Re: Quasistatic conditions (was: Re: Relativity question)

[David Bowman <dbowman@TIGER.GEORGETOWNCOLLEGE.EDU>]

Regarding Pentcho's question:

> --- David Bowman <dbowman@TIGER.GEORGETOWNCOLLEGE.EDU> wrote:
> > Recall that both joules and bits
> > measure *extensive* quantities and temperature is an *intensive*
> > quantity that can be expressed as a partial deriviative of
> > extensive internal energy w.r.t. extensive entropy (under quasistatic
> > conditions where no macrowork is done during the variation).
>
> Weren't quasistatic conditions ones in which maximum work is
> extracted from the system?

No.  Quasistatic conditions are those that perturb an equilibrated
system during a process so slowly and gently that the system
effectively doesn't significantly fall out of equilibrium during the
change.  At each moment during a quasistatic process the system can
be considered as being in equilibrium (or at worst maybe a metastable
state that acts like equilibrium).  The quasistatic limit is the
limit whereby a process-caused change occurs much more slowly than
the characteristic equilibration time for the system.  Whether or not
work is done during such a process is irrelevant to the definition of
being quasistatic.

> Please give examples of quasistatic changes.
>
> Pentcho

Most processes can to a pretty good approximation be considered as
being quasistatic as long as we focus on sufficiently small length
scales and look at tiny subsystems rather than a large global system
during the process (major exceptions being explosions into a vacuum,
shock waves, spinoidal decompostion, phase transitions, fully
developed turbulence and the like).  This is because most systems
can be thought to be in a state of near local equilibrium even if
the global system as a whole is manifestly not in equilibrium.  A
subregion is sufficiently small for a process occurring in it to be
thought of as being quasistatic in that subregion if the time scale
of the duration of the change process over the subregion is much
longer than the time it takes for a sound wave to cross the subregion
(in response to mechanical pressure imbalances) and much longer than
the time it takes for heat to diffuse across the system (in response
to temperature imbalances) and much longer than the time it takes for
a chemical reaction to go most of the way to completion in the region
(in response to imbalances in chemical potentials).  A subregion
needs to be small enough on the macroscopic scale so that it can
effectively be seen as being nearly uniform in its intensive fields
and for the characteristic response times for fluxes of extensive
flows moving in response to gradients of those intensive fields to
occur on a much faster timescale than the time scale of the imposed
changes caused by changes in the boundary conditions for the
subregion of interest due to other changes taking place external to
that subregion.

But we are not free to keep making our subregions arbitrarily small.
The characteristic size of our subregions must still be hugely
macroscopic (i.e. in the thermodynamic limit) when viewed from a
fully microscopic point of view.  This means that, among other
things, in each of the subregions there are a huge number of
microscopic degrees of freedom, and that the relative magnitudes of
the statistical fluctuations in the subregions' thermodynamic
properties remain a tiny fraction of their average values, and that
the linear sizes of the subregions are much larger than the
coherence lengths for any any all short ranged order parameters in
them.

The reason why fully developed turbulence, phase transitions, spinoidal
decomposition and the like can not be decomposed into a set of
subregions that are effectively undergoing quasistatic processes is that
the length and time scales of the statistical fluctuations occurring in
them (from the microscopic dynamics) extend all the way up to the fully
macroscopic level, and there is just no intermediate length and time
scale regime, to use for our subregions, that is simultaneously large
compared to the significant effects coming from the microscopics and yet
small compared to the macroscopic changes that are taking place that
define the process as seen at the macroscopic level.

David Bowman