Coarse Graining in Statistical Physics: Resolving the 2nd Law of Thermodynamics

[Bigfoots mum]

A common exam question for my statistical physics course asks you to explain how we 'reconcile the issue of the 2nd law of thermodynamics with physics at the miscroscopic level'.

It mentions that we should make particular reference to the gibbs entropy and how it may be resolved through coarse graining. It then asks how a Langevin approach 'provides a realisation of such a procedure'.

My attempt: My understanding of course graining at the quantum level is that we effectively reduce the resolution at which we observe our system via the averaging of some parameter, eg the density, and in doing so we lose information. Consequently the Entropy increases. Is this reasonable? I am still not happy with my understanding of this however.

As for the Langevin part, I am really not sure how to explain this. Is it something to do with how in the Langevin approach he uses a Stochastic differential equation which effectively produces the same results as the Diffusion equation derived from the master equation for a random walk?

Sorry for the essay!
Any help greatly appreciated

 

[NateD]

. Yes, your understanding of coarse-graining is reasonable. Coarse-graining is a process of reducing the resolution at which we observe our system by averaging out some parameters, such as density, and in doing so, information is lost and entropy increases. The Langevin approach provides a realization of such a procedure, as it involves a stochastic differential equation that produces the same results as the diffusion equation derived from the master equation for a random walk. This equation models the behavior of a system by taking into account the effects of random fluctuations on its microscopic state. In this way, the Langevin approach can be used to reconcile the second law of thermodynamics with physics at the microscopic level.