# 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. ### How much physics is needed for Bialek's Biophysics book?

Hello, I am originally a medical doctor and now doing a PhD in neuroscience. I have no formal physics / math training beyond high school level but I self-studied single variable and multivariable calculus as well as differential equations from MIT's OCW website, did examples, exams etc. I also...
2. ### Canonical partition function for two coupled oscillators

I got the hamiltonians for n1 and n2 as (n1+1/2)hw and (n2+1/2)hw. Since the an ensemble is made by N distinguishable pairs of quantum oscillators, the general canonical partition function for the system is 1/N!((sum(-BH(n1))sum(-BH(n2))), where B is the thermodynamic beta. I got to the step...
3. ### Is there a "critical temperature" for 2D Boson gas?

The density of states of a 2D gas in a box is g(E)=\frac{Am}{2\pi\hbar^2}\quad. From this we can obtain T=-\frac{2\pi\hbar^2N}{mAk_B\log (1-z)} Inserting z \to 1 gives T_c=0. We conclude that the 2D boson gas doesn't form BEC.However, on the other hand, according to the Bose-Einstein...
4. ### I Statistical ensemble in phase space

Hi, I've a question about the concept of ensemble is statistical physics. Take a conservative system in a given macrostate (e.g. with a given energy): there will be a number of phase space's microstates compatible with the given macrostate. If I understand it correctly, basically the...
5. ### A Energy hypersurface in a phase space (statistical physics)

what is the reason for that the energy hypersurfaces in a phase space, which belong to systems with constant energy are closed? ( see picture )
6. ### I Microstates of an atom in an energy state

I have a question about a sentence in the book Introduction to Thermal Physics (Daniel v. Schroeder). So in chapter 6, Schroeder talks about an atom isolated. This means its energy is fixed. The atom is in some state. The energy states of the atom have degenerated. All microstates with that...
7. ### A Definition of entropy for indistinguishable and distinguishable particles

I have a rather general question about the definition of entropy used in most textbooks: S = k ln Ω, where Ω is the number of available microstates. Boltzmann wrote W rather than Ω, and I believe this stood for probability (Wahrscheinlichkeit). Obviously this is not a number between 0 and 1, so...
8. ### I Problems involving combinatorics of lattice with certain symmetries

I was reading about numerical methods in statistical physics, and some examples got me thinking about what seems to be combinatorics, an area of math I hardly understand at all beyond the very basics. In particular, I was thinking about how one would go about directly summing the partition...
9. ### I Partition function of mixture of two gases

I have a question about statistical physics. Suppose we have a closed container with two compartments, each with volume V , in thermal contact with a heat bath at temperature T, and we discuss the problem from the perspective of a canonic ensemble. At a certain moment the separating wall is...
10. ### I The Equilibrium Macrostate: Reif's Statistical Physics

Reif, statistical physics "The equilibrium macrostate of a system can be completely specified by very few macroscopic parameters. For example, consider again the isolated gas of ##N## identical molecules in a box. Suppose that the volume of the box is ##V##, while the constant total energy of...
11. ### I Reading course in statistical physics

This is the beginning of an online reading course of the book "Statistical physics" by Reif, volume 5 in the Berkeley physics course, using PF. We'll start with chapter 3 and loop back to the initial 2 chapters if necessary. All questions should be specifically about what is written in the this...
12. ### Intro Physics Opinions on books for (self) studies in statistical physics

Nearly two decades after I graduated with an engineering degree, I'm currently studying for a master's with a particular emphasis on conceptual/theoretical statistical physics. Based on my interests and stylistic preferences, I'm using the following books to build my understanding of physical...
13. ### Statistical physics, using the ideas of Fermi Energies, etc. for a star

a) V=(4/3)pi(r^3) N=M/m_n (M=mass of neutron star, m_n=mass of neutron) Subbed into E_f = (hbar^2 / 2m) (3(pi^2)N / V)^(2/3). T_F = E_F / k_B b) dU = (dU/dS)_s dS + (dU/dV)_s dV p = -(dU/dV)_s dV V=(4/3)pi(r^3) -> r = cubedroot(3V/4pi) subbed into U_g = -(3/5)(G M^2 / r) take (dU/dV) plug into...
14. ### A Volume constraint in micro-canonical derivation of statistical physics

Another question about the use of the micro-canonical ensemble in deriving distributions. On the Wikipedia-page the authors mention that the total volume of the system has to be constant. See...
15. ### Interpretation of Net Peak Area in Gamma Spectroscopy

Hello, My question relates to gamma spectroscopy. I understand how the net peak area is calculated for any photopeak. Fortunately, gamma-spec software (e.g., Genie-2000 from Canberra) provides Net peak area and associated uncertainty (for Cs-137 661.7 keV peak, as an example). My question: are...
16. ### A Understanding an Approximation in Statistical Physics

In a book that I am reading it says $$(V - aw)(V - (N-a)w) \approx (V - Nw/2)^2$$ Where ##V## is the volume of the box, ##N## is the number of the particles and ##w## is the radius of the particle, where each particle is thought as hard spheres. for ##a = [1, N-1]## But I don't understand how...
17. ### Physics Non-equilibrium statistical physics and complex systems

Is Non-equilibrium statistical physics and complex systems a good area of study to go into? Is it a well respected field? Thank you
18. ### I Gibbs paradox: an urban legend in statistical physics

Hi, I recently discovered that there is no real paradox in the question of the mixing of classical distinguishble particles. I was shocked. Most books and all my professors suggest that an extensible entropy could not be defined for distinguishble particles. I believe that many of you will be...
19. ### Difficulty with Lagrange multipliers in Kardar's Statistical Physics book

Alright, so I did some progress and then I got stuck. After some time I went to check the solution. Up to some point, it's all well and good: I understand everything that is happening up to the point where he takes the partial derivative of S wrt ρ(Γ). I don't understand how he gets the...
20. ### A Statistical physics : Irreversibility

I was reading mehran kardar (books and lectures) it says the concept of irreversibility comes from an assumption (in which we increase the length scale by interaction disctance between two particles). So My question is the concept of irreversibility is still valid in the case of 1 particle...
21. ### Courses Statistical Physics vs QFT vs General relativity

Good day, I'm starting my master in physics, and it's time for me to choose my courses. I will take one or two of the following three courses, which are: Statistical Physics, QFT and General relativity. Now, I'm finding it very hard to decide as on the one hand, I'm interested in QFT and...
22. ### I Exploring Entropy in Intro to Statistical Physics by Huang

Hi, I am currently reading Introduction to statistical physics by Huang. In the section of entropy, it reads But what if I choose ##R-P## as a closed cycle? Then in a similar process, I should have ##\int_{R} \frac {dQ} {T} \leq \int_{P} \frac {dQ} {T}## and ##S \left ( B \right ) - S \left (...
23. ### Five State Quantum System, understanding the question

I’ve never worked with a quantum system with more that two states 1, -1, and I’ve just gotten this homework problem. I'm not sure what it means. Does this mean it has five states? Why are there two 0’s and two 1’s?
24. ### I How does the N signify the indistinguishability in the Gibbs Paradox?

Gibbs introduced the N! to then make S extensive. He then attributed the N! to the particles being indistinguishable. How does the N! signify the indistinguishability?
25. ### I Superposition of Phases: A Key Concept in Connecting QFT and Statistical Physics

Homework Statement: relation between qft and statistical physics Homework Equations: domains with equal values I read a french paper about Kenneth Wilson. i translate several sentences (with google): it was demonstrated in 1960 by Kenneth Wilson that renormalization formed an incongruous...
26. ### I Interpretations of QM vs. statistical physics as an "interpretation"?

Personally I tend to believe all (or almost all) of the interpretations of QM are unsatisfactory simply because they tell us something that we already know but do not tell us something we don't know. That is, they do not predict new phenomena or principles or properties of matter, etc. that can...
27. ### Does classical statistical physics predict newer things vs. thermodynamics?

I'm wondering if the passage from a classical thermodynamic theory, i.e. which does not resort to an atomistic theory and methods of probability and statistics, to classical (i.e. non-quantum) statistical mechanics, led to new discoveries and especially if it was able to explain properties of...
28. ### Solving Ising Spin 1 Model w/ Transfer Matrix Method

I did the first part using the transfer matrix method: $$Z = Tr(T^{N})$$ In this case, the transfer matrix will be $$T(i,i') = \begin{pmatrix} e^{\beta J} & 1 & e^{-\beta J}\\ 1 &1 &1 \\ e^{-\beta J} & 1 & e^{\beta J} \end{pmatrix}$$ To get the trace of $T^N$, you find the...
29. ### Schools Who are the Top Non-Equilibrium Research Groups in North America and Europe?

I realize the question is quite broad but what research groups working on statistical physics, stochastic processes, and complex systems are generally considered the best? Would like to know about Europe and America alike.
30. ### One-dimensional polymer (Statistical Physics)

Homework Statement Consider a polymer formed by connecting N disc-shaped molecules into a onedimensional chain. Each molecule can align either its long axis (of length ##l_1## and energy ##E_1##) or short axis (of length ##l_2## and energy ##E_2##). Suppose that the chain is subject to tension...
31. ### I Understanding Energy States in Complex Systems

I'm having trouble picturing the energy states for some systems. For instance, I was reading Reif's Fundamentals of Statistical and Thermal Physics, and at some point he talks about the energy states of a pool acting as a heat reservoir interacting with a bottle of wine. The problem is that...
32. ### Quantum Gases - Mixing of 3He and 4He

Homework Statement Consider a solution in which 99% of the atoms are 4He and 1% are 3He. Assuming that the 3He atoms behave as an ideal gas of spin-1/2 particles determine the Fermi energy of the 3He atoms. You may assume that one mole of 4He occupies a volume of 28 cm3.Homework Equations EF =...
33. ### Statistical physics and magnetization

Homework Statement Consider a system of three aligned spins with S=1/2. There are couplings between first neighbors. Each spin has a magnetic moment ## \vec{\mu} = s \mu \vec{S}##. The system is in a field ## H= H\vec{u_z}## at thermal equilibrium. The hamiltonian is: ##H=J[S(1)S(2)+S(2)S(3)]...
34. ### I Dimensional analysis involving partial derivatives

It is mentioned in Reif's book, statistical physics, that trough dimensional analysis it can be shown that: $$\frac{1}{\beta} = kT$$ where ##\beta## equals ##\frac{\partial \ln \Omega}{\partial E}## and k is the Boltzmann constant. I don't quite see how to reach this result, can anyone give me...
35. ### I Statistical Physics - Equilibrium

Good evening, I have a question to a short introduction to statistical mechanics in a book about molecular dynamics simulation. It introduces the fundamental assumption: Every microscopic state with a fix total energy E is equally probable. I attached the section. I understand it all, except...
36. ### Statistical physics question - particles in a magnetic field

Homework Statement [/B] I'm stuck on part (b) and (c) of the following question Homework Equations The Attempt at a Solution The partition function was ##Z_N = 2 cosh(μBβ)## where ##β = \frac {1}{kT}##. From there I used ##U = - \frac {∂}{∂β} ln (Z_n)## to get ##U = -NμB tanh( \frac...
37. ### Studying Learning the non-physics part of Statistical Mechanics

Hello, this is my first question on PhysicsForum. I am primarily interested in statistics/machine learning. I have recently discovered that many of the ideas used in machine learning came from statistical physics/ statistical mechanics. I am just wondering if it's a bad idea to attempt to learn...
38. ### A What happens when bosons become distinguishable?

Assuming a system of bosons at high density and low temperature so that they obey Bose-Einstein statistics. If one had a high resolution, ultrafast tomographic imaging system that would allow to track every particle in this system and therefore make the particles distinguishable, what would...
39. ### A Why is the partition for Fermions a sum of Boltzman factors?

The partition function should essentially be the sum of probabilities of being in various states, I believe. Why is it then the sum of Boltzmann factors even for fermions and bosons? I've never seen a good motivation for this in literature.
40. ### I Partition Function Derivation: Where Did I Go Wrong?

Self-repost from physics.SE; I underestimated how dead it was. So this follows Schroeder's Intro to Thermal Physics equations 6.1-6.7, but the question isn't book specific. Please let me be clear: I know for a fact I'm wrong. However, it feels like performing seemingly allowed manipulations, I...
41. ### Fermi temperature of a 1D electron gas

Homework Statement Consider a one-dimensional metal wire with one free electron per atom and an atomic spacing of ##d##. Calculate the Fermi temperature. Homework Equations Energy of a particle in a box of length ##L##: ##E_n = \frac{\pi^2 \hbar^2}{2 m L^2} n^2## 1D density of states...
42. ### I Density of States -- alternative derivation

I am trying to understand the derivation for the DOS, I get stuck when they introduce k-space. Why is it necessary to introduce k-space? Why is the DOS related to k-space? Perhaps if someone could come up to a slightly different derivation (any dimensions will do) that would help. My doubt ELI5...
43. ### Surprise? Entropy changes for systems in a canonical state

Every year since the 90's I come back to some of my pet topics in physics, like statistical physics. This time it was the reading of a Wikipedia article on entropy that surprised me. The derivation of the second law from the Gibbs entropy was unknown to me. I didn't know how heat, how change of...
44. ### I Why drop the vibrational ground state energy

This is from *Statistical Physics An Introductory Course* by *Daniel J.Amit* The text is calculating the energy of internal motions of a diatomic molecule. The internal energies of a diatomic molecule, i.e. the vibrational energy and the rotational energy is given by...
45. C

### Programs What is the best path to get into statistical physics?

Hello, I was just curious about what academic education is the best to get into statistical physics, and more specifically the statistical physics of optics and lasers. I have considered a few possibilities. Getting a PhD in statistics but take physics electives and most physics courses that...
46. A

### Statistical Physics: Quantum ideal gas

Homework Statement I'm reading the book about Statistical Physics from W. Nolting, specifically the chapter about quantum gas. In the case of a classical ideal gas, we can get the state functions with the partition functions of the three ensembles (microcanonical, canonical and grand...
47. ### A Longitudinal and transverse response function

I was reading the book "finite temperature field theory" (https://www.amazon.com/dp/0521820820/?tag=pfamazon01-20) and encountered a problem on page 111 about linear response theory. Consider a system with some conserved baryon matter perturbed by a source J_\mu, coupled to the baryon current...
48. ### A Classical statistical physics -- Number of microstates

Phase volume is it the same as the number of total microstates in some physical system? Phase volume= volume of phase space. Or there is some difference?
49. ### A Deriving the Kubo Formula for Viscosity in Thermal Relativistic QFT

I am looking for a derivation of the following formula $$\eta=\lim_{\omega\rightarrow0} \frac{1}{2\omega}\int dt dx\langle[T_{xy}(t,x),T_{xy}(0,0)]\rangle,$$ where $T_{xy}$ is a component of the stress-energy tensor. This is claimed in for instance https://arxiv.org/pdf/hep-th/0405231.pdf...
50. ### Other Statistical Physics and Biology

I'm undergrad physics student and I have read some statistical physics like equilibrium statistical physics, Langevin model and Fokker-Planck equation. I have developed interest in application of statistical physics in biology like protein folding. So what are the other research topics that lie...