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

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1answer
186 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
votes
1answer
295 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
919 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
3answers
319 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 ...
13
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3answers
344 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
144 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
682 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 ...
4
votes
2answers
160 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
8k 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 ...
8
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3answers
1k 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
348 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
177 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 ...
1
vote
4answers
2k 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
150 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 ...
1
vote
2answers
144 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
231 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
299 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
662 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
188 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
287 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
158 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
400 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 ...
17
votes
1answer
835 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
407 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 ...
3
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4answers
5k 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
143 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.
7
votes
3answers
814 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
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1answer
63 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
106 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
274 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
270 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 ...
8
votes
2answers
595 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
196 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
530 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 ...
7
votes
7answers
742 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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0answers
93 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
891 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
votes
2answers
421 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 ...
2
votes
2answers
329 views

Convergance of a system to Boltzmann distribution

Consider a system with finite-dimension state X and energy E(X), with dynamics which follow the Langevin equation $\frac{dX}{dt}=-\nabla_X{E(X)}+\eta(t)$ where $\eta$ is white noise ...
5
votes
1answer
1k views

What does the concept of phase space mean in particle physics?

I came across the concept of phase space in statistical mechanics. How does this concept come about in particle physics? Why was it introduced and how is it used? What does it mean when ...
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vote
2answers
429 views

Maxwell-Boltzmann distribution and total energy per unit volume

We know that $$n(E) ~=~ \frac {2 \pi (N/V)}{(\pi k_B T)^{3/2}} E^{1/2} e^{-E/(k_B T)} dE,$$ where $V$ is total volume. If then, how do we derive total energy per unit volume from this equation?
22
votes
7answers
1k views

How is $\frac{dQ}{T}$ measure of randomness of system?

I am studying entropy and its hard for me to catch up what exactly is entropy. Many articles and books write that entropy is the measure of randomness or disorder of the system. They say when a gas ...
2
votes
0answers
96 views

Randomly sampling a “well-mixed” solution of Brownian particles

I place $N$ Brownian particles in $V$ liters of solution, shake until I assume that the particles are "well-mixed", and sample and randomly sample an $S$ liter volume. What is the probability ...
1
vote
1answer
53 views

In which way is decoherence not symmetric between the two considered systems?

If a quantum system interacts with a "big" quantum system, you have dephasing. The models of decoherence all have this atog aproach to them, about what is to understood of the interaction of the ...
7
votes
3answers
306 views

Is particle number a problem for formulating statistical physics in a mathematically rigorous manner?

Quantities like the chemical potential can be expressed as something like $$\mu=-T\left(\tfrac{\partial S}{\partial N}\right)_{E,V}.$$ Now the entropy is the log some volume, which depends on the ...
3
votes
2answers
962 views

Latent heat vs temperature of phase transitions?

Is the latent heat associated with phase transitions correlated with the temperature at which they occur? The latent heat is related to the difference in energy between the two phases, and the ...
11
votes
2answers
423 views

Can $10^{23}$ stars be treated with methods of statistical mechanics?

Statistical mechanics is used to describe systems with large number of particles ~$10^{23}$. The observable universe contains between $10^{22}$ to $10^{24}$ stars. Can we treat those many stars as a ...
5
votes
7answers
3k views

Is it theoretically possible to reach 0 kelvin?

I'm having a discussion with someone. I said that it is -even theoretically- impossible to reach 0K, because that would imply that all molecules in the substance would stand perfectly still. He said ...
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vote
1answer
131 views

Where is the critical moment where the microcanonical ensemble enters the justification for the equilibium state?

As explained in many books, for the microscopic justification of the second law of thermodynamics (lets formulate it as the total entropy takes maximum among all possible exchanges of two systems), ...
2
votes
2answers
258 views

Average Neighbouring Impurity Separation in a Random 1D chain [closed]

I have a finite and discrete 1D chain (edit: linear chain, i.e. a straight line) of atoms, with unit separation, with a set number of impurities randomly distributed in the place of these atoms in ...