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"In classical thermodynamics, a single particle doesn't have a temperature." This is false. A single particle can still be described by the maximum entropy pro
by asafira 9y ago
"In classical thermodynamics, a single particle doesn't have a temperature."
This is false. A single particle can still be described by the maximum entropy probability distribution given its average energy, and that will give rise to a definition of temperature.
- rxhernandez 9y agoWhen I did my physics undergrad I skipped thermodynamics and went straight to statistical mechanics, so forgive me if I missed something. Ostensibly, it would seem a classical version of thermodynamics wouldn't deal with particles at all as the current model of particles(even Bohr's model) is much newer than classical thermodynamics.
- readams 9y agoBy "classical" it's reasonable to assume they mean "not quantum"
- rxhernandez 9y agoThat and my lack of a thermo class is why I prefaced it with ostensibly.
- comicjk 9y agoA "particle" in statistical thermodynamics is a mathematical idea that doesn't necessarily match any fundamental particle in physics. For example, air is made of molecules with complex quantum bonding states, yet many of air's properties can be derived by considering it simply as a collection of point masses.
- llamaz 9y agoi.e. a Green's function (disclaimer: I know more about maths than physics)
- kgwgk 9y agoThe current model of particles is also newer than statistical mechanics. Clausius, Maxwell, Boltzmann and Gibbs were all dead by the time Bohr’s model appeared.
- wyager 9y agoClassical thermo (as I learned it in undergrad) works in terms of quantized oscillators, which actually works quite well with quantum mechanics.
- madhadron 9y agoOh dear. This is a common problem. Classical thermodynamics is a theory in its own right. Statistical mechanics is used to bridge microscopic structure to thermodynamic properties. Unfortunately, physicists don't learn thermodynamics. It's pretty much only taught to mechanical and chemical engineers.
- kgwgk 9y agoThe classical [statistical mechanics] theory is based on classical harmonic oscillators (which can have any frequency/energy). Quantization is introduced by Plank in 1900.
- jamesrom 9y agoWhat you just said is a complicated way of saying that a particle can describe temperature.
- asafira 9y agoHmm. I'm not sure what you mean ... if you have the chance, do you think you can try to explain what you mean?
- bkcooper 9y agoThis is false. A single particle can still be described by the maximum entropy probability distribution given its average energy . . . I'm not sure that construction makes sense. For a single particle not interacting with anything, imposing the maxent constraint on average energy just sets the energy of the particle and there's no room left for a distribution. As soon as its interacting with another system you're good, but then the temperature that you arrive it is a characteristic of the bath, not the particle itself.
- asafira 9y agohow does the average energy set the energy of the particle? To me, for any configuration of the particle x, the average energy of the particle is given by sum over all configurations of p(x) E(x) and there's the probability distribution over configurations.
- alecst 9y agoI think what the OPs mean is that in the classical case, the lone, noninteracting particle has a fixed, definite energy and not an average energy. There are no other configurations to consider, besides the set of points that the particle may be in space, but that is irrelevant to the energy and temperature. Maybe what you're saying is true if you consider a single quantum particle, I'm not sure.
- asafira 9y agoI don't think invoking quantum mechanics is necessary here honestly. Let's say I flip a coin; most people would model the outcome as a p = 1/2 chance of heads and p = 1/2 chance of tails. This is fairly standard, of course, but I think it illustrates my point. Of course, in reality there is only 1 outcome that's going to happen, but literally the best model of the system we can come up with, given our ignorance, is that it's 50/50 heads and tails. So, what I am saying is that given that we know relatively little about the particle --- what it's average energy is --- we can come up with a probability distribution over states with that average energy that represents our "best guess" or "least biased" probability assignments.
- techdragon 9y agoI'm not sure that it's so straightforward a situation as that. Since the "one lone particle in the universe" is firmly in Mach effect / Mach principle territory. https://en.m.wikipedia.org/wiki/Mach%27s_principle https://en.m.wikipedia.org/wiki/Mach%27s_principle