From: Sterling Paramore (paramore_at_hec.utah.edu)
Date: Fri Feb 09 2007 - 16:03:02 CST
If the system is NVE (adiabatic), then no heat can be dissipated
regardless of how fast the force is applied. Thus the only way the
energy can change is by doing work.
Conservation of energy is true regardless of system size or even whether
the system is ergodic. Of course in simulations, this may be violated
to small order due to numerical imprecision, but the violation can be
diminished by decresing the timestep.
This may be a bit off topic, but it also should be mentioned that the
Jarzynski "Equality" is actually an Identity (requiring no assumptions
other than, perhaps, ergodicity) for classical time-reversible
deterministic equations of motion. Denis Evans (Mol. Phys. 2003) wrote
a really cool paper proving this.
Lewyn Li wrote:
> Hi Sterling,
> Under First Law, deltaE = q + w. If the process is adiabatic (q
> = 0), then you are right in saying that deltaE = w. But if some of
> the work is dissipated as heat, then deltaE does not equal w. Whether
> or not some of the work is dissipated as heat can be a function of how
> quickly the force is applied.
> Furthermore, all laws of thermodynamics apply to ensemble
> averages. For single-molecule trajectories of finite time, unless one
> can establish ergodicity, it may not be valid to apply any First law
> arguments to a single (or even a few) finite-time trajectories.
> You can, of course, attempt to apply the "Jarzynski's equality
> (JE)" (and extensions thereof) to the trajectories to compute the free
> energy. However, one should be aware that some of the experiments
> "proving" JE have been called into questions.
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