The second law wasn’t intended to be probabilistic but it turns out that way. It is only highly, and I mean highly, improbable that a glass of watter sitting in a 70[sup]o[/sup] environment will warm up to 72[sup]o[/sup]. Since there are air molecules in the room that are hotter than that, it just might be that the average temperature of the molecules striking the glass will be the hot ones.
I wouldn’t wait around for it though.
Sure, but if the very definition of time itself is such that increase in time is pegged to increase in entropy, then it wouldn’t even be possible for entropy to decrease over time. In which case, violations of the Second Law wouldn’t be merely improbable; they would, by definition, be impossible. Under such a definition of time, the Second Law would be an analytic truth, holding necessarily, tautologically, in virtue of the mere meanings of its terms. (Which doesn’t seem to be how people view it, suggesting that my understanding is flawed). Do you see what I’m asking?
Not really. Thermodynamics and the field of statistical mechanics, of which it is a subset, is a statistical treatment of physical models. In the aggregate, entropy of a close system can’t decrease, and in fact we find that it doesn’t, nor do cycles spontaneously reverse themselves without energy loss. If you’re trying to parse the laws of thermodynamics, as stated into English, into statements of pure logic about the fundamental mechanics of discrete systems or individual bodies then you’re going to get into trouble, because that’s not what thermodynamics talks to. It assumes that cause and effect exists (but is measurable for complex systems only as a stochastic aggregate), and then indicates that the energy utilized to cause an effect can never be fully recovered, hence giving a preferred (and indeed, imposed) direction on how things go.
Stranger
Just to make it clear where I am coming from, the basic thing is that I have heard it said that the arrow of time is defined as the arrow of entropic increase, and I would like to understand what exactly is the meaning of this statement. I apologize for any (embarrassing) density I am displaying in trying to reach that understanding. It’s not my intention to be difficult.
When you say “the entropy of a closed system can’t decrease”, do you mean “there is a mindbogglingly small but positive probability for a closed system’s entropy to decrease” (in line with what David Simmons said before with his water example) or do you mean “it would be nonsense (given the modern scientific definition of time) to speak of the entropy of a closed system decreasing” (the same way it would be nonsense to speak of a married bachelor or an asymmetric circle or travelling a distance of 10 miles over 5 hours at an average speed of 3 MPH)? Or something else entirely?
I don’t think I’m trying to speak about individual bodies, as such, but perhaps I am speaking of particular system configurations instead of probability distributions over system configurations, and perhaps this is a trap which I should not, for some reason, fall into. Given one configuration of a system, and another configuration of the system, where the second has more entropy than the first, is it definitionally the case that the second is to be regarded as coming later in time than the first, the statement about chronology being nothing more than another way of wording the statement about entropy?
What does it mean to assume that cause and effect exist? Is this another way of wording statements about entropy change, or is it something else?
Over any sufficient length of time the glass of water must cool off. However, there is no theoretical bar to a bizzare event like a small heating up taking place. It’s just unlikely. So ulikely that I suspect if all the atoms in the universe were glasses of water, they had existed since the beginning of the universe and you took their temperature every second there might not yet have been an example of spontaneous heating for even an instant. But I think there is no reason there couldn’t be.