The word 'equilibrium' implies to us something which is in balance. In physics we envision forces to be in equilibrium, while in chemistry equilibrium refers to a dynamic process.

When we write a chemical reaction, we think of reactants combining to form products.

'equilibrium' is also the proper domain of Float's workstation and Internet server. The hostname reflects the server's stability, running the Linux/GNU operating system./

In physics, equilibrium occurs when all forces acting on a body are completely balanced -- hence there is no resultant force, and no acceleration.

Also: Static Equilibrium

Physics Jargon Metanode

Name of a new climb completed late last year by Neil Bently. It is on gritstone and has recieved a tentative grade of E11. This make it the hardest trad climb in the world. If you fall off you are likley to kill yourself. Neil fell off one one of his attempts, his belayer ran quickly away from the cliff and managed to take in enough rope to prevent Neil from taking a groundfall.

Much introspection followed, a new climbing film (called equilibrium, odd eh!) documents the first ascent. I've not seen it, but the reiew mentions that it is filled with much Bergmanesque silences and shots of Neil in existential angst as he contemplates the route, all good clean fun.

Since the movie debuted, I've been keeping track of IMDB user comments and polling people I know. I have determined that I am the only non-critic (and by critic, I mean someone who gets paid to write reviews) who disliked this movie. In fact, currently, the movie enjoys a higher rating on IMDB than the Devil's Advocate or Full Metal Jacket, both of which, although not in the same vein as this movie, nonetheless deserve a much higher place in the movie rankings than below Equilibrium. So, there is either something wrong with me, or I saw a totally different version than the rest of the human race has seen. Time will tell.

Update (2003.03.23) - Apparantly, I am not totally insane. bipolarbear says: I just saw equilibrium, and came on here to write a review in a fit of rage over this appalling movie... but you've already done it! :-D


Equilibrium

Released December 6, 2002 (Limited Release, US)
Working title: Librium
Directed by Kurt Wimmer
Running time: 107 minutes
Rated R

Cast (shortlist):

Christian Bale              Clerick John Preston
Taye Diggs                  Clerick Brandt
Emily Watson                Mary O'Brian
Angus MacFadyen             Master Clerick
Sean Bean                   Clerick Partridge
William Fichtner            Rebel Leader

Here's a true story: This evening, I went to see a movie called "Equilibrium." Now normally, I save every movie ticket and throw them in a shoebox filled with precious mementos. On my trip through the parking lot, I pulled out my Zippo and proceeded to burn my ticket. Then proceeded to speed home, so I could take an extremely violent shit. I don't know what was worse; how painful the bowel movement was, or how painful the movie was.

Roger Ebert gave this movie 3 stars out of 4. As soon as I'm done writing this review, I'm going to track him down and force-feed him his review. Laced with strychnine. I realize you're probably thinking, "Shouldn't the punishment fit the crime?" But frankly, I'm a busy man, and I don't have time for 6 months of chakra torture.

It's possible you're asking yourself, "Equilibrium? That's funny, I don't remember any commercials on the TV/Radio/Internet." And you'd be right - as far as I can determine, there were no TV or radio spots, and the trailer has only been available on Apple.com since December 2nd. I can only imagine that the producers, upon seeing the final edit, realized they had an absolute bomb on their hands and attempted to cut their losses.

I suppose you're expecting some sort of review of the movie, so I guess I should make an attempt. Then again, if I put as much effort into this review as writer/director Kurt Wimmer put into his screenplay, I could call it a day right now.

"Equilibrium" gives us a society, Libria, which is opiated by a drug known as Prozium, a necessity after World War III. The survivors in power decided that it was man's emotion that led to war, and in order to prevent any such future occurrences, they constructed a society based on emotionlessness. This is aided by the destruction of all art, music, and cultural relics, not to mention 3 doses a day of the aforementioned Prozium injection.

Those who forsake the drug and embrace their humanity are known as "Sense Offenders," and these criminals are tended to by an elite class of soldiers known as Grammaton Clericks. And by "tended to," I mean "Terminated with extreme prejudice."

Within the first 20 minutes of the film, we've encountered Clerick John Preston, played by Christian Bale, watched him kill his partner for being a Sense Offender, and discovered his wife was executed for Sense offenses 4 years earlier. But thanks to his Prozium doses, he doesn't seem to mind much. Watching this movie, I suddenly wished they made a drug which made horrible movies tolerable.

All is well and good in emotionless Libria, until Preston accidentally knocks a vial of his Prozium off the bathroom sink, and doesn't have time to pick up another dose before interrogating Mary O'Brien. As a sidenote, Mary is played by Emily Watson, whose performance was nothing short of a sidenote. Suddenly, he is overwhelmed with emotion, and continues to abstain from his medication, leading him to question authority and rebel. And by "rebel," I mean "Terminate with extreme prejudice."

I suppose you're expecting me to say something along the lines of, "At this point, the movie degenerates into a Matrix-wannabe." Unfortunately, the movie was one from the moment Preston and his partner show up to tend to the first lot of Sense Offenders. Christian Bale was dripping with Keanuosity, from the slicked-back black hair, black garb, and generally emotionless acting ability.

Although one would be hesitant to mention the dullness of his performance, given the fact he was on the drug, he was only on the drug for the first 20 minutes. After that, I would've expected him to suddenly become warm and likeable. Instead, he merely dives into his best Keanu Reeves impersonation and begins dealing with ludicrous amounts of heavily armed soldiers in his attempt to overthrow Libria's regime. And by "dealing with," I mean, "Terminating with extreme prejudice."

During the course of the movie, we are subjected to no less than 6 major gun fight scenes, not a single one of them memorable. The Clericks display incredible superhuman agility and strength, which would be fine if this was the Matrix, but this isn't. It's set in the future, in the "real world," and yet we're supposed to digest the idea that humans can jump 20 feet into the air and dodge the bullets of 20 close-range gunmen using "statistical probability."

I suppose by now you're thinking to yourself, "This movie sounds awful. I should go see it just for the cheese factor." This is where I warn you that I saw the Transporter, the One, and xXx, and I enjoyed both on a cheesy action movie level. I feel confident saying this movie makes abysmal blush. Gut-wrenchingly-awful could stand next to this movie and therefore look attractive in comparison. After seeing this movie, ritual seppuku seemed like a fun way to pass the time.

This movie will be the low marks on the resumes of actors and actresses like Christian Bale, Taye Diggs, Sean Bean, and Emily Watson. Kurt Wimmer, whose visuals were forgettable and his screenplay full of clichés and attempts to rip off many other successful movies and books, will hopefully never write a screenplay again. I never thought I'd see a movie "inspired" by 1984, Brave New World, and the Matrix which was so...I seem to be running out of synonyms for "bad." You get the idea. I sincerely hope the entire special effects team returns to throwing together low-budget effects for advertising, because Terminator 2 had more believable special effects.

In short: Do not see this movie. Ever. If you see it on movie store shelves, run in the opposite direction, screaming. If not for yourself, then at least for the children. Do it for the children.

Final Verdict (out of 5): 0 - This one doesn't even get out of the starting gate


If you want to see the movie, just watch the trailer. If you've read this and seen the trailer, then you've pretty much seen all there is to see. http://www.apple.com/trailers/miramax/equilibrium.html

If you did see the movie, hate mail can be directed to: http://www.dimensionfilms.com/

If you'd like to see what I was talking about with regard to Ebert's review, it can be found here:
http://rogerebert.suntimes.com/apps/pbcs.dll/article?AID=/20021206/REVIEWS/212060303/1023

A few notes regarding Ebert's review. It is my theory that he did not, in fact, see the movie, and he was merely fed facts to digest.

  1. His cast list is incorrect. Now, it is Ebert's job to watch movies. And he's undoubtedly seen many movies with William Fichtner in them. He should realize that the rebel leader was good 'ol Will, and not this "Franceco Cabras." Interestingly enough, the IMDB reflects the same error.
  2. He also spells Clerick incorrectly. A minor point, but worth noting.
  3. In the movie, it is Preston's partner, Partridge, who conceals the book of W.B. Yeats poetry. This was a VERY important plot point, and I can't imagine anyone who actually saw the movie would be mistaken over this. However, Partridge and Preston look similar on paper, and could easily be confused while reading about the movie from studio-prepared synopsii.
  4. He incorrectly states that Nick Nunziata from CHUD.com may have invented the term "gun-kata." If he'd been watching the movie, he may have noticed it spoken of at least 3 or 4 times. Again, it was hard to miss. As a sidenote, his English in this sentence is extremely fragmented and hard to read. I think he may have rushed this review out the door before bothering to read it.
  5. I am nearly 100% positive that the record being listened to by Preston is not a jazz record, but that of a symphony. To be more specific, it was Beethoven's 9th. Now, he may not be a classical music afficionado, but one would think he could take a look at the credits, or, at the very least, tell the difference between an age-old classic symphony and jazz. Once again, I cannot understand how one who claims to have seen the movie could have missed this.

Equilibrium

We are not equal. We never will be, we never have been. And as long as they're teaching little children to understand their surroundings with asinine questions like, "what's different in these two pictures?" we will continue to be programmed to acknowledge and have issues with those differences, rather than embracing them. Or, for that matter, embracing those uncanny commonalities that bring us together. That is, when those commonalities result from something other than a heightened lust for primetime television programming. But, I digress.

But I'm not rambling for the sake of some cynical outburst reflecting a doomed future of humanity. I want to speak of Kurt Wimmer. The year 2002 brought us a memorable, yet obscure cinematic feature, bearing the writing and directing talents of Wimmer. Equilibrium. Yes, another film toying with the ideas of 1984 and Brave New World, as so many filmmakers before him have hoped to bask in the reflected glory of some of history's greatest literature. But what made Equilibrium unequaled by any other effort of similar nature, was the class, style, and decisive simplicity of the whole production.

I didn't think it would be necessary for me to sit here and bleed praise for a personal favorite piece of cinema. But having just subjected myself to a merciless review *ahem* that revealed a blinding ignorance and lack of taste on behalf of the critic, as well as a grossly liberal use of quotation marks, I feel it is important as one who can appreciate the simple elegance of a lesson we must never forget, to defend this film with its own merits, rather than with inarticulate whines reflective of narrow, self-indulgent opinions and shallow, sheltered points of view. This was a great film. I lack any appropriate adjective to truly describe and reflect the integrity of this work, but it had just that, integrity. Dignity. Class.

Is it cliche to tell of a ominous future of desperate conformity, and an uncompromising control over personal lives? Yes. Why, yes indeed, that's been done before! But, then again, hasn't everything been done before? The premise of Equilibrium is a classic one: in a bleak future with nothing to live for, one who enforces the white-knuckled grasp upon the citizens has a revelation of sorts, fulfills the expectations of a dynamic character, learns a valuable lesson, experiences a sizable loss, and proves themselves a hero, one way or another. Yes, I know, we've seen it all before. But this idea, this concept, it's been used over and over again because it works. And no matter how many 1984ish, Farenheit 451ish, or Brave New Worldish plots develop out there, and no matter how many you sit through, it will never stop being an inescapable lesson for us to learn, remember, and reflect on. Step outside yourself and your comfortable, safe surroundings. Look objectively at our society. What we're becoming. Isn't that cause enough to worry? Isn't that reason enough to produce medium after medium of warning to these earthly inhabitants of what we must forever avoid becoming?

Equilibrium's specific premise is this: after WWIII, world powers came to the understanding that there was no way the human race could ever survive another conflict so devastating, and finally went to the root of conflict instead of just trying to throw treaties and embargoes and offensive strikes around where needed to try and patch up the mess that world affairs tend to be. The root of the conflict being, obviously, human emotion. Those evil chemical reactions, making us feel things, that make us want to DO things. With the aid of a new drug, Prozium, the citizens of Libria no longer have to worry about such pesky thoughts, and become solemn, grey, dull, but oh-so-productive members of society. And it must be mentioned, that all things that may inspire or encourage the practice of "feeling" are highly illegal contraband, or as you might know them: art and culture and beauty and music and poetry and colour and life. And all those other things that we live for. All those things that we'd die for.

John Preston, portrayed distinguishedly by Christian Bale, is a Grammaton Cleric. It is his job, his calling, his *duty* to scour the fluidly functioning machine of a city for "sense offenders," those defiant persons who cast aside their daily interval and hoard away treasures of any measure of sentimental value, willing to die for it. Willing to die, for the chance to live? Now yes, I will admit, that does sound a bit trite, but, to anyone who has been deeply moved, moved to the point of being unable to stand it (being moved by something other than a made for tv movie), it may sound cliche, but it should sound true. Just because it's predictable, doesn't mean it's any less valuable to the soul. In fact, it's always those eternal ideas and fears that are so familiar, haunting even. Of course they would follow a formula. The human condition follows a formula. Do we then merely dismiss it?

The fight scenes. I fail to understand how even the most sloped foreheads could not furrow in intrigue upon viewing the spectacular choreography and stylish composition of these sequences. Unlike "The Matrix," suspension wires and special effects aren't exploited to the point of suffocation; these moves aren't overdone with gratuitous acrobatics, they are purely and simply just the smoothly executed piruoettes and the coldly confident carryout of traditional techniques. The key with the action in Equilibrium, is simple composition. It just looks good. To anyone who has ever taken a photography class or critiqued a painting, or to those who just have a natural eye for this kind of thing, the utter stylishness of the framing, the layout of scenes, the movement of cameras, the angles of shots, they all fluidly add up to a *feel* to the movie that is nothing short of powerful. What some reviewers *ahem* can't seem to see is how that visual power so effectively and seamlessly reinforces the literal meanings and messages behind the film, with every faction of filmmaking working together to produce a film that is more than just actors playing a story, it is a complete work of art. Complete, and also, quite importantly, unified, and standing solid upon its own. It remains free from unnecessary tangles in the storyline, the tale shoots straight and simple, such a basic moral and concept at work here, but it is in the simplicity that the impact acquires its power. Again, simplicity in story with corresponding simplicity in direction.

We should not let ourselves overlook the fact that it is often the most simple, obvious, reiterated message that we need to hear the most. Or that an expression of what we already know is often the boldest and deepest reaching. "You have been found guilty of the crime of feeling." In a world where even the most simple and pure of feelings are outlawed, it would be the little things that make you feel the most. And the makeup of the film does nothing short of reflect that, yet again, for though the most emotional scenes are so simple and yes, cliche, it is in their lack of complexity that we are allowed to feel so intensely. The depths of joy and the heights of pain--without one we cannot have the other. I don't think you can remind people nearly enough of the importance of that essential balance, of the universal truth that with every up there is a down, of the significance of remembering that even the greatest sorrows are all ultimately worth it.

I feel sorry for anyone that has failed to appreciate this motion picture for the boldly dignified work of art that it is. I feel sorry for anyone that scoffed at the incredible acting ability of someone that can portray a character that doesn't feel anything. I feel sorry for anyone that failed to be moved by this film for reasons of their own emotional inhibitions, their own unwillingness to let go.

But I can only hope there are more people out there that will be able to find themselves speechless after this film. Those who have eagerly and impatiently made everyone they know sit down and watch it. Those who take stock of whatever wonderful or rotten emotions and experiences they're struggling with at the moment, and despite how bad it can be, they remind themselves of how fortunate they are to be capable of feeling this deeply at all. To feel so strongly. To have something matter so much. To allow something touch your soul.

This is a phenomenal work of cinema. I suggests that every out there should see it, at least once. If it is not all that I have ranted and poured my very heart out about, I apologize, I have wasted 107 minutes of your life. But if it makes anyone think, if it makes anyone question, if it moves anyone at ALL near to the point it has moved me, then it is 107 minutes of life well spent. Really, who doesn't have less than two hours to spare, when the reward has a possibility to be so magnificent.

At least spare 107 minutes of your life for this endeavor, because I've already spent near that amount just writing my abridged praise for the film. I didn't intend for my rambling to escalate to such a length, but one must defend what they think is beautiful.

One must always defend what they believe in.

In the face of the two wildly extreme and diametrically opposed reviews above, I feel it's kind of my duty to present some sort of sanity to this node. My overall feeling was that this was a flawed, but pretty good, action movie.

After a devastating third world war, mankind finds itself in a dystopic 1984-style future where all citizens of the free state of Libria are required to take drugs every day in order to suppress their emotions, thus preventing the terrifying possibility of a fourth. Also forbidden are such emotional stimulants as poetry, art, music and literature. Outlaws who stay off the dose and collect such banned media live in the wrecked old cityscape of the Nether - or in secret within Libria. They are hunted down and executed with efficiency by the lawmen of the movie - the Grammaton Clerics.

Christian Bale plays John Preston, a high-ranking cleric who, after emotionlessly executing his colleague Partridge (Sean Bean) for "sense offense", misses a dose of Prozium by accident and proceeds to discover emotion for himself. Skip to a predictable ending.

It has its flaws. The style of Libria is slick, but the world is not deep or intriguing. There is no suspicion of far deeper machinations like you get in The Matrix (which, inferior sequels notwithstanding, is a brilliant movie). There are revelations which are rather unsurprising. Christian Bale plays an emotionless automaton extremely well... he plays a slowly awakening, feeling human being pretending to be an emotionless automaton pretty well as well. His slowly awakening, feeling human being could use work though. The dialogue is as flat as one would expect in a world without emotion - and also unmemorable and at times, plain badly-written. There are also some cavernous plot holes - like how can Preston have a wife and two children if there is no emotion and hence no love? Minor spoiler: Ubj pna gur onq thlf xvyy gur tbbq thlf fb rnfvyl ng gur fgneg bs gur zbivr, ohg gur onq thlf trg jvcrq bhg ol gur tbbq thlf ng gur raq?

Gun-kata, the much-talked-about martial art that was invented for the movie, is an interesting notion. Preston and the other clerics and high-ranking officials are highly skilled in gun-kata, which is employed in most of the movie's action sequences. The Master Cleric (Angus MacFayden) explains that the places where the antagonist or antagonists will shoot in any given gun battle are statistically predictable - gun-kata involves simply not being there, moving where the bullets aren't, while simultaneously unloading lead into all who oppose you. It's a great idea, with fantastic possibilities, which, in the movie, hilariously boils down to standing in the middle of everybody and not moving while you shoot them two by two. (Preston wields two guns at all times.) Ah well. There is one sequence though which did show me something genuinely innovative - or at least, something which I in my far-from-all-conquering cinematic experiences had not encountered before. It involved two people fighting at VERY close range with a pair of pistols. Each was blocking and pushing away the other's weapons with their hands in order to avoid being shot - and obviously, neither could increase the distance between them without becoming a sitting target. Reminded me a lot of sword-fights in Robin Hood movies. I liked that bit.

The soundtrack, composed by Klaus Badelt, is a point heavily in the film's favour. It is moody, suitable and non-invasive at all times. It is also insanely difficult to get hold of because no soundtrack album for this movie exists. I was eventually able to find it thanks to some help from message board users on an Equilibrium fan site: http://www.freewebs.com/equilibrium-movie/index.htm. Good luck with that.

Overall I found it an enjoyable but ultimately unremarkable use of 107 minutes. Imagine, if you will, The Matrix, but without its philosophy, symbolism, style, technology, or 85% of its special effects budget - and if you still like the sound of that, rent Equilibrium.

Basics

Equilibrium, in the sciences, is a property attributed to a particular state of a system. It is defined by requiring that the state should not change over time.

Equivalently, in equilibrium the equations of motion of the system, which determine the rate of change of its state, are all zero. If X is some in principle observable quantity describing the state of the system, then

dX/dt = 0.

This is elementary enough. But we know that in the real world nothing actually exists in equilibrium, since the Universe as a whole is evolving and nothing is completely isolated from the rest of the world. So, how can the concept of equilibrium be meaningfully defined, and why is it useful?

Definitions and types of equilibrium

Static vs. dynamic

Static equilibrium is when the system stays the same because nothing is happening at all. If we had a perfect crystal of diamond at absolute zero in zero gravity it would be in static equilibrium. In classical or Newtonian mechanics, where objects are modelled as rigid bodies made up of a homogeneous and inert medium, static equilibrium is when the total force acting on a body (related to its acceleration by Newton's Second Law) is zero. (This is also known as mechanical equilibrium.)

In real life, everything has a nonzero temperature and nothing is completely rigid. Even a star made of a perfect octahedral diamond crystal would, over time, become spherical as its atoms relocated to minimize their potential energy. Nevertheless, static equilibrium may be a good approximation if we want to answer a question for which we expect thermal excitations and atomic rearrangements to be negligible. For example, the question "If I put a plate on this table tonight, where will it be in the morning?".

Dynamic equilibrium is a situation where some elements of the system are moving, but the state of the system as a whole is not changing. For example, consider a frictionless perfectly circular flywheel in a perfect vacuum. All parts of it are moving, but its state at any future time will be exactly the same as its state now. Or consider a section of pipe carrying a constant (non-turbulent) flow of fluid. Related, but not really equilibrium, is the situation when a system goes through cycles, returning to the same point at each cycle.

Again, exact dynamic equilibrium does not happen in reality, but it may be a good approximation depending on the questions we want to ask about the system. For example much of the interior of the Sun can be thought of as being in dynamical equilibrium with a constant outward flow of energy, although the Sun does and will evolve over billions of years. On a more mundane level, a person is likely to be in more or less the same state every week due to regular patterns of eating and excreting, so on average, over short periods, we can treat people approximately as dynamic equilibrium systems.

Stable vs. unstable vs. metastable

The stability of a equilibrium state (usually discussed for a static equilibrium) has to do with its response to small perturbations away from the point of equilibrium. For a stable equilibrium, the system will move towards the equilibrium after the perturbation is applied; for an unstable equilibrium, the system will move further and further away from equilibrium, no matter how small the initial perturbation.

The classic example is a ball sitting in the bottom of a valley (stable) or on top of a hill (unstable). With a spherical, perfectly smooth ball and hill, the equilibrium would truly be unstable and it would be impossible to balance the ball on top. There is also, of course, the saddle point which is stable in one direction but unstable in the perpendicular direction. Anyone trying to ride a horse for the first time knows that the saddle point is, strictly, an unstable equilibrium.

In real life, balls sitting on top of hills are in metastable equilibrium: this means that after a small perturbation (knock) they return towards their original position, but after a large perturbation they roll far away. Also, of course, the ever-present thermal and quantum fluctuations prevent the existence of a truly unstable equilibrium.

Metastable equilibrium is an extremely important concept in both everyday life and science: a house is just a collection of building materials in metastable equilibrium. In the study of phase transitions, interesting things happen when a substance reaches metastable equilibrium: one gets phenomena like supersaturated solutions or superheated liquids (the mug of water from the microwave at over 100°C that suddenly boils), which can result in a sudden release of energy, or the formation of structures (e.g. drops of dew on a spider's web).

Alan Turing's classic work on pattern formation during animal gestation (morphogenesis) makes use of unstable and metastable equilibrium. To put it simply, the leopard got its spots because a uniform distribution of chemicals over its body became, at some point, an unstable state; at this point tiny random fluctuations in the concentrations started to grow exponentially, the so-called Turing instability. Similar scenarios occur in cosmology, for example in the formation of monopoles and cosmic strings.

Statistical equilibrium, thermodynamic equilibrium and fluctuations

Systems that are not at absolute zero (i.e. everything in the real world) will have nonzero amounts of kinetic energy or thermal energy, which means that their degrees of freedom (meaning, roughly, the ways in which they can move about) will be excited. In normal matter, this will include vibrational modes, rotational modes, hyperfine structure, phonons, in fact all sorts of excited states. In short, things move around a lot.

In order to do thermodynamics or statistical mechanics, following Boltzmann, we consider a situation in which all of this riotous motion can be described on average by a statisticaldistribution. We accept that we are going to be ignorant of the exact configuration of the system, but we gain a very powerful general framework for talking about its bulk properties.

What does this have to do with equilibrium? Well, equilibrium is about the most basic concept in thermodynamics and stat. mech., without which we couldn't talk about such things as temperature or entropy. In order to measure temperature, you need to get two or more bodies into thermodynamic equilibrium with one another, such that on average no energy is being exchanged between them.

Actually, microscopic processes that we are ignorant of are continually transferring energy back and forth, but the things which we can measure, and the statistical distribution of energy, are not changing. If we consider all the microscopic processes that could influence the distribution, then average over them, the condition that the distribution function be the same over time is an extremely powerful one and leads to the Maxwell-Boltzmann distribution law.

In thermodynamic equilibrium, to put it simply, every degree of freedom has an energy 1/2 k T, where k is Boltzmann's constant and T is the temperature. This is known as equipartition. (Compare the virial theorem.) Quantum mechanics alter this picture somewhat, but it's important to note that thermal fluctuations would exist even in the absence of quantum effects. Thermodynamical equilibrium is a way of applying equilibrium to real objects, at the cost of admitting our ignorance of their precise microscopic details.

Chemical equilibrium

Chemical equilibrium is a similar concept, but rather than being concerned with the distribution of energy, it applies to the number of different types of species in a system. For example, a system containing atoms, electrons and ions like a plasma or aqueous solution is in chemical equilibrium when, on average, the microscopic processes leave the number of each species unchanged over time.

The story of a system approaching equilibrium, and its ultimate fate

However, even these statistical types of equilibrium are not precisely realistic, because it takes an infinite time for any system to reach equilibrium. A system will typically follow an exponential decay in its approach to equilibrium, getting arbitrarily close to, but never reaching it. It's fairly easy to see why: if the system is changing state, it's not in equilibrium. In order to approach equilibrium, it has to be changing state. But the processes that make it do so get weaker and weaker the closer it gets to equilibrium. So it doesn't get there in a finite time. But the concept is still useful because if we wait long enough, the system will get as close as we like to equilibrium, so eventually we can measure its temperature (say) to any given accuracy.

The notion of equilibrium also has very powerful consquences in conjunction with the Second Law of Thermodynamics: it allows us to predict what will happen in the far future of any system. The Second Law states that a closed system always changes in the direction of increasing entropy. Putting this together with the notion of a thermal equilibrium state, we deduce that the thermal equilibrium state of a closed system is the state with maximum entropy.

Now, given any initial conditions, a closed system will, given enough time, always end up in a state of thermal equilibrium (or heat death). (See also The Heat Death of the Universe. Of course, whether the Universe is a closed system is debatable.) This is an interesting, if depressing, example of scientific prediction: without knowing any details of the initial state of a system, we can predict (up to our ignorance of its microscopic behaviour) its ultimate fate.

Away from thermal equilibrium: chance would be a fine thing

We should always remember that the Second Law, like all of statistical mechanics, is only a statistical law about what is likely to happen. In fact, the law relies on the mathematical fact that states with greater entropy are overwhelmingly more likely than states with less entropy, for the simple reason that there are many, many, many more of them. Without going into any details, you can deduce that there is a non-zero probability that, just by chance, the entropy of a system will decrease. And the smaller the decrease in entropy, the larger the chance is of it happening.

So, if we take our closed system in equilibrium with the maximum amount of entropy, it will continually be fluctuating into states with very slightly less entropy (and back again). It is possible, although really quite incredibly unlikely, that there will be a large negative fluctuation in entropy and the system will be, as it were, resurrected from its heat death.

In fact, there is a theorem proved by Henri Poincaré that for any closed system satisfying deterministic physical laws (with other assumptions I won't go into), the system will, eventually, return to its original state. This is the "Poincaré recurrence". So if we start out in a state with low entropy, it must at some point in the future return to it, apparently violating the Second Law!

However, the time this takes is much, much, much longer than the time it takes for a system to get to equilibrium, or at least so close to it as makes no difference. The history of the system while it waits for its Poincaré recurrence will be extremely boring, consisting of very short periods fluctuating away from equilibrium and æons at, or very close to, maximum entropy. So, although technically the Second Law isn't always true, and thermal equilibrium isn't always the final state of a closed system, the concepts remain valid for all practical and scientific purposes, and you can stop waiting for your slice of buttered toast to reverse the trajectory that has just sent it into stable equilibrium on the carpet.

E`qui*lib"ri*um (?), n.; pl. E. Equilibriums (#), L. Equilibria (#). [L. aequilibrium, fr. aequilibris in equilibrium, level; aequus equal + libra balance. See Equal, and Librate.]

1.

Equality of weight or force; an equipoise or a state of rest produced by the mutual counteraction of two or more forces.

2.

A level position; a just poise or balance in respect to an object, so that it remains firm; equipoise; as, to preserve the equilibrium of the body.

Health consists in the equilibrium between those two powers. Arbuthnot.

3.

A balancing of the mind between motives or reasons, with consequent indecision and doubt.

Equilibrium valve Steam Engine, a balanced valve. See under Valve.

 

© Webster 1913.

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