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As I read somewhere, it said that the universe is heading toward disorder a.k.a entropy increasing.
Now as far as I know from the second law of thermodynamics it states that entropy is indeed increasing and in the end, the entropy of the universe will be maximum, so everything will evolve toward thermodynamic equilibrium (e.g same temperature everywhere in the universe).
So my question is: isn't equilibrium order? Why is entropy called a measure of disorder if more entropy means more order?
I personally find the terms consistent. Think of the entropy as Boltzman proposes: $S=k \, \ln W$ Meaning high entropy states can be realized via many different configurations. Truly ordered state (assume you arrange a sculpture from atoms) can be realized via much smaller number of microscopic states. So again, equilibrium is not order - it is a mess.
equilibrium is not order - it is a mess I might quote you for this some day. +1
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What you are missing is the microscopic definition of entropy, once you know that, you will understand why people say that entropy is disorder.
Equilibrium as order
First, let's address your valid intuition that equilibrium as a form of order. Indeed, if everything is in thermal equilibrium, you just need to measure the temperature somewhere, and then you will know the temperature of everything. In our out of equilibrium, my body, my laptop, the room, outer space, all have different temperatures, and I need more information to know the state of everything, and I feel this is less "ordered" than the thermal equilibrium case.
What transpires is that less information needed corresponds to a higher degree of order. Well, let's keep that in mind for the next bit.
Entropy is microscopic disorder
In Physics, we know that the properties of macroscopic objects are determined by the motions of the particles that compose them. In particular, temperature of a gas is the disorganised jiggling of the atoms making it up.
As you increase the temperature, the atoms will move more and more erratically, and will have diverse speeds at any given time.
As you cool it, the particles will move slower and slower, until perhaps they freeze in place, forming a solid.
Which of the two - the still, regular lattice of the solid or the whizzing commotion of the particles that forms a gas - seems to you more disordered? Definitely the second. You know from thermodynamics that the gas has higher entropy than the solid. Indeed, there is a precise formula linking the macroscopic state variable $S$, entropy, and the microscopic conception of disorder I described.
Conclusion: the two ideas are reconcilable
In the projected "heat death" of the universe, everywhere there is constant temperature and density. In that sense, the universe is homogeneous and thus ordered. But microscopically - in the movements of the particles - that is the state in which there is the least order: no structure whatsoever, just a big soup of whizzing particles.
First of all as stated by Madan Ivan: equilibrium is not order. But you can get certain systems that are in a meta-stable "local" equilibrium (here meaning that you need some energy to move it from there), for example a crystal. These can be highly ordered.
Intuitively: if you smack the crystal with a hammer it breaks to pieces. This brings your closer to the global equilibrium. In the universe as a whole there is energy exchange between such subsystems and the second law of thermodynamics states that the overall order decreases by these processes.
So I think your problem is the two uses of the word equilibrium. Meta-stable equilibria can be order while the one that is used in the second law is the global minimum.
A comment on entropy in general: there isn't just one, there is a lot of them. In thermodynamics only there are 3 distinct ones. The names I use in the following are not official, since the literature mostly does not distinguish between them.
It can be shown that both 1. and 3. are important quantities, but the second law applies to the 3. one.
References: Unfortunately I can only link to this http://www.oxfordmartin.ox.ac.uk/event/1348 which is where I got the information from.
Entropy is not disorder; it is a lack of information.
Consider the entropy formula $S = k_b \log \Omega$. Here, $\Omega$ is the number of microstates (sets of particle positions/momenta) corresponding to an observed macrostate (something macroscopic we can observe, like 'the gas has volume $V$ and pressure $P$). What this formula means is that the entropy is proportional to the amount of information we are missing -- the number of extra bits we would need to know, on top of knowing the macrostate, to full specify the microstate.
For example, consider heat transfer $Q$ and work $W$. Though both exchange energy, only the first increases entropy. That makes sense, because the only difference between heat transfer and work is that heat transfer is done in a disordered way. We don't know exactly how it happened, so our lack of information goes up.
Since heat transfer increases entropy, the maximum entropy is achieved at thermal equilibrium. At that point, we basically know nothing at all.
No actually this is one perpetuating myth about entropy that even scientists themselves (and school curricula) propagate.
To answer this and dispel the myth, ask this simple question: disorder with respect to what exactly?
Why is a uniform gas disordered than a gas with two phases?
Of course a uniform gas has more (another) symmetry, in fact aquires the symmetries of the underlying environment. But so does the the two-phase gas, it has a certain symmetry (and not others) deriving from the underlying environmental process. So far so good. Where is the "disorder" exactly, and with respect to what and to whom is this a "disorder"? i think you get the point meant here.
Clearly there is a very subjective (to mention the least) concept of disorder used here which is not explained anywhere. Just stated as fact which is not.
Some take this further equating entropy with death vs life which is even more absurd. One can have a series of cages perfectly ordered, yet one will not have life in them.
Please consider this before you just accept anything thrown at you sounding scientific (while it is not)
PS
If you want the full scientific version of this answer check (especialy) the works of I. Prigogine on Entropy, Complex Dynamic Systems and Biological Systems. e.g "From Being to Becoming: Time and Complexity in the Physical Sciences"
Other schools of thermodynamics also have similar approaches and hard facts to consider. For a popular, yet somewhat thorough exposition check, for example: "The Arrow Of Time: A Voyage Through Science To Solve Time's Greatest Mystery"
To summarise:
entropy
Refer to "What is the second law of thermodynamics and are there any limits to its validity?"
abstract
In the scientific and engineering literature, the second law of thermodynamics is expressed in terms of the behavior of entropy in reversible and irreversible processes. According to the prevailing statistical mechanics interpretation the entropy is viewed as a nonphysical statistical attribute, a measure of either disorder in a system, or lack of information about the system, or erasure of information collected about the system, and a plethora of analytic expressions are proposed for the various measures. In this paper, we present two expositions of thermodynamics (both ’revolutionary’ in the sense of Thomas Kuhn with respect to conventional statistical mechanics and traditional expositions of thermodynamics) that apply to all systems (both macroscopic and microscopic, including single particle or single spin systems), and to all states (thermodynamic or stable equilibrium, nonequilibrium, and other states). .. Here entropy emerges as a microscopic nonstatistical property of matter.
Entropy is one of the most basic facts (and least understood, analysed) related directly to causality, the arrow of time, quantum-mechanics and evolution.
In fact most (if not all) time-reversible equations are wrong (ot at least crude approximations) rather than entropy and the time arrow itself.
To quote the cosmologist Arthur Eddington:
The law that entropy always increases holds, I think, the supreme position among the laws of Nature. If someone points out to you that your pet theory of the universe is in disagreement with Maxwell's equations - 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.
The references given above dispel all these misconceptions.
Entropy is a tricky concept and hard to understand. Personally I tend to avoid speaking of systems and phenomena in terms of entropy and/or temperature because they say very little of the dynamics, and I believe dynamical laws are the ones driving the universe.
When we hear that systems tend to increase entropy, we are saying there are dynamical laws driving them towards states of higher entropy. But this comes from our knowledge that for simple systems with elementary microscopic behavior (like ideal gases, or ideal liquids) when comparing two states of equilibrium, the one with higher entropy is more stable.
This might be misunderstood as an evidence that systems in general evolve by increasing entropy, which can be proven wrong. In fact the universe evolves in such a way that instead of tending to be homogeneous, is highly organised (galaxies, stars, planets, living beings).
My approach to this would be twofold: first microscopic dynamics is not elementary, which means that molecules have more degrees of freedom than we conceive when we tend to think only in terms of entropy to predict the behavior of the system. This is the same idea of Gibbs when he extended classical thermodynamics by allowing the number of molecules to change, which accounts for systems in which reactions may occur. But we can think of other types of "qualitative changes" (as I like to call them), as did Terrell Hill in his conception of Thermodynamics of Small Systems.
Secondly, I think we should not forget that the dynamics of evolution of physical system are fundamentally different from what we expect by saying that systems tend to increase their entropy, this is simply not verified, and in my opinion, misleading.
A final note in saying that Temperature, as Entropy, refers to equilibrated states and is also wrongly believed to behave the way energy does. But this is not the case: the dynamics of systems does not depend on temperature, but on the relative energies of the involved parties. Microscopically speaking, the collision dynamics depends on the relative energies or momenta, rather than on their average. Also in a non-equilibrated system, temperature (understood as mean kinetic energy) will largely fluctuate spatially before the whole system achieves the equilibrium.
PS: Sir Roger Penrose has very interesting arguments on the concept of Entropy and Universe evolution in this talk
The entropy law can be (comically) reinterpreted like "equilibrium is a state of maximum possible disorder under given physical constraints". So... things keep getting worse until it's as bad as it can get. Intuitively, large entropy means that things look more or less the same (macroscopically) for many different microscopic realizations. When the system evolves, it's statistically easy to find yourself in one of the many high-entropy states, but very rarely you can randomly stumble upon an ordered state. Imagine trying to shake a box of coins: what's the probability that you'll get all tails? The equilibrium state (you keep shaking the box - simulation of thermal motion) will be somewhere around half tails half heads, plusminus the standard deviation, typical for this system (after binomial distribution). So... disorder. In other comparison, parents all over the world know that the room only gets messier and reaches a state of chaos (this being the equilibrium state). You must put in work to make it tidy again, and it doesn't stay that way for very long.
I'm giving a common sense illustration because the physics has already been covered by other posts. People keep saying entropy is a difficult concept to grasp, but that's only if you don't explain it right.
Entropy is all about processing of energy, and we say that entropy increases when energy is converted into a less useful form - the spread of energy. In the maximum state of disorder it's impossible to extract energy to do work.
The fundamental reasons for entropy to increase are random quantum fluctuations that stimulate energy state transitions that in turn dissipate energy into the enviroment. For example, a quantum tunneling is stimulated by random quantum fluctuations and after the tunneling a part of the energy is dissipated into the enviroment (and entropy of the closed system has increased). We also have the phenomenon of quantum jump where quantum fluctuations stimulate electron to move from one stationary energy state onto a lower state, and during the process a part of the energy is dissipated into the enviroment as a photon.
Slowly but surely random quantum fluctuations break down all energy concentrations. That is, in the distant future, the order of the Universe has vanished and only random disorder prevails.
Terms are conventions. With a point of view from the humans we are the order. Collecting something and order it in shells is order. But I agree with you that to order something needs energy and this led to misorder and this could be a possible convention too. But it is not.
Entropy is the characteristic of nature that anything closed physical system given time will loose its energy and degenerate.
Or alternatively,
That coherent forces in nature like electromagnetism in a closed physical system will deteriorate and become more incoherent over time.
The cause of the above two definitions of entropy is the law of thermodynamics that every closed physical system will loose its self-energy over time due the interaction with its environment.
When a closed system looses its self-energy its structure becomes for most system types, less coherent and disordered. However there are systems that when loosing energy over time can come to a state of equilibrium and thus more ordered with time.Like a hot gas inside a closed box.
Therefore IMO entropy more accurately should not be defined synonym with disorder property with passage of time but rather with the loss of its self-energy over time by a closed system.
Entropy and thermodynamics are really the same thing.
