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.

View More On Wikipedia.org
Recent contents Top users
  1. S

    A Relations between statistical physics and theoretical CS

    Hi everyone. I wasn't sure where to post this thread, so I figured I'll post this under General Physics. Out of interest, I've been perusing online about connections that exist between statistical physics and theoretical computer science. For example, consider the following report by Pietro...
  2. bananabandana

    Are the Gibbs and Boltzmann forms of Entropy equivalent?

    Homework Statement Are the Gibbs and Boltzmann entropies always equivalent? Homework Equations $$ S=k_{B}ln\Omega $$ [Boltzmann entropy, where ##\Omega## is the number of available microstates $$ S=-k_{B}\sum_{i}p_{i} ln(p_{i}) $$ [Gibbs entropy, where ##p_{i}## is the probability of a...
  3. 1

    I Why do we calculate the density of states using k-space?

    In statistical physics the calculation to obtain the density of states function seems to involve an integral over an eighth of a sphere in k-space. But why do we bother moving from n-space to k-space, if there's a linear relation between n and k i.e. n = (L/π)k ? Why don't we just integrate over...
  4. amjad-sh

    I Partition Function: 2 Approaches & Questions Answered

    I was reading about partition function. I noticed that there are two approaches toward partition function. The first approach: Suppose we are dealing with a closed system where the system is composed of heat bath (R) and inside it there is a very small system (E), the two systems are in thermal...
  5. bananabandana

    I Energy levels generally invariant under fixed V, changing T

    Why is is true that for a given system, if I fix the volume and increase the temperature, you'd expect the occupancy of the energy levels to change, but not the levels themselves? Can I think of this in terms of the fact that the boundary conditions for the solution of the TISE are fixed, such...
  6. L

    Statistical physics. Density matrix

    Homework Statement A system is subject to Hamiltonian ##\hat{H}=-\gamma B_z \hat{S}_z##. Write down the density matrix.[/B]Homework Equations For canonical ensemble ##\hat{\rho}=\frac{1}{Tr(e^{-\beta \hat{H}})}e^{-\beta \hat{H}}## In general ##\rho=\sum_m |\psi_m\rangle \langle \psi_m|## The...
  7. S

    Estimate vibrational frequency of N2 molecule

    Homework Statement Experimental data for the heat capacity of N2 as a function of temperature are provided. Estimate the frequency of vibration of the N2 molecule. Homework Equations Energy of harmonic oscillator = (n+1/2)ħω C=7/2kB Average molecular energy = C*T But this is an expression...
  8. L

    Other Research topics in Statistical Physics

    Currently I'm in the last year of the Physics course and I've been thinking about working in a project of undergraduate research, specifically in Statistical Physics. Two years ago I've already done a project like that in Fluid Mechanics combined with Gauge Theories and in that project I've...
  9. K

    Average height of molecules in a box as a function of temperature

    Homework Statement A circular cylinder of height H is filled with monatomic gas molecules at temperature T. The cylinder stands on the surface of the Earth so that the gas molecules are subject to the gravitational field g. (a) Find the average height, z , of the molecules in the cylinder as...
  10. A

    Statistical Physics Textbook: F Mandl or Other Suggestions

    Anyone know where i can get statistical physics by F Mandl? or can recommend any other textbook for a course in statistical mechanics.
  11. rolotomassi

    Statistical physics for system of dipoles

    There is a project I'm working on to model the phase transition of 2 polymers with and without an external E-field. The approach I am taking is first to consider 2 types of dipoles, with a constant external field in the 'up' direction. I'm thinking in two dimensions for now. The dipoles can...
  12. V

    Maxwell distribution of relative velocities

    I want to calculate the distribution function for the relative velocity v_r = v_1 - v_2 of two particles. Each particle velocity follows the Maxwell distribution for velocities. They have the same mass and temperature. Can I just multiplicate the Maxwell distributions of the two particles (and...
  13. C

    Potts Model in statistical physics

    Homework Statement The 3 state Potts model is defined by $$-\beta \mathcal H = J \sum_{r,r'} (3 \delta_{\sigma(r), \sigma(r')} - 1) + h\sum_r \delta_{\sigma(r),1},$$ with J > 0 to encourage neighbouring Potts spins to have same value and h orienting field. The spin like variables can take...
  14. R

    Statistical Physics: Proving "if p(a)=p(b)=p then p(ab) ≤ p^2

    How to prove this "if p(a)=p(b)=p then p(ab) ≤ p^2Homework EquationsThe Attempt at a Solution
  15. Gvido_Anselmi

    Statistical physics and unfounded arguments

    Hello everybody. I've recently finished work through Weinberg's course in QFT which made my understanding of theoretical physics quite peculiar. For example, I can't understand statistical physics from Landau&Lifshitz book at all as there are a lot of unfounded arguments. I wonder firstly is it...
  16. rolotomassi

    Statistical physics: Landau theory liquid crystal (2D)

    Homework Statement A simple model for liquid crystals confined to 2 dimensions is o assume each molecule can only align in one of 2 perpendicular directions. To construct a landau model its convenient to define order parameter, s : s = 2 ( Np - 0.5Nt ) / Nt Np - number molecules...
  17. M

    Intro Physics Thermodynamics and Statistical Physics book

    Hey guys, I've never studied this subject before (except basic thermal physics in high school), and I have a course on it this semester. I'm in a semi international program, and this course isn't taught in English (but the tutorials are, thankfully), so I will need to study on my own. In...
  18. Matt atkinson

    Statistical Physics: Cubic lattice of two molecules

    Homework Statement A mixture of two substances exists on a cubic lattice of N sites, each of which is occupied by either an A molecule or a B molecule. The number of A molecules is NA and the number of B molecules is NB, such that NA + NB = N. The energy of interaction is k_BT\chi_{AA} between...
  19. C

    Work and isothermal compressibility

    Homework Statement 1 kg of water is at room temperature and the pressure is isothermally increased on the system from 1 atmosphere to 1000 atmospheres. What is the work done? What is the change in heat? What would be the temperature change if this was done adiabatically? The volumetric...
  20. O

    Simulating dark matter by assuming stable solution

    Hey, I've a short question. Is there any research attempting to constrain models of dark matter by assuming stable solution for the universe? I'm interested in knowing whether this gives any sensible constraints on the dark matter models. I'm still fairly new to studying dark matter but as I...
  21. M

    From classical statistical physics to quantum physics

    Hello, This is more a question about history of science in general. During my lectures on statistical physics, I noticed that some of the problems that Bolztmann faced lead to the introduction of: ##h/2\pi## (to introduce the unit of an action leading to a "unitless" partition function) which...
  22. A

    Prerequisites for Statistical Physics

    I am planning to take a course on Statistical Physics in my university. The main text to be followed is Statistical Physics by F. Reif. As of now, I have completed university level courses on Calculus, Differential Equations, Linear Algebra. What other knowledge would be required to help me get...
  23. U

    What Does R(n) Represent in a One-Dimensional Chain Model?

    Homework Statement Consider a chain with N >> 1 segments of length 1. One end of the chain is at the origin, the other at a point R. In this onedimensional model the segments may face left or right. The number of segments facing right is n. 1: What is the number of possible configurations in...
  24. B

    Looking for best reference in statistical physics

    Hi, I am looking for a reference book in statistical physics which comprising any possible aspect of statistical physics. Can anybody help? Thank you
  25. P

    Equilibrium Statistical Physics, Plischke ex. 1.2

    Homework Statement See: attached imageHow do we get the final equation? I'm obviously missing out on something..
  26. V

    Statistical Physics vs QFT for quantum information processing

    Good day, I'm starting my master in physics, and it's time for me to choose my courses. I've decided that I probably want to pursue the direction of quantum information processing, and I'm trying to pick my courses with that in mind. For my first semester I'll be taking four courses: Quantum...
  27. M

    String theory and Statistical Physics

    When do these two fields of physics overlap other than when we discuss entropy of supersymmetric black holes? Does statistical mechanics or statistical physics support any aspect in string theory or vice verse? I have read some place that the string theory reduces to the standard model by doing...
  28. F

    [Statistical Physics] Microstates in a large system/Boltzmann entropy

    Homework Statement For a box containing 1m^{3} of nitrogen at S.T.P., estimate the number of microstates which make up the equilibrium macrostate. Homework Equations S = Nk_{b}(ln\frac{V}{N} + \frac{5}{2} + \frac{3}{2}ln\frac{2πmk_{b}T}{h^{2}}) where the entropy of a volume, V ...
  29. F

    [Statistical Physics] No. of dice rolls so prob of getting a 6 is >90%

    This question is really wearing me out, any ideas? Homework Statement How many times must I throw a fair dice in order to make the probability of getting at least one ‘6’ greater than 90%? With this many throws, what is the probability of getting three ‘6’s? It's the first part I'm...
  30. Matt atkinson

    Statistical Physics - blackbody radiation

    Homework Statement A cavity contains black body radiation at temperature at T=500K. Consider a optical mode in the cavity with frequency w=2.5x10^(13) Hz. Calculate; (a)the probability of finding 0 photons in the mode. (b)the probability of finding 1 photon in the mode (c)the mean number of...
  31. F

    [Statistical Physics] Probability of finding # photons in the mode

    Homework Statement A cavity contains black body radiation at temperature T = 500 K. Consider an optical mode in the cavity with frequency ω=2.5x10^{13} Hz. Calculate a) the probability of finding 0 photons in the mode b) the probability of finding 1 photon in the mode c) the mean number...
  32. S

    Statistical physics - average length of polymer

    Homework Statement A polymer consits of ##10^{20}## monomers, each 2 nm long. One end of the polymer is hanged at the ceiling on the other end, we have a load of ##4\cdot 10^{-10}g##. Calculate the average potential energy!Homework Equations The Attempt at a Solution Well... I don't know...
  33. T

    Books with examples and resolutions of Statistical Physics problems?

    Hi, I'm completely lost in this discipline. Does anyone know of a good book with solved exercises and some examples, particularly on the 3 types of ensembles (microcanonical, canonical and large canonical), quantum mechanics statistical physics, and fermions/bosons gases? Thank you.
  34. I

    Archived Statistical physics Q: macrostates

    Homework Statement There are 5 Bosonic particles N = 5 populating 2 degenerate energy levels E1 and E2 such that: E1 < E2, N2 ≤ N1 and the respective statistical weights are g1 = 3 and g2 = 2. . What are the possible macrostates of this system?The Attempt at a SolutionI'm not sure if the...
  35. P

    Statistical Physics Explained: What It Is, How It Works

    Could someone explain what this branch of physics encompasses? Is it just using statistics and probabilities to explain phenomena?
  36. L

    Understanding Statistical Physics: Exploring Micro and Macrostates

    Please help me, what are micro and macrostates, what are accessible states?
  37. D

    Statistical physics reflection principle

    Homework Statement Consider a random walker in one dimension, which can take right or left steps with equal probability. Assume that the walker starts at the location k>0 and there is an absorbing wall at point labelled as 0, that means if the walker reaches 0 the process stops and he stays...
  38. M

    Debye model in Statistical Physics

    Was Debye's basic idea for a solid body to neglect the dispersion Einstein talked about in his model?
  39. N

    Statistical Physics number of particles with spin 1/2 in a B-field

    Homework Statement Homework Equations The Attempt at a Solution To be honest I'm clueless. I've missed a large amount of the course and just struggling to find any sources that explain this. I don't want the answer to the question, I want to figure that out for myself. What I really need is...
  40. sunrah

    Significance of n-sphere in statistical physics

    Homework Statement Just trying to understand something my instructor said. For large n, the volume of the sphere exists in a thin shell at its surface. He asked us what relationship this has to statistical physics. Homework Equations The Attempt at a Solution The only thing I can...
  41. M

    Quantum Scale, Statistical Physics

    So the probabilistic studying of Quantum statistics of Böse-Einstein suggests that we permutate the number of objects (objects, are the blocks (Gi-1), and the particles in the boxes Ni) and divide those by Ni! And (Gi-1)! Because these particles are identical. But the case of Fermi-Dirac, where...
  42. Jalo

    Statistical Physics - average energy of a system.

    Homework Statement Imagine a system, in contact with a heat reservoir, with three particles. Each particle may be in a state of energy 0 or ε. What's the temperature of the reservoir such that the mean energy of the system, <E>, is 1.2ε? Homework Equations The Attempt at a...
  43. N

    Problem 5.15 of Statistical Physics by Reif ( Calculation of entropy)

    Homework Statement 1 kg of water with specific heat (C) of 4180 Joules /kg/degree is given at 0°C. It is taken to 100°C by two methods :- (i) by bringing it in contact with a reservoir at 100°C. (ii) by bringing it in contact with a reservoir at 50°C , and then with another reservoir at...
  44. R

    Book recommendations for Non-Equilibrium Statistical Physics

    Hello. I am currently working on my master's thesis in entropy production in non-equilibrium systems using stochastic methods. I am also working on boosting my understanding of statistical physics by studying many different textbooks on the subject, and on related subjects such as...
  45. E

    Statistical physics: counting states, entropy and temperature

    Hi everyone, I've hit a bit of a snag with part c of this problem (can't figure out how to invert a function T(ν)), so I'm starting to question whether I have the previous parts correct. Homework Statement Consider a system of N identical but distinguishable particles, each of which has a...
  46. J

    Pascal's law out of statistical physics

    Hi I wanted to get Pascal's law \Delta p= \rho g ( \Delta h) out of the context of statistical physics by the use of a partition function. I failed. Do you know how to solve this problem? Greetings
  47. P

    Statistical Physics: very large and very small numbers

    Working on statistical physics i came across this expression: p = (1/44)^(10^5) = 10^(-164345) However TI-83 calculator is unable to verify it (gives answer 0). Can someone tell me how to get from (1/44)^(10^5) to 10^(-164345) analytically?
  48. matt_crouch

    Fermions that can access 10 distinct energy states; Statistical Physics

    Homework Statement Consider a system made of 4 quantum fermions that can access 10 distinct states respectively with energies: En=n/10 eV with n=1,2,3,4,5,6,7,8,9,10 1) Write the expression for the entropy when the particles can access all states with equal probability 2) Compute...
  49. K

    Nernst effect and statistical physics

    I need document or ebook talk about Nernst effect in statistical physics. who know that say for me? Gmail: manhkien_bka@gmail.com
  50. T

    [Statistical Physics] Spin-1 atoms in uniform magnetic field

    Homework Statement A crystal contains N atoms which posses spin 1 and magnetic moment \mu. Placed in a uniform magnetic field B the atoms can orient themselves in three directions: parallel, perpendicular, and antiparallel to the field. If the crystal is in thermal equilibrium at temperature...
Back
Top