Let me quickly remind what I was trying to point out in the previous post on the second law.
Recall that we also derived how long we should wait. Probability of simultaneously seeing \(N\) molecules in a sphere of radius \(r\) inside a volume of \(\pi R^2 h\) was equal to \begin{align} P\big\{\mathbf{X^{1:N}} \in \mathcal{D} \big\} = \Big(\frac{2r^2}{R^2h}\Big)^N, \label{eq:final} \end{align} which emphasizes that the how long we should wait strongly depends on the system size, i.e., the variables \(R\), \(r\), and \(h\). Think about it for a second, it makes perfect sense. Imagine that your system is a really really small cube which can surround only one drop. Probability of seeing that drop in your tiny cube will be much higher than probability of seeing it in your coffee mug. For the coffe mug case you may have to wait, practically forever.
Another misconception about the second law rises from the fallacy of equating disorder with entropy. If entropy (practically) always increases, how is it possible for us to see so many patterns forming around, random water molecules turning into snowflakes, or basically how life, such ordered organisms, can even exist? I know I sound like a creationist. And yes, this is exactly what they say. If we summarize the idea, creationists claim,
So next time you see a creationist talking about extracting order from disorder, tell him to try to cool down his kitchen by leaving the refrigerator door open. If he succeeds, then it means he's right.
When you cool things down, i.e., decrease the thermal energy of a system, you also narrow down the energy distribution of the molecules. You reduce entropy. Your refrigerator also does the same thing to keep your ice-cream cold. It reduces entropy, locally. Keep in mind that the second law is valid for a closed system. Your refrigerator (or you) consume electricity (just like you consume food) to cool things down (to keep your body at 37 \(\circ\)C), but it turns most of this energy into heat, plus with some chemical waste (you simply sweat and poop). Overall, your refrigerator increases entropy by a large amount, even though it locally decreases it [1].
Does life reduce entropy? Yes, it reduces entropy locally, while it increases it globally. The trick here is to keep in mind that when you analyze the entropy of an organism, you must also consider its surroundings. Otherwise, God forbid, you may end up being a creationist.
References
[1] Peter M. Hoffman, Life's Ratchet : How molecular machines extract order from chaos.
[2] http://www.talkorigins.org/faqs/thermo/creationism.html
"Second law doesn't say that it is impossible to see a case such that the entropy decreases. Instead, it says that most of the time (usually very close to always), systems tend toward their most probable state [1], which is not the state where the entropy decreases."From now on, we know that second law is a statistical law. An ink drop can form in an homogeneous solution, or your cold coffee can spontaneously boil. Only just if we are willing to wait long enough, strange things can happen by chance.
Recall that we also derived how long we should wait. Probability of simultaneously seeing \(N\) molecules in a sphere of radius \(r\) inside a volume of \(\pi R^2 h\) was equal to \begin{align} P\big\{\mathbf{X^{1:N}} \in \mathcal{D} \big\} = \Big(\frac{2r^2}{R^2h}\Big)^N, \label{eq:final} \end{align} which emphasizes that the how long we should wait strongly depends on the system size, i.e., the variables \(R\), \(r\), and \(h\). Think about it for a second, it makes perfect sense. Imagine that your system is a really really small cube which can surround only one drop. Probability of seeing that drop in your tiny cube will be much higher than probability of seeing it in your coffee mug. For the coffe mug case you may have to wait, practically forever.
Another misconception about the second law rises from the fallacy of equating disorder with entropy. If entropy (practically) always increases, how is it possible for us to see so many patterns forming around, random water molecules turning into snowflakes, or basically how life, such ordered organisms, can even exist? I know I sound like a creationist. And yes, this is exactly what they say. If we summarize the idea, creationists claim,
"The second law of thermodynamics requires that all systems and individual parts of systems have a tendency to go from order to disorder. The second law will not permit order to spontaneously arise from disorder. To do so would violate the universal tendency of matter to decay or disintegrate [2]."This is the kind of mistake we always do when we try to abstract a mathematical concept. When an example illustrates a mathematical concept, we tend to remember the example rather than the mathematics itself. Furthermore, we extract some features from that example which seems important to us, and yet may be irrelevant with the underlying mathematical model. Afterwards, when we see these features in another phenomenon, we quickly associate it with the example in mind, and at the same time, with the mathematical concept. Long story short, since it requires less cognitive load, we tend to replace mathematics with metaphors. The pay-off is to think that creationists may have a point at all.
So next time you see a creationist talking about extracting order from disorder, tell him to try to cool down his kitchen by leaving the refrigerator door open. If he succeeds, then it means he's right.
When you cool things down, i.e., decrease the thermal energy of a system, you also narrow down the energy distribution of the molecules. You reduce entropy. Your refrigerator also does the same thing to keep your ice-cream cold. It reduces entropy, locally. Keep in mind that the second law is valid for a closed system. Your refrigerator (or you) consume electricity (just like you consume food) to cool things down (to keep your body at 37 \(\circ\)C), but it turns most of this energy into heat, plus with some chemical waste (you simply sweat and poop). Overall, your refrigerator increases entropy by a large amount, even though it locally decreases it [1].
Does life reduce entropy? Yes, it reduces entropy locally, while it increases it globally. The trick here is to keep in mind that when you analyze the entropy of an organism, you must also consider its surroundings. Otherwise, God forbid, you may end up being a creationist.
References
[1] Peter M. Hoffman, Life's Ratchet : How molecular machines extract order from chaos.
[2] http://www.talkorigins.org/faqs/thermo/creationism.html
