What is Statistical physics: Definition and 145 Discussions

Statistical physics is a branch of physics that evolved from a foundation of statistical mechanics, which uses methods of probability theory and statistics, and particularly the mathematical tools for dealing with large populations and approximations, in solving physical problems. It can describe a wide variety of fields with an inherently stochastic nature. Its applications include many problems in the fields of physics, biology, chemistry, neuroscience. Its main purpose is to clarify the properties of matter in aggregate, in terms of physical laws governing atomic motion.Statistical mechanics develops the phenomenological results of thermodynamics from a probabilistic examination of the underlying microscopic systems. Historically, one of the first topics in physics where statistical methods were applied was the field of classical mechanics, which is concerned with the motion of particles or objects when subjected to a force.

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  1. S

    Learning Statistical physics, which book?

    Hello everybody, I am a graduate physics student. I am trying to learn statistical physics and I have extreme difficulty in learning it. I do not find good books and don't get the ideas behind the concepts. the books I consulted where the Greiner, Kittel and Fliessbach. Books used in German...
  2. J

    Quantum Mechanics- statistical physics fermi-dirac distribution.

    Homework Statement Consider a free-electron gas at a temperature T such that kT << E_f Write down the expression for the electron number desnity N/V for electrons that have an energy in excess of of E_f. Show by making the change of variables (E-E_f)/kT = x. that the number desnity is...
  3. E

    Studying Where is good for studying statistical physics?

    Maybe this is the first post I enroll.(I wanted to change my id because I am not expert actually but I don't know how to change my id.) Anyway the main points of this post are as follows: Hello, I am an undergraduate student in Asia. Soon I have to apply for graduate, but I have no idea. I...
  4. S

    Use of quantum ideas in classical statistical physics

    When we study a classical system of distinguishable particles, we use parameters \epsilon_{j} for the energy states and n_{j} for the number of particles in \epsilon_{j}. But clearly, the energy states are not discrete in classical systems. Surely, this is nonsensical. Why are we doing this then?
  5. Q

    Quantum Thermo statistical physics

    Homework Statement rotational energy of diatomic gas (note : h = hbar) Er = h2/2I * r(r+1) , r = 0,1,2 ... it is (2r+1) fold degenerate find the partition function and hence the heat capacity at low temperatures. The Attempt at a Solution Z = ∑ g(Er) e-BEr = ∑ (2r+1) e-Bh2/2I *...
  6. S

    A question in statistical physics

    1. A gas molecules of mass m are in thermodynamic equilibrium at a temperature T. If v_{x},v_{y},v_{z} are the components of velocity v, then the mean value of (v_{x}-{\alpha} {v_{y}}+{\beta} {v_{z}})^2 is: a.(1+\alpha^2+\beta^2)\frac{k_{b}T}{m} b.(1-\alpha^2+\beta^2)\frac{k_{b}T}{m}...
  7. J

    How Does Temperature Influence Magnetic Alignment in Spin-1/2 Particles?

    Homework Statement Consider a system of N non-interacting distinguishable particles spin half particles each of which has magnetic moment u and the system is at an equilibrium temperature T in a magnetic field B such that n particles have their magnetic moments aligned parallel to B. Find the...
  8. S

    How Does Temperature Affect Particle Distribution in Two-State Systems?

    Homework Statement Consider a system of N particles, with two available energy states, 0 and E. What is the ratio of particles occupying the first state, n0, to particles occupying the second state n1?Homework Equations single particle partition function Z=\Sigmaexp(-ei/kt) system partition...
  9. S

    The single particle density of states (Statistical physics)

    Homework Statement I'm having a little bit of trouble getting started with this problem. Can I get a little help? Using: (number of states in the six-dimensional region d^{3}x d^{3}3p) = (d^{3}x d^{3}p)/h^{3} Which provides a convenient route to the single-particle density of masses. a)...
  10. H

    Partition function in Statistical Physics

    Hi! I am for the moment reading a course in statistical physics where the author has definied not less then three diffrent partitionfunctions. W, Z an Z which are called the microcanonical partitionfunction, canonical partitionfunction (?) and the grand canonical partitionfunction. I...
  11. H

    Statistical Physics: Solving Homework on Ideal Gas Heat Transfer

    Homework Statement For an ideal gas PV = nRT, n is the number of moles. Show that the heat transfer in an infinitesimal quasistatic process of an ideal gas can be written as: dQ = 1/nR ( C_v * V * dP + C_p * p * dV) Homework Equations First law of thermodynamics: dQ = dE + pdv (dE /...
  12. O

    Statistical physics at constant temp

    Homework Statement A system of 32 spin-½ dipoles (each of moment μ) is held at a constant temperature in an external magnetic field, where on average, 20 dipoles are aligned with the magnetic field of strength B. a) What is the temperature, in terms of given parameters? b) What is the...
  13. X

    Statistical physics - average potential energy and gravity field

    Please help me solve this problem: Homework Statement http://img688.imageshack.us/img688/8140/86617607.jpg The attempt at a solution http://img63.imageshack.us/img63/9531/79093945.jpg This is my whole procedure...
  14. I

    Statistical Physics Homework: Compare Arbitrary & Boltzmann Distributions

    Homework Statement Consider a thermal system at temperature T where the probability of finding the system in a microstate r with energy Er is given by an arbitrary probability distribution pr that is normalised so that Sum(pr) = 1. Let kB denote Boltzmann’s constant and consider the Boltzmann...
  15. C

    How do you get good at statistical physics?

    Hello there, I'm a second year physics student who like most, has exams around the start of the next year and as such, have started revising for my exams. The term has introduced new physics I wasn't initially familiar with such as Quantum mechanics and advanced differential calculus. Another...
  16. L

    Statistical Physics Books: Reif, Kittel & More

    Hi there, I'm searching for a good book for statistical physics. Professor as told us that the bibliography was Reif or Kittel (thermal physics) However, both are a little bit old, and some not very formal. I'm wondering if something more formal, more recent, with more or less the same...
  17. T

    On equivalence of QFT and Quantum Statistical Physics

    Does fact that QFT in imaginary time is equivalent to QSP represents the proof that many-particle quantum physics is equivalent to quantum theory of fields? To elaborate a little, I had some discussion with some engineers, and when I was explaining them Standard Model I had to invoke concepts...
  18. L

    Statistical Physics - counting states

    1. Homework Statement [/b] There are N 3-dimensional quantum harmonic oscillators, so the energy for each one is: E_i = \hbar \omega (\frac{1}{2} + n_x^i + n_y^i + n_z^i). What is the total number of states from energy E_0 to E, and what is the density of states for E? The Attempt at a...
  19. G

    How Does Adding Energy Affect Entropy in Harmonic Oscillators?

    Homework Statement Consider a system of 8 one-dimensionaly harmonic oscillators. Initially this system has 3 quanta of energy. Byhow much does the entropy change if you add one more quanta of energy? Homework Equations S=k*ln(omega) omega=(q+N-1)!/(q!*(N-1)!) The Attempt at a Solution...
  20. F

    How Do Gases Reach Equilibrium in Partitioned Containers?

    Homework Statement A box is separated by a partition which divides its volume in the ratio 3:1. The larger portion of the box contains 1000 molecules of Neon gas, the smaller one contains 100 molecules of He gas. A small hole is made in the partition, and one waits until equilibrium is...
  21. V

    Bosons and statistical physics

    Hello, I am stuck on the first part of this question. There are several parts that follow that depend on this bit, and I know I can do them if I can just work this out. Any help would be gratefully received. Homework Statement Consider an isolated system of N identical spin-0 bosons...
  22. N

    Statistical Physics: Partition function and fermions

    Homework Statement Hi all. The partition function for fermions is (according to Wikipedia: http://en.wikipedia.org/wiki/Partition_function_(statistical_mechanics)#Relation_to_thermodynamic_variables_2) given by: Z = \prod\limits_i {\left( {1 + \exp \left[ { - \beta \left( {\varepsilon _i -...
  23. N

    Video Lectures on Statistical Physics and Quantum Physics

    is there any video lectures source which is about statistical physics or quantum physics like MIT Lectures. I found some lectures about quantum physics but these are only related with it and it couldn't be considered as essential source.
  24. C

    How Does the Distribution of Heads in Coin Flipping Change with Large N?

    Homework Statement Flip N fair coins. The distribution for different numbers of heads and tails should be peaked at N/2. When N is very large, the peak will be very high. Let x = N(head)-N/2, required to find an expression for this distribution near the peak, i.e. x<<N. Homework Equations...
  25. Cincinnatus

    Learning Statistical Physics for Beginners with Maths Background

    I've recently gotten interested in statistical physics. Notions derived from this area are frequently applied in learning theory and other areas of biology which are of interest to me. I'm wondering if anyone knows of a good book or web resource for learning about statistical physics that...
  26. M

    Statistical Physics: Solving Exam Questions and Using External Resources

    Almost no one has answered.To take some external help, i write all questions here, maybe someone have an answer. 1)An aluminium cube cooled down to 90 Kelvin.At this point there is too many microstates available.how much heat we need, to increase these microstates in factor of 10^{10} ...
  27. E

    Statistical Physics: Solving C_P & Problem 4

    [SOLVED] statistical physics Homework Statement http://ocw.mit.edu/NR/rdonlyres/Physics/8-044Spring-2004/85482B93-6A5E-4E2F-ABD2-E34AC245396C/0/ps5.pdf I am working on number 3 part a. I am trying to calculate C_P. From the first law of thermodynamics: dQ = dU -dW = dU +PdV (does anyone...
  28. E

    Solving Problem 3 in MIT's Statistical Physics Course

    [SOLVED] statistical physics Homework Statement http://ocw.mit.edu/NR/rdonlyres/Physics/8-044Spring-2004/AC9B128C-9358-4177-BFE6-A142E0FD897B/0/ps4.pdf I am working on Problem 3. So I want to calculate the integral of dW along each of those paths. But how can I relate dW to dV? dW is equal...
  29. J

    Statistical Physics: Pressure Diff. in Moving Cylinder

    Homework Statement A spaceship that is cylindrical of area A and Length L decelerates at a constant rate a. The air treated. What is the difference in pressure due to the motion from the front to the back of the ship. The acceleration is parallel to L and air was in thermal...
  30. Z

    Statistical Physics: Paramagnetic Solid with Spin S=1 and Magnetic Momentum µ_B

    I have a paramagnatic solid, where the atoms have a spin S=1 , and a magnetic momentum \mu_{B} We have a magnetic field: \vec{B} Under the influence of B the atoms can take 3 value of energy e,-e,0 e=g.\mu_{B}.B The solid is maintained at a Temperature T and N number of atoms. The question are...
  31. L

    Statistical Physics Homework: Neutrinos in Thermal Equilibrium

    Homework Statement The result n_{0 \gamma} = \left( \frac{k_BT_{0r}}{hc} \right)^3 \int_0^{\infty} \frac{8 \pi x^2 dx}{e^x-1} = 2 \frac{\zeta(3)}{\pi^2} \left( \frac{k_BT_{0r}}{hc} \right)^3 is obtained for photons by integrating over the Planck distribution appropriate for bosons. In...
  32. X

    Bariometric formula in Statistical Physics (particle density per unit volume)

    Hi there. In my homework, I had to calculate the variation of the pressure with the altitude for a classical gas. I know that I should calculate the density of particles per volume element. I found this pdf on the net (http://cannoli.mps.ohio-state.edu/phy847/phy847-p2.pdf) . If you see...
  33. K

    O Physics: Finding Heat Capacity and Entropy Change in Thermal Processes

    Hi I'm having a bit of trouble with 2 homework questions. Firstly, I need to show that (Heat Capacity/Specific Heat) = 1+2f using the fact that Cp= (1+f/2)Nk and Cv= (f/2)Nk I've tried to work this out by cross multiplying these, but I don't think I'm doing the maths right...
  34. B

    Meaning of formula from statistical physics

    Hi. Can anyone explain the meaning of this formula from statistical physics to me: S = -k\sum_r{p_r\ln p_r} Ok, I know that S is the entropy, the p's are probabilities of some sort - but somehow this is not satisfactory :-)
  35. B

    Statistical Physics: Problem 9 - A Spin Model

    Hi. I'm having trouble with this statistical physics thing again. I am given this exercise: Problem 9 – A spin model In a solid at temperature T the atoms have spin 1 so that the m quantum number takes on the values m = 0, ±1. Due to an interaction with the electrostatic field in the...
  36. S

    Books: Advanced Statistical Physics Books for Understanding Concepts

    Hi. I need some useful and conceptual book in advanced statistical physics. I can understand the mathematics in some famous book such as Pathria, but I have trouble understanding some concepts in that area. Any suggestion?! Thanks in advance. Somy
  37. B

    Heat capacity (statistical physics)

    Hi. I've just started a course on statistical physics and the first assignment is this: A system possesses 3 energy levels, E_1 = \epsilon, E_2 = 2\epsilon and E_3 = 3\epsilon. The degeneracy of the levels are g(E1) = g(E3) = 1, g(E2) = 2. Find the heat capacity of the system. I've...
  38. E

    Solving Statistical Physics Equations of Motion for N-Particle Systems

    Let be an statistical system of N particles with their Hamiltonian.. H=\sum_{i=0}^{N}\frac{p_{i}^{2}}{2m}+V(q1,q2,...,qN) then you could obtain their equations of motion in the form: dp_{i}/dt=-dH/dp_{i} and dq_{i}/dt=p_{i}/m but of course if N is big you could take years and...
  39. J

    Thermal equilibrium in statistical physics

    I am mixed up about thermal equilibrium in statistical physics. And I hope you excuse me if I use unconventional words, I am from Sweden, my book is in german and I try to express myself in english. In my book (Noltings "Grundkurs theoretische Physik, Band 6") thermal equilibrium is defined...
  40. E

    Chemical potential (statistical physics)

    Hi all, I have a question about the chemical potential \mu from statistical physics: Why is the chemical potential \mu for a photon gas (or phonon gas) zero? Thanks in advance Edgardo
  41. P

    Calculating Entropy of 2D Free Particles: Statistical Physics Challenge

    Hi all. So something's bothering me; Given the def. S=-k(sum on r: pr*ln(pr)) for the entropy, find the entropy of N>>1 free particles moving in a 2d box with energy E. Now, don't I have a continuum of states here? How do I do that? Thanks :smile:
  42. N

    Statistical Physics question

    According to QM, a diatomic gas molecule possesses rotational energy levels given by En = (1/2I)(h^2)n(n + 1). h is meant to be h-bar, Planck's constant over 2π here and I = moment of inertia. Energy level n has a degeneracy of 2n + 1. Find the partition function of the rotational motion of a...
  43. N

    How Do You Calculate Microstates for a Constrained Spin System?

    Consider 2 systems of spin 1/2 paramagnets, which may point either up or down wrt a magnetic field. The first system contains 8 paramagnets and the second contains 6 paramagnets. Suppose the energy of the combined system is constrained such that the total number of spins pointing up in the 2...
  44. R

    Questions on Statistical Physics

    Hi everyone, I have two questions from my latest homework set that are driving me nuts, so here goes: 1) "Recalling that the Fermi-Dirac distribution function applies to all fermions, including protons and neutrons, each of which have spin 1/2, consider a nucleus of 22Ne consisting of 10...
  45. T

    Statistical Physics: Discovering Condensed Matter & Solid State

    Lately I've been reading a lot of statistical physics and I really enjoy it. I was curious what sorts of physics more study in this area would lead me to. Condensded matter? Solid state?
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