# Re: SMD and CPT? (fwd)

From: Sterling Paramore (paramore_at_hec.utah.edu)
Date: Fri Feb 09 2007 - 16:08:38 CST

Marcos,

Well, I'd like to keep the First Law no matter what. So I'd say that
for adiabatic extension, however the energy changed should be exactly
equal to the work. I would think that it would end up being \int F*d,
but I could be wrong.

-Sterling

Marcos Sotomayor wrote:

>
> Hi Sterling,
>
> Let me be more specific. First, when the external force applied to
> your system is time-dependent, the Hamiltonian of your system is not
> conserved anymore and does not represent the total energy. Moreover,
> the expression F \times d, as far as I can tell, is no longer the work
> done on the system (usually one assumes a time independent
> hamiltonian/force to derive that expression). So my sentence should
> have read like: " The quantity F \times d (previously work done)
> should only be similar to the energy change". Please correct me if I
> am wrong on that.
>
> I think you are right in that the total amount of work done by the
> external force does match the energy change, but you cannot use Fd to
> measure it. Therefore, the first law of thermodynamics is not
> violated. There is a nice article on a similar topic that you may want
> to check:
>
> "Invariants for time-dependent Hamiltonian systems"
> Jurgen Struckmeier and Claus Riedel
> Physical Review E 64 026503
>
> Regards,
> Marcos
>
>
>

This archive was generated by hypermail 2.1.6 : Wed Feb 29 2012 - 15:44:23 CST