The study of large systems through coarse graining microscopic descriptions, providing a more detailed understanding of thermodynamics.

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1answer
688 views

Limit of Fermi-Dirac distribution as $T$ goes to zero

Hopefully this is a simple question, I just can't seem to get my mind around it. I'm to take the limit of the Fermi-Dirac distribution for $T \rightarrow 0$. In this limit the chemical potential is ...
3
votes
1answer
1k views

What is non-thermal plasma?

I read about non-thermal plasma, but I still have some questions: The ions and neutral particles are not in thermal equilibrium with the electron, does that mean that the overall temperature is low ...
3
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2answers
1k views

The definition of entropy in quantum mechanics

I have seen entropy with several different definitions. Like Von Neumann entropy and Rényi entropy, etc. So I am curious why there are so many different definitions in quantum mechanics while only ...
2
votes
2answers
683 views

Spin 3/2 Statistical Mechanics Problem

I am trying to solve a problem from the book 'Introductory Statistical Mechanics' (Bowley, Sanchez). The question reads: Calculate the free energy of a system of N particles, each with spin 3/2 with ...
1
vote
1answer
297 views

An explanation for the Landauer's principle

Has anyone understood the Landauer's principle? What is the current status? In specific, is there a theoretical derivation of the Landauer's Principle?(not the heuristic one based on Salizard's ...
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1answer
288 views

Do laws of thermodynamics have a place in Theory of Everything? [closed]

I am having a difficulty understanding why second law of thermodynamics is still a valid universally accepted concept. I understand it works on paper for describing isolated heat systems. However, I ...
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5answers
2k views

Does high entropy means low symmetry?

According to Bogolubov postulate (various texts name it differently) in Non-equilibrium thermodynamics, the number of needed parameters to describe our system is decreasing with time, and finally at ...
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0answers
74 views

Edwards-Anderson Hamiltonian of a Hopf link

I was calculating the Edwards-Anderson Hamiltonian of a Hopf link. A hopf link is like attachment 1. I have drawn the Seifert surface of that link. The surface is shown in attachment 2. It also ...
1
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2answers
179 views

Is it possible to find the number of gas atoms/molecules in a box when the number is small?

Given very low number of particles in a system (e.g. in the 100s), is there a way to accurately measure the number of particles in the system? Assume temperature, pressure and volume is constant and ...
4
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4answers
450 views

Why can $\beta$ not be linearly proportional to $T$, that is $\beta = constant \times T$?

$\beta$ in statistical mechanics is equal to $\frac{1}{k_BT}$ in in thermodynamics, but I do not understand why $\beta\propto T^{-1}$ instead of, say, $\beta\propto T$?
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3answers
1k views

Formal demonstration that minimizing the free energy equals maximizing the entropy

I never had great intuition when it came to thermodynamic concepts and potentials even though reading a textbook and completing the exercises has never been a huge problem. In one of them, I was ...
6
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3answers
2k views

Why does the law of increasing entropy, a law arising from statistics of many particles, underpin modern physics?

As far as I interpret it, the law of ever increasing entropy states that "a system will always move towards the most disordered state, never in the other direction". Now, I understand why it would ...
6
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1answer
215 views

Can closed loops evade the spin-statistic theorem in 3 dimensions?

The famous spin-statistics result asserts that there are only bosons and fermions, and that they have integer and integer-and-a-half spin respectively. In two-dimensional condensed matter systems, ...
3
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1answer
308 views

Simulating quantum network of harmonic oscillators

Let's say that I have a system of $n$ particles $p_1,\ldots,p_n\in\mathbb{R}^3$ (where $n$ here is on the order of 10,000). Furthermore, suppose we have a graph $G=(V,E)$ describing some network, ...
4
votes
2answers
1k views

What is a bulk phase transition?

I have been able to google "bulk phase transition" and get plenty of results that verify that something called a bulk phase transition exists, however, I cannot seem to find a precise definition of ...
6
votes
2answers
334 views

Why does bad smell follow people (assuming they are not the source)?

When you are sitting in a room where there is a source of bad smell, such as somebody smoking or some other source of bad smell, it is often a solution to simply move to another spot where bad smell ...
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3answers
385 views

Chemical reaction as state transition?

When considering diffusion of chemicals, the reaction part is business of chemical kinetics, where the relevant characteristics of different substances come from collision theory together with some ...
1
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1answer
159 views

How to interpret a negative failure rate?

In statistical engineering the "hazard rate" of a distribution is defined as: $$r(x)=\frac{f(x)}{1-F(x)}$$ where $f(x)$ and $F(x)$ are the PDF and CDF. Basically $r(x)$ is the odds that, having ...
2
votes
2answers
865 views

Confusion about Free Energy and the Hamiltonian

I'm probably making a relatively basic mistake here, but I'm a bit confused about the relation between the Hamiltonian and Helmholtz free energy. From what I can see, the free energy can be written ...
5
votes
2answers
169 views

Pair interactions on finite square lattice

I am looking for an exact or approximate solution to a statistical lattice-particle problem: Given a lattice of size $L\times L$ where $\rho\cdot L^2$ particles are randomly distributed, calculate ...
2
votes
6answers
13k views

What is a microstate, macrostate and thermodynamic probability in statistical mechanics?

Currently I am learning Maxwell-Boltsmann distribution (MBD) and in that I am learning about microstate, macrostate and thermodynamic probability (TDP). I understood the derivation of MBD but I am ...
9
votes
3answers
2k views

What are some of the best books on complex systems?

I'm rather interested in getting my feet wet at the interface of complex systems and emergence. Can anybody give me references to some good books on these topics? I'm looking for very introductory ...
5
votes
1answer
454 views

Ideal gas and diatomic gas with same temperature

If a box of ideal gas and another box of diatomic gas are in thermal equilibrium, does it mean that the average translational energy of ideal gas particle (A) is the same as that of diatomic gas ...
2
votes
2answers
189 views

Diffusion of probability amplitudes

Let's say I have a probability amplitude $\psi:\Sigma\rightarrow\mathbb{C}$ for some domain $\Sigma$ (so, $\psi$ satisfies $\int_\Sigma |\psi|^2=1$). Is there a way to use $\psi$ as initial ...
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vote
4answers
3k views

Physics of a burning log of firewood

According to my knowledge, heat is nothing but the result of the vibrations of atoms and molecules. I guess this mean that in heating up a gas or liquid, we are increasing the rate at which the ...
2
votes
2answers
160 views

Graph Invariants and Statistical Mechanics

Many intuitive knot invariants including Jones' polynomial are inspired by statistical mechanics. Further profound connections have been explored between knot theory and statistical mechanics. I was ...
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2answers
156 views

Similarity of probability amplitude functions

Let's say I have two probability amplitude functions given by $\psi_1$ and $\psi_2$. That is, $\psi_i:\Sigma\rightarrow\mathbb{C}$ for some domain $\Sigma$ with $\int_\Sigma|\psi_i|^2=1$ for ...
2
votes
1answer
259 views

Open boundary condition and Glauber Dynamics

Warning: by background is in math, not physics. I've just recently started working with things that are close to theoretical physics. So please note that I'm still very confused by the jargon. Maybe ...
6
votes
2answers
311 views

Mathematical probabilistic interepretation of probability amplitude

As a warning, I come from an "applied math" background with next to no knowledge of physics. That said, here's my question: I'm looking at the possibility of using probability amplitude functions to ...
5
votes
3answers
774 views

Are negative temperatures typically associated with negative absolute pressures?

Negative temperatures and negative absolute pressures are both possible in physical systems. Negative temperatures arise in (for example) populations of two-state systems, which have a maximum amount ...
2
votes
4answers
204 views

What is the simplest system that has both, discontinous and continous phase transitions?

I am looking the simplest system that has both discontinous phase transition and a continous phase transition between the same phases (you can change one parameter). discontinous transition: first ...
2
votes
1answer
351 views

Black hole entropy

Bekenstein and Hawking derived the expression for black hole entropy as, $$ S_{BH}={c^3 A\over 4 G \hbar}. $$ We know from the hindsight that entropy has statistical interpretation. It is a measure ...
9
votes
1answer
188 views

Why are topological solitons present in some phases for lattice models?

Over a spatial continuum, it is easy to see why some topological solitons like vortices and monopoles have to be stable. For similar reasons, Skyrmions also have to be stable, with a conserved ...
2
votes
2answers
450 views

Micro-canonical ensemble and classical reality

I seem to find a contradiction in the notion of probability density used by Landau and the notion of micro-canonical ensemble. To see this, take an isolated classical system and we know ...
21
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1answer
1k views

Why is the partition function called ''partition function''?

The partition function plays a central role in statistical mechanics. But why is it called ''partition function''?
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2answers
497 views

State-dependent diffusions: Fick's law vs. Fokker-Planck's, which and why?

Consider a "state-dependent diffusion": a diffusion process for which the diffusion coefficient $D(x)$ depends on the (stochastic) state $x$ of the system. (An example is provided by the diffusion of ...
4
votes
5answers
6k views

What are distinguishable and indistinguishable particles in statistical mechanics?

What are distinguishable and indistinguishable particles in statistical mechanics? While learning different distributions in statistical mechanics I came across this doubt; Maxwell-Boltzmann ...
3
votes
1answer
153 views

Why is the $\langle v_{x}^{2} \rangle=\frac{1}{3} \langle v^2 \rangle$?

For a randomly moving particle. Or, I suppose that 1/3 could generalise to 1/n, where n is the non rotational degrees of freedom for that particle. Related reference Kinetic Theory of Gasses.
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3answers
939 views

Relation between statistical mechanics and quantum field theory

I was talking with a friend of mine, he is a student of theoretical particle physics, and he told me that lots of his topics have their foundations in statistical mechanics. However I thought that the ...
1
vote
1answer
68 views

Pressure change due to fan removing air from a non-airtight room

The following problem occurred to me today: Suppose a $100\mathrm{cfm}$ fan is pushing air out of a large room which is airtight except for a $10 \mathrm{cm}^2$ hole. The air pressure outside the ...
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0answers
109 views

What is meant by correlation propagation?

What is meant by correlation propagation in physics? I have an intuitive understanding but are there any introductory notes ( more mathematical oriented) and with some physical examples?
4
votes
2answers
288 views

Entropy: two explanations for the same quantity?

I studied thermodynamics and I saw the following definition for entropy: $$ \Delta S = \int_1^2 \frac{\text{d}Q}{T} $$ that we use to calculate $\Delta S$ for different types of transformations. In ...
4
votes
1answer
309 views

Entropy, flow of informations and fundamental theories

In the hierarchy of theories, first comes hamiltonian theory, from which one deduces kinetics theory, and at last thermodynamics and fluid theories. From a kinetics point of view, entropy and ...
9
votes
1answer
747 views

Why doesn't the percentage of oxygen in Earth's atmosphere diminish significantly with altitude?

According to numerous sources online, the percentage of oxygen is approximately the same at sea level and 10,000 meters. Since oxygen is heavier than nitrogen, shouldn't the percentage of oxygen ...
1
vote
1answer
211 views

What is theory of Free Energy Perturbation? How is it applicable to chemical science?

What is theory behind free energy perturbation? Is it way too difficult to understand? Can someone explain it in simple terms.
4
votes
3answers
606 views

number of microstates associated with two-level quantum systems

this is a very simple question, but apparently one that has no simple answer, at least from standard quantum mechanics theory I'm trying to figure the number of simple quantum states (microstates) of ...
8
votes
7answers
845 views

Is it wrong to talk about wave functions of macroscopic bodies?

Does a real macroscopic body, like table, human or a cup permits description as a wave function? When is it possible and when not? For example in the "Statistical Physics, Part I" by Landau & ...
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vote
0answers
94 views

usage of partition function in some number of particles in one-dimensional axis

I just learned some introductory quantum meachnics, but not statistical mechanics, so I am curious how partition functions would be used in the following case: Suppose there are three particles in ...
5
votes
3answers
1k views

Is temperature an extensive property, like density?

I was thinking about it some time ago, and now that I've discovered this site I would like to ask it here because I couldn't work it out then. I know that the higher temperature the air in my room ...
3
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2answers
485 views

Time to establish saturated vapour pressure above liquid

Thought experiment - a liquid is in a closed container in equilibrium with its vapour, and then suddenly all the vapour is pumped away. Switch off the pump so that instantaneosuly there is no vapour ...