Yes, the deluge of doubts that assail me after assuming this have now convinced me that dE=0 cannot be a criterion for equilibrium. I think the underlying reason that I was led into believing so was that (potential) energy minimization seemed to work so well in classical mechanics (although I am...
I don't see how that would work...
How can dE always be zero? When we can vary d\mathbf{x}, d\mathbf{N}, etc. in an infinite number of ways, how can we have that dE is zero for all the possible varianions?
I've been reading Mehran Kardar's Statistical Physics of Particles. I remember one problem that led me to this confusion. In the exercises for the first chapter on Thermodynamics, the solution to the first question (given in the book) seems to imply this. Here's the question:
Surface tension...
In case it doesn't make sense, \mathbf{J} is a generalized force (in the case of gases, this would be -P), and \mathbf{x} is a generalized displacement (in the case of gases, that would be V).
This is more of a recurring conceptual doubt that I keep on running into when solving thermodynamics problems. We are taught that variations between extensive state variables in equilibrium are given by the following 'fundamental formula':
dE = TdS + \mathbf{J}\cdot{d}\mathbf{x} +...
The basic idea behind a tensor is actually a lot simpler than you might imagine, at least if you only want a physical intuition.
When you need to assign a quantity to each direction in the x, y, and z, you get a vector. But many times in physics, you'll have to specify two directions to get one...
Bam! :wideeyed:
Okay, that was the crucial insight...everything makes sense now. :smile:
Yes, this makes a lot of sense. Something on these lines was suggested in this article, which I found in the suggested articles on your's. BTW, the examples given in your article were really nice!Finally...
I began reading Mehran Kardar's Statistical Physics of Particles and about halfway through the first chapter, there was a discussion on the second law of thermodynamics. He makes no mention of the old tenet that 'the total entropy in the universe must always increase' (I'll refer to this as the...
Never mind that...the mention of GaAs threw me off. I held the notion that polymers (like polyethylene) were used for optical fibres. After some reading I learned that they are used in cladding, while the actual transmitting material is made up of those you mentioned.
And yes, 'optical...
That's really interesting! I hadn't thought about thermal imaging having to worry about water vapour in the atmosphere.
Now, I always thought that the miles of optical fibres which we lay into the seas is where all the internet communication goes on. So, is the NIR communication a relatively...
I was reading about a process called up-conversion mentioned in Robert Boyd's Non-Linear Optics. It is essentially a special case of sum frequency generation (in sum frequency generation, two waves of different frequencies are sent into the crystal, and out comes a wave with a frequency equal to...
Okay, I understand now. There is no reason for the representation space and the group's representation to be required to have the same number of parameters. I don't know why I felt that was necessary.
Thanks for the example, I really needed it.
This is precisely what is troubling me. We need three parameters to define the rotation, and yet the object we are rotating has only two free parameters. Shouldn't the number of free parameters for both be the same? A greater number of parameters would imply a greater number of objects; if the...
This question is mostly about group theory but I would like to understand it in the context of qubits rotating in a Bloch Sphere.
What my understanding of things are right now:
In the rotation Lie Group ##SO(3)##, we have three free parameters (##\frac{n(n-1)}{2}##), and this is also why we end...