From: Matt Mahoney (matmahoney@yahoo.com)
Date: Fri Jan 25 2008 - 08:53:07 MST
--- Daniel Burfoot <daniel.burfoot@gmail.com> wrote:
> On Jan 24, 2008 1:18 PM, Matt Mahoney <matmahoney@yahoo.com> wrote:
> > > 4) Conservation of energy can be interpreted as conservation of code
> > length,
> > > due to the similarity between the Boltzmann factor and the Shannon
> > optimal
> > > codelength rule.
> >
> > Conservation of mass/energy limits the size of the universe. The
> > relationship
> > you suggest between thermodynamic and information theoretic entropy is
> > unrelated to energy. It is related to the direction of time. A
> > computation
> > irreversibly loses information, so its uncertainty about its environment
> > increases.
>
>
> This is what I mean. Consider a system of interacting particles with various
> energy states. The probability that a particle is in a given energy state
> is:
>
> p(E)=exp{-E/kT}/Z
>
> Assuming the simulation encodes the state of the particles using an optimal
> code, the code length requirement is:
>
> -log P(E) = E/kT + log(Z)
>
> The 1/kT factor is shared by all the particles in the system, and the log(Z)
> term does not change with changes in the particle's energy state. Thus an
> interchange of energy between any two particles will result in zero net code
> length difference.
Actually T is not shared by all particles, so energy is conserved while
entropy increases.
-- Matt Mahoney, matmahoney@yahoo.com
This archive was generated by hypermail 2.1.5 : Wed Jul 17 2013 - 04:01:01 MDT