In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. It does not assume or postulate any natural laws, but explains the macroscopic behavior of nature from the behavior of such ensembles.
Statistical mechanics arose out of the development of classical thermodynamics, a field for which it was successful in explaining macroscopic physical properties such as temperature, pressure, heat capacity, in terms of microscopic parameters that fluctuate about average values, characterized by probability distributions. This established the field of statistical thermodynamics and statistical physics.
The founding of the field of statistical mechanics is generally credited to Austrian physicist Ludwig Boltzmann, who developed the fundamental interpretation of entropy in terms of a collection of microstates, to Scottish physicist James Clerk Maxwell, who developed models of probability distribution of such states, and to American Josiah Willard Gibbs, who coined the name of the field in 1884.
While classical thermodynamics is primarily concerned with thermodynamic equilibrium, statistical mechanics has been applied in non-equilibrium statistical mechanics to the issues of microscopically modeling the speed of irreversible processes that are driven by imbalances. Examples of such processes include chemical reactions or flows of particles and heat. The fluctuation–dissipation theorem is the basic knowledge obtained from applying non-equilibrium statistical mechanics to study the simplest non-equilibrium situation of a steady state current flow in a system of many particles.
Hi,
I've acquired a few stat mech texts.
1)Landau & Lif****z: A Course in Theoretical Physics: Statistical Mechanics part 1 and 2
2)Huang
3)Chandler
Which of these should I start with to self-study statistical mechanics? I'm eager to read one of the famous Landau texts, but I'm afraid...
Has statistical mechanics anywhere disproven the ancient Greek idea that hard, indestructible objects (the original "atoms"), that experience no force other than that of impacts, can form the substratum of all material bodies and forces?
I've been reading Boltzmann's "Lectures on Gas Theory"...
Check out this great book on Stat Mech by - Dr. James Sethna
http://pages.physics.cornell.edu/sethna/StatMech/
This book's cool containing lots of application to Computational Stat Mech.
Homework Statement
Consider a two level system where the ground state is doubly degenerate and the exited state of energy E is four fold degenerate. Write down the partition function and mathematical expressions for the populations of the two levels.
Homework Equations
z=e-E/kt
ni =...
In statistical mechanics, we define
\frac{1}{\tau}=\left( \frac{\partial \sigma}{\partial U} \right)_N
This formula gives the temperature as a function of the energy of the system and N. So knoweldge of U and N determines the temperature of the system. Conversely, at least when the...
Hey folks,
studying for the qualifying exam and i wanted to run this by the forum. A model system has a density of states
g(E) = X for 0 < E < A
g(E) = 0 for A <= E <= B
g(E) = Y for B < E
the total number of particles in the system is given by N = X A.
Now this looks like a very simple...
A circular cylinder of radius R rotates about hte long axis with angular velocity omega. The cylinder contains an ideal gas of atoms of mass M at temperature tau. Find the expression for the dependence of the concentration n(r) on the radial distance r from the axis in terms of n(0) on the axis...
I am supposed to show that N!/(N-n)! = N^n where 1<<n<<N
I used stirling's approximation to show that N! = e^(NlnN-N) and (N-n)! = e^[(N-n)ln(N-n) - N + n].
I took the ratio of these two terms to get e^[NlnN-N-(N-n)ln(N-n) + N - n]. I canceled terms and get N!/(N-n)! =...
we have a hollow cubical box with sides of length a with perfectly conducting walls, such that the electric field tangential to the surfaces of the walls must be zero. we need to show that the system of standing waves:
Ex = Ax*cos(Kx*x)*sin(Ky*y)*sin(Kz*z)*exp(iwt)
Ey =...
we have to outline a proof to show that beta =1/(Kb*T) for a gas of fermions. we are supposed to put this system in thermal contact with a system obeying classical statistics, so that the two systems have the same beta, invoke the zeroth law to sat that they have the same temperature, and then...
A weight of mass m is fixed to the middle point of a string of length l and rotates about an axis joining the ends of the string. The system is in contact with its environment at temperature T. Calculate the tension R between the ends of the string in terms of its dependence upon distance x...
Cosma Shalizi has a brief paper in the arxiv:
http://www.arxiv.org/PS_cache/cond-mat/pdf/0410/0410063.pdf
containing a proof that if you use Bayesian degree of belief oriented probability in forming statistical mechanics a la Jaynes, entropy comes out non-increasing; the arrow of time...