Statistical physics: Cosmos — All that is, or was, or ever will be

Statistical physics

cosmos 6th May 2019 at 7:21pm

Statistical physics deals with the description of systems for which a deterministic description is either useless or impossible, so that one uses a statistical description.

Here a deterministic description is understood in the context of the relevant physical description. For example Schrodinger's equation is deterministic, if the relevant physical description is the wavefunction. It is non-deterministic if one takes position and/or velocity as the relevant physical descriptions. However, it is known that one can't describe quantum mechanical evolution purely with a statistical theory of position and velocity, without sacrificing some rather well-established physical principles or predictions.

If the system is effectively classical (either because it is macroscopic, or for some other reason, that is probably ultimately related to Quantum decoherence), the need for a statistical description arises when the system is sufficiently chaotic. Most often this requires the system to: have many components and/or be coupled to a system with many components.

For this reason, statistical physics is mostly applied to the description of systems of many particles in a gas, liquid or solid; or to one or a few particles coupled to one such large system.

There are two main branches of statistical physics:

Equilibrium statistical physics deals with such systems at equilibrium, that is, when the relevant macroscopic averages of the statistical description don't change with time. In practice, one often has two approaches:

For a small system coupled to a large chaotic system, one often has to use a probability distribution function over the relevant degrees of freedom (amazingly, for equilibrium, this always takes the form of a Boltzmann distribution.
For a large system, one can often bypass the distribution function and deal with the relevant averaged quantities directly, resulting in a thermodynamic description.

Non-equilibrium statistical physics deals with such a system out of equilibrium, so that averages can change in time. This is much harder to do in full generality, as systems offer much more diversity out of equilibrium, as may be expected. One often has three approaches:

For a small system coupled to a large chaotic system, one has a stochastic process, which describes the evolution under the random influence of the large chaotic system.
For a large system which is only slightly out of equilibrium, so that relevant macroscopic averages analogous to those used in thermodynamics can still be defined, one can describe the system using Non-equilibrium thermodynamics
For a large system that is considerably out of equilibrium, one has to use the tools of Kinetic theory to describe it. However, if the system is very far from equilibrium, even these may be inappropriate, and finding an appropriate description may be extremely hard. An example of this are systems with strong Turbulence. Our only approaches to understand these systems are often phenomenological.

Intro vid to modern stat phys

Thermodemonics https://fqxi.org/community/articles/display/234?fbclid=IwAR3ueguT_2YeeO_EolzFaU28l1-SPglHJtKbV1vFYyfyIYVeQZw8nSCpfM0

See also Complex systems, and Sloppy systems

Entropy, Order Parameters, and Complexity

Long-range interacting systems

Oxford physics course

Oxford maths course

Bangalore School on Statistical Physics - V (video lectures)

Bangalore School on Statistical Physics - VI (I'm on the 1st lecture on Long-range interacting systems

Ergodic theory

See about disordered systems in Condensed matter physics, as these are interesting systems studied using statistical physics.

Indian Statistical Physics Community Meeting 2016