Recent content by Ted Ali

Temperature ##T## is given by equation ##(2)##, in the microcanonical ensemble and calculated in Wikipedia (https://en.wikipedia.org/wiki/Einstein_solid). The final result is: $$\frac{q}{N} = \frac{1}{e^{hf/kT} - 1}\hspace{1cm} (9)$$ The chemical potential ##\mu## is given by ##(1)##, when ##U...

In addition to the homework statement and considering only the case where ##U= constant## and ##N = large## : Can we also consider the definition of chemical potential ##\mu## and temperature ##T## as in equations ##(1)## and ##(2)##, and use them in the grand partition function? More...

Should ##N## have an upper bound other than infinity? Should we consider an interaction between systems (instead of the isolated Einstein solid), governed by the grand canonical ensemble? Is the derivation of the chemical potential ##(\mu)## in the microcanonical ensemble, not applicable in the...

The main question is whether ##q## should be considered a constant, or else, dependent on every value ##N## takes, in the sum.

$$Q_{(\alpha, \beta)} = \sum_{N=0}^{\infty} e^{\alpha N} Z_{N}(\alpha, \beta) \hspace{1cm} (3.127)$$ Where ##Q## is the grand partition function, ##Z_N## is the canonical partition function and: $$\beta = \frac{1}{kT} \hspace{1cm} \alpha = \frac{\mu}{kT} \hspace{1cm} (3.128)$$ In the case of an...

According to the book "Principles of Statistical Mechanics" by Amnon Katz, page 123, ##\alpha## must be such that ##\exp ( -\alpha N ) ## can be expanded in powers of ##\alpha## with only the first order term kept. Is this the necessary and sufficient condition for small deviations from...

Attempt to a solution: $$dU = TdS - PdV + \mu dN \text{ } (4).$$ Since ##q = constant## we have from equation (1), that ##dU = 0 \text{ } (5)##. Also ##PdV = 0 \text{ } (6).## As a result $$TdS = - \mu dN \text{ } (7).$$ But ##\mu = - T \left( \frac{\partial S}{\partial N} \right) \text{ } =...

For ##q >> N ##. ##\Omega \approx \left( \frac{eq}{N} \right)^N \text{ } (2)## (Schroeder, An introduction to thermal physics (2.21)). Can we argue that: ##\Delta I = - \Delta S \text{ } (3)?## How large can ##\Delta N##, be? Thank you for your time.

Hello! I would like your help to study Science graduate level books and articles, in the following subjects: 1. Far from equilibrium statistics. 2. Information theory and entropy. 3. Negentropy. 4. And Maxwell's demon. My main goal is to be able to understand and explore the Maxwell's demon...

Hello! I would like to apply Brillouin's negentropy principle to an isolated Einstein solid, with a decreasing number of oscillators. We assume that the number of oscillators are initially N and the energy quanta (q the number) remain constant. Firstly, I would like to know if this principle is...

When I started this thread, I thought that the topic and answers, would be trivial! I now think it is not. I found the following/attached article through a Google search. In the second paragraph of the Introduction we read: "The aim of this work is to extend the model proposed by Einstein for...

Hello Everyone! I am interested in examining the case of an isolated Einstein Solid (ES) with a decreasing number of oscillators. The total amount of energy of the ES is considered fixed. Whenever an oscillator abandons our model, it "leaves behind" the amount of energy it contained, so that the...

Hello everyone! I am a physics undergrad student. I hope that my questions here will be interesting enough, for you members, to answer them! Regards, Ted.