaneous change, Clausius introduced the concept of entropy as a precise way of expressing the second law of thermodynamics.

The Clausius form of the second law states that spontaneous change for an irreversible process in an isolated system that is, one that does not exchange heat or work with its surroundings always proceeds in the direction of increasing entropy. For example, the block of ice and the stove constitute two parts of an isolated system for which total entropy increases as the ice melts. This equation effectively gives an alternate definition of temperature that agrees with the usual definition.

Assume that there are two heat reservoirs R 1 and R 2 at temperatures T 1 and T 2 such as the stove and the block of ice. Thus, the observation that heat never flows spontaneously from cold to hot is equivalent to requiring the net entropy change to be positive for a spontaneous flow of heat. Suppose a heat engine absorbs heat Q 1 from R 1 and exhausts heat Q 2 to R 2 for each complete cycle. The same reasoning can also determine the entropy change for the working substance in the heat engine, such as a gas in a cylinder with a movable piston.

The internal energy of the gas might also change by an amount d U as it expands. For example, the gas could be allowed to expand freely into a vacuum and do no work at all.

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This equation defines S system as a thermodynamic state variable, meaning that its value is completely determined by the current state of the system and not by how the system reached that state. Entropy is an extensive property in that its magnitude depends on the amount of material in the system. All spontaneous processes are irreversible; hence, it has been said that the entropy of the universe is increasing: that is, more and more energy becomes unavailable for conversion into work.

We welcome suggested improvements to any of our articles. You can make it easier for us to review and, hopefully, publish your contribution by keeping a few points in mind. Your contribution may be further edited by our staff, and its publication is subject to our final approval. Unfortunately, our editorial approach may not be able to accommodate all contributions.

Our editors will review what you've submitted, and if it meets our criteria, we'll add it to the article. Let's say it has a mauve molecule right over here. So this system that is larger, there's more places for the molecules to be and there's actually more molecules in it.

This can actually take on more configurations or more states. I've just drawn one of them but there's many more. If you imagine these molecules all bouncing around in different ways there's many, many different states that it could take on. So the system without even knowing what the actual molecules are doing at that given moment in time, we would say that there's more possible states relative to this one, this has fewer possible states. And because this system over here has more possible states, more configurations, it would take more to tell you exactly where everything is. We would say that this has more entropy.

So when we talk about disorder, we're really talking about the number of states something could have.

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And it makes sense that this thing you could imagine there's a lot more stuff moving around and a lot more different directions and they have a lot more space to move around. So it makes sense that the system as a whole has more entropy. So when we talk about entropy we're not talking about any one of the particular states, any one of the particular configurations, we're talking about the system as a whole without really knowing exactly where the molecules are.

In this example with the rooms, we're just talking about particular states. Messy is a particular state, clean is a particular state.

But we're not talking about the number of configurations that a room could actually have. In fact if this room is larger, this room actually could have more configurations. And if we're talking about the molecular level if this room was warm and this room were cold, and actually if this room is just larger, it's going to have more molecules in it.

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And those molecules are going to be in way more configurations that they could be arranged so there could be an argument that this actually has a higher entropy. And so using that same reasoning, let's go back to that comparison of the moon and the sun. Which of these would have more entropy? Well let's think about it. The sun is larger, it has way, way more molecules and those molecules are moving around way faster and they're hotter and they're moving past each other. While the moon is small, it's cold, it has fewer molecules.

It's for the most part rigid, it doesn't have a very high temperature so these things aren't moving around a lot. It has way fewer states, way fewer configurations than the sun does. So the sun's entropy, if you view it as a system. If you view the sun as a system, it's entropy is way higher than the moon.

It's entropy is much larger than the entropy of the moon. Think about it, how much information you would need.