Entropy
Fascinating aspects to the 2nd Law of Thermodynamics
When professors first introduce entropy and the 2nd Law of Thermodynamics, we hear them refer to a term called Time's Arrow. In the second law dS = dqrev/T, where S = entropy, q = heat, and T = temperature. Time's Arrow attempts to talk informally about the asymmetry (or anisotropy) of the universe.
For example, if a bottle of perfume were spilt, the molecules would generally diffuse throughout the entire room. However, we can never take a room with diffuse perfume molecules and expect that they would spontaneously congregate into the bottle of perfume. This is an example of a reaction that is asymmetric with respect to time.
One of the most important things to remember about the change in entropy for an equation. If DS is positive for any process, then that process will spontaneously proceed towards the common sense direction1. In other words, if DS is positive, then a kettle will cool down.
Why does my disheveled apartment not constitute an increase in entropy?
My apartment is very disordered, but this is not an example of an increase in entropy. A shuffled deck of cards or a professor's desk is also not an example of an increase in entropy. The change in entropy of these systems is all the same, zero.
K.G. Denbigh adequately summarizes this point
"If one wishes to substantiate a claim or a guess that some particular process involves a change of thermodynamic or statistical entropy, one should ask oneself whether there exists a reversible heat effect, or a change in the number of accessible energy eigenstates, pertaining to the process of in question. If not, there has been no change of physical entropy (even though there may have been some change in our 'information').2"
F.L. Lambert notes that a collection of items in the macro world does not constitute the necessary conditions for a thermodynamic system. The reason being is that these items are not continually in bombarding with one another and exchanging energy within their environment. Moreover, these processes are not spontaneously happening3.
It is relatively easy to see now that our a disheveled apartment is not an indication for an increase in entropy. First, while we may shuffle the location of these macro objects, there is not change in the number of accessible energy eigenstates. In this example, if I had a baseball glove on the table versus in the closet. These two state would be identical, because these two states exist at an equal energy level (or an equal state of disorder) and would be considered degenerate. Second, the particles of this system are not in constant contact with each other forming the necessary conditions to be considered a thermodynamic system.
Time travel is one aspect of the asymmetry of time, which can be a lot of fun to think about. If a person hopped into a time machine and disappeared, a scientist trained in Newtonian physics would immediately wonder about this conceivable failing of the law of conservation of mass. Modern physics however intricately ties space and time together, conveniently naming it "spacetime".
"The three dimension of space and a single dimension of time define a four-dimesional arena in which, over its lifetime, an object describe a long tube, known as its 'worldline". The spacetime woven by general relativity is a more flexible fabric then Newton's and allows distortions in spacetime so as to allow worldlines to revisit sections of it that they have already passed through.4"
In 1949, Kurt Godel demonstrated the mathematics necessary for spacetime to revist previous sections. However, his solution was based only on a rotating universe, which we know from modern astronomy to be incorrect4,5.
Kip Thorne (Cal Tech) has recently proposed another mechanism for time travel. "Local distortions in space at two points narrowly separated in hyperpspace cause them [wormholes], so the theory goes, to bulge out and connect.4" This hyperspace is the 4-dimensional "spacetime." Wormholes are said to exist in John Wheeling's famous quantum foam, or energy distortions on a scale of a hundred trillion, trillion times smaller than an atom4.
In science if something is not specifically excluded, then it must be allowed. Since modern physics specifically does not exclude time travel, then it must be allowed, at least at this point in the debate.
Thermal Death
Theory
"In the middle of the last century, R. Clausius and W. Thomson, the authors of the second principle of thermodynamics, attempted to apply the second law to the universe as a whole, and arrived at a completely false theory, known as the "thermal death" theory of the end of the universe."
According to one scholar:
"This bleak view [thermal death] of the universe is in direct contradiction to everything we know about its past evolution, or see at present. The very notion that matter tends to some absolute state of equilibrium runs counter to nature itself. It is a lifeless, abstract view of the universe. At present, the universe is very far from being in any sort of equilibrium, and there is not the slightest indication either that such a state ever existed in the past, or will do so in the future. Moreover, if the tendency towards increasing entropy is permanent and linear, it is not clear why the universe has not long ago ended up in a tepid soup of undifferentiated particles.6"
In 1877, Boltzmann developed a new 2nd Law. In his theory, entropy is a function of the probability of a given state of matter. The higher the probability, the higher its entropy. In this theory, all systems point towards a state of equilibrium. Boltzmann was the first one to deal with the problems of the transition from the microscopic (small-scale) to the macroscopic (large-scale) level in physics.
Following Maxwell's example, he attempted to solve the problems through probabilities of a system. "... Boltzmann took no account of such forces as electromagnetism or even gravity, allowing only for atomic collisions." So, Boltzmann's has a limited number of situation in which it is applicable6.
Brownian Motion
In 1827, Robert Brown, and English botanist noticed that pollen grains, when suspended in water, jiggled about under the lens of a microscope following a zigzag path. This motion is called "Brownian motion".
Brownian motion was explained by Desaulx in 1877. "
"In my way of thinking the phenomenon is a result of thermal molecular motion in the liquid environment (of the particles)." This is indeed the case. A suspended particle is constantly and randomly bombarded from all sides by molecules of the liquid. If the particle is very small, the hits it takes from one side will be stronger than the bumps from other side, causing it to jump. These small random jumps are what make up Brownian motion.7"
Einstein claimed his Nobel prize in 1905 for the mathematical theory to explain Brownian motion.
Yet, despite the fact that Brownian motion exhibits the necessary environment for a thermodynamic system, it would technically violate Entropy6.
Time variable
One seeming contradiction to the theory of Entropy is how you get a time dependent out of an equation of time independent. We talked earlier about the asymmetry of time, yet the actual equation of Entropy contains no term of time. How can there be a dependence on time when there is no time factored into the equation. This question has been perplexing scientists for years, and as of now, no one seems to have an answer.
Another (yes, even cooler) applet of
Brownian Motion
The Coolest Brownian Motion applet
1http://www.2ndlaw.com/entropy.html
2Denbigh, K.G. Br.J.Philos.Sci. 1989, 40, 323-332.
3Lambert, F.L. Shuffled Cards, Messy Desks, and Disorderly Dorm Rooms - Examples of Entropy Increase? Nonsense! J. Chem. Educ. 1999, 76, 1385.
4http://phys.uregina.ca/classes/phys200/timetravel.html
5Horwich, Paul. Asymmetries in time. Copyright MIT 1988.
6http://www.marxist.com/science/arrowoftime.html
7http://www.xanadu.math.utah.edu/java/brownian motion/1/
Last Revised: 11.21.00
Author: Steve Adamson