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

learn more… | top users | synonyms

0
votes
1answer
36 views

White noise in the Langevin model and it's autocorrelation function

I am having some trouble understanding and interpreting the noise term in the Langevin equation for a colloidal particle in a fluid. By the Langevin model, I mean the following model as the equation ...
1
vote
1answer
52 views

Two definitions of the density matrix?

There seems to be two different definitions of definitions of density matrices in Physics. In Quantum Information we define a the density matrix associated with a wave function $ | \psi \rangle$ as ...
1
vote
0answers
44 views

Can the second law of thermodynamics be violated in a small enough system if tried repeatedly enough?

Second law of thermodynamics is observed in the universe because statistics favors it, right? And in large enough system this statistical tendency becomes certainty. Does it also mean that negative ...
8
votes
3answers
114 views

Gross “temperature” of a globular cluster

Globular clusters can be very large, which means we can do statistics about the stars in them. And that means we can try matching their star-as-particle potential/kinetic energy distribution against ...
0
votes
1answer
25 views

Why use dimensionless heat capacity?

Perhaps this is blindly obvious, but in typical discussions of statistical mechanics (with, say, constant volume) one often finds that, rather than using the heat capacity $$ C_V = \frac{\partial ...
0
votes
0answers
24 views

How to interpret two distinguishable particles with N possible states?

NOTE: Please do not provide an answer to the questions. If I am incorrect, please explain why, and if I am correct, please try to further my understanding. I think that this is a constructive way to ...
0
votes
0answers
42 views

Calculation of charged sphere distribution near a wall in Cartesian coordinates

I am following a similar derivation as found in the beginning of this paper "Quantitative aspects of the growth of (charged) silica spheres" by A.P. Philipse. This paper calculates the growth of a ...
3
votes
0answers
95 views

Understanding various types of motion

In classical statistical mechanics, given a system of particles, one often goes about classifying various dynamics (or types of motion) the system may exhibit on different time scales, but studying ...
4
votes
1answer
66 views

A seemingly paradox for Eigenstate Thermalization Hypothesis (ETH)

ETH states that for a system, all of its eigenstates thermalize. To be more specific, consider an energy eigenstate of the full system $H|n\rangle=E_n|n\rangle$. If the full system is in this ...
0
votes
0answers
32 views

Is the equipartition theorem derivable from more basic principles [duplicate]

Is the equipartition theorem really a theorem and derivable from more basic assumptions or is it just a hypothesis. Some of the ways energy is partition is not to squared quantum numbers (e.g. ...
1
vote
1answer
32 views

What is the word describing the pairs: temperature and energy, chemical potential and particle number?

I keep forgetting the word describing the pairs of coupled quantities in stat. mech. e.g. inverse temperature $\beta$ and internal energy $E$ or chemical potential $\mu$ and particle number $N$. I ...
0
votes
0answers
47 views

Connection between statistical and quantum mechanics

I am aware of Gibbs measures, given the energy (Hamiltonian) of an arrangement, one can determine the frequency of the arrangement. Plug the energy level in the Boltzman equation and there you go. I ...
3
votes
1answer
55 views

Is the principle of indifference enough to derive the microcanonical ensemble?

The microcanonical ensemble is usual motivated solely by the principle of indifference. Textbooks usually say something along the lines of "If the only thing we know about a system is its total ...
0
votes
0answers
20 views

Gradient effects in continuum mechanics

What I have learned is that inhomogenous materials (materials with different material properties over space and time) can be treated by the homogenization technique ...
-1
votes
0answers
26 views

Why does the Stefan-Boltzmann law work for power absorbed?

The setup is as follows: There is a body of emissivity $e$ and surface temperature $T$ whose surroundings have a temperature $T_s$ and may be assumed to be a black body. The body radiates at a ...
0
votes
1answer
40 views

Conservation of energy and realm of possibility

The law of conservation of energy states that energy cannot be created or destroyed. Based on this principle, you can safely conclude that any effect resulting from a cause must somehow keep all ...
2
votes
1answer
65 views

Hamiltonian or free energy corresponding to 2+1D Kuramoto-Sivashinsky model

I am trying to understand if the deterministic 2+1D Kuramoto-Sivashinsky equation $$ \partial_t h = -\nu \nabla^2 h - K \nabla^4 h + \frac{\lambda}{2} (\nabla h)^2, $$ where $\nu$, $K$, $\lambda$ ...
1
vote
0answers
39 views

Intuition on Gibbs measures

I am (roughly) aware of the way Gibbs measures are used to solve physical systems (e.g. the Ising model). We can basically boil it down to pinpointing a Hamiltonian. My question is, consider a ...
0
votes
0answers
16 views

Application of the Mean Field Approximation for molecules

When I studied the Ising Model in a course on Statistical Physics one approach that was presented was to use the Mean Field Approximation. In the ocasion I've noticed that it is also called "molecular ...
3
votes
1answer
130 views

Why don't we observe spontaneous symmetry restoration in nature?

Why do we always observe spontaneous symmetry breaking in nature and not restoration? Does there exist some argument with the 2nd law of thermodynamics and the entropy of the universe increasing? If ...
1
vote
0answers
31 views

Statistical mechanics - average particle energy, average kinetic energy

I'm looking at derivations for average particle energy giving $E=kT$: http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/bolapp.html And average particle kinetic energy giving $K_E=\dfrac{3}{2}kT$: ...
1
vote
0answers
44 views

Deriving the correlation function of a system interacting with a bath of harmonic oscillators

I'm working on the book Quantum Effects in Biology by Mohesni et all. My question is however not biology related, it is about a section on quantum master equations in the weak system-bath coupling ...
1
vote
0answers
92 views

How to derive equation for time it takes photons to diffuse through the Sun

I am wanting to use the Rosseland radiative heat flux equation to find the time it takes for photons to diffuse through the sun. The answer I am wanting to derive is: $$\tau_D~\frac{\rho \bar C_p ...
3
votes
0answers
41 views

Manking sense of an entropy equal $k_B\frac{1}{2}\ln(2)$

In problems of impurities coupled with electrons in a conduction band, like the Kondo model, is common to represent the entropy contributed by the impurity, in terms of bits, i.e. in units of ...
5
votes
4answers
386 views

Why is entropy an extensive quantity?

If we have two identical isolated macroscopic systems both with energy $E$. The number of accessible states of each of them is $\Omega(E)$ and hence the entropy is $\ln\Omega(E)$. Now if we put them ...
2
votes
0answers
38 views

Decimation of a triangular lattice [closed]

Consider the network of spins shown below. The Hamiltonian is given by $$H = - \sum_{\langle i j k \rangle} [J \sigma_i \sigma_j \sigma_k + J_0]$$ with $J,J_o \geq 0$ and $\langle i j k \rangle$ ...
1
vote
0answers
30 views

What is melting / boiling from the statistical viewpoint?

Microscopically, solids are usually described as "completely ordered" and "strongly bound", liquids "somewhat ordered", and gases "unbound" and "disordered". Thermodynamics predicts that the ...
4
votes
0answers
48 views

How can we show that the BBGKY hierarchy is time symmetric?

I am trying to mathematically show that the BBGKY hierarchy for s particles is time symmetric by setting $t\rightarrow -t$. Using the Wikipedia notation for the s-particle we have $\frac{\partial ...
0
votes
0answers
37 views

How to deduce the modified Flory-Huggins equation in this form?

In the paper of "Solution Properties of Poly(N-isopropylacrylamide)" (M. Heskins and J. E. Guillet, Journal of Macromolecular Science: Part A - Chemistry, Vol. 2, Issue 8, pages 1441-1455, 1968), they ...
0
votes
1answer
36 views

Voltage homogeneity across cell membrane

During respiration, individual cells produce a relatively large potential difference ($\sim 100$ mV) between the inside and outside, using energy to pump $H^+$ out of the cell to the liquid ...
0
votes
1answer
35 views

Derivation for the most probable macrostate for distinguishable particles using lagrange's method of undetermined multipliers

We have an expression for $\Omega$ (occupation of each macrostate) in terms of $n_i$ (occupation numbers) . We want to find the $n_i$ which maximises $\Omega$. We now that ...
4
votes
0answers
58 views

Interpreting the Fourier transform of a Gibbs measure

Recall that a Gibbs measure gives a probability distribution on states $x$ of the form $$ p_X(x) = \frac{1}{Z(\beta)}\exp(-\beta E(x)) $$ As I understand, the function $E$ is interpreted as the ...
0
votes
0answers
25 views

What does 'fully excited' actually mean?

In statistical mechanics you often hear the phrases such as 'when the degrees of freedom are fully excited then....'. An example would be the validity of the equipartition theorem. But what is the ...
-1
votes
1answer
56 views

Cross-differentiation to derive the maxwell relation $\left(\frac{\partial T}{\partial V}\right)_S = -\left(\frac{\partial P}{\partial S}\right)_V$ [closed]

How can I use $T=\left(\frac{\partial E}{\partial S}\right)_V$ and $P=-\left(\frac{\partial E}{\partial V}\right)_S$ to derive $$\left(\frac{\partial T}{\partial V}\right)_S = -\left(\frac{\partial ...
3
votes
1answer
99 views

Quantum field theory: zero vs. finite temperature

I have recently been made aware of the concept of thermal field theory, in which the introductory statement for its motivation is that "ordinary" quantum field theory (QFT) is formulated at zero ...
0
votes
1answer
34 views

Microcanonical ensemble: imanation for $N$ particles

Q: Consider an isolated system of $N$ non-interacting spins or magnetic dipoles with magnetic moment $\vec{\mu}=\mu_{z}\hat{z}$ and spin S=$1$, so we have $m_{z}=(-1,0,1)\hat{z}$, in a magnetic ...
1
vote
1answer
73 views

Statistical Physics: How do we derive this equation?

I'm reading through Statistical Physics by F. Mandl and there is a step in arriving at an equation that I don't follow. He uses $$P = \sum_r p_r \left(-\frac{\mathrm dE_r}{\mathrm dV} \right) ...
1
vote
2answers
33 views

Inverting density in favour of fugacity

In these notes on pages 80 and 81 the following step was used The density in terms of fugacity is $$ \frac{N}{V} = \frac{z}{\lambda^3}\left ( 1+ \frac{z}{2 \sqrt{2}} + \ldots \right ) $$ and this ...
5
votes
0answers
39 views

Is there any useful sense in which entropy fluctuates?

One of the classic distinctions between young Boltzmann and old Boltzmann was his view on entropy. Young Boltzmann had his H-theorem where a mechanical quantity H was supposed to represent entropy. ...
0
votes
0answers
14 views

Counting the accesible microestates compatible with the macrostate conditions

Let be a system consisting of $N$ magnetic dipoles with magnetic dipole $\vec{\mu}$ in a magnetic field $\vec{B}$. I want to count the micro states accessible to the macro estate defined by $E=-\mu B$ ...
0
votes
1answer
48 views

What happens to Boson and Fermi gases at very low temperature?

At low temperatures Fermi gases pile up to the state with the Fermi-energy having one particle in each state and Boson gases form Bose-Einstein condensates. However, the only derivations I have seen ...
0
votes
0answers
22 views

Phase diagram binary mixture

The Gibbs Phase Rule states: F = C - P + 2. From this it is possible to construct a phase diagram. In case of a 1-component system C=1 and where P denotes the number of phases in equilibrium. In case ...
5
votes
0answers
39 views

Violations of Onsager reciprocity?

As far as I understand it, the modern statement of Onsager reciprocity is that the linear-response transport coefficient matrix, when transposed, is equal to that of the time-reversed system (reversed ...
1
vote
1answer
37 views

Physical reason why Prandtl number is order unity for gases?

Is there a physical reason behind the fact that for gases the thermal diffusivity is on the same order of magnitude as kinematic viscosity (and as such a Prandtl number of order unity) and if so what ...
0
votes
1answer
39 views

Conceptual problem on Maxwell's velocity distribution law

I already read about Maxwell's velocity distribution law for gas molecule. And the expression for that distribution is following dnc=4πnA^3e^(-bc^2)c^2dc Now if we assume that the molecules have no ...
1
vote
1answer
49 views

Statistical Mechanics: Computing a system's microstate multiplicity

I have a general question concerning how to compute the microstate multiplicity of a system, in my lecture notes, for a system of $N$ weakly coupled oscillator and $Q$ energy quantas, the multiplicity ...
2
votes
1answer
52 views

Why does this formula for the partition function not include the multiplicity?

I am having problems understanding the formulas used for describing the partition functions and the probability distributions for canonical ensembles. In the first case I have two formulas for the ...
0
votes
0answers
24 views

Linear thermal expansion from statistical mechanics?

I came across a question recently regarding work done by an expanding metal and the origin of the energy used for the work, and most of the responses pointed the person to look more at the enthalpy ...
0
votes
0answers
24 views

Microscopic Definition of Heat and Work

If I am given a statistical System, then I can define state-variables like Energy, Entropy or other Observables, and then I can (at least for equilibrium states) give the Change of Energy as: ...
2
votes
0answers
20 views

Constancy of Coefficients of Additive Integrals Throughout Subsystems of a Closed System

I'm studying Landau and Lifshitz's Statistical Physics, Part 1, 3rd edition and am looking for clarification on the following statement, which appears on page 11 in the section on The Significance of ...