>From just the abstract alone, I can't see how this differs from the
Solomonff universal prior?

Cheers

On Wed, Jan 16, 2013 at 07:29:33PM -0500, Stephen P. King wrote:
> Dear Bruno and Friends,
> 
>     The paper that I have been waiting a long time for.  ;-)
> 
>  http://arxiv.org/abs/1010.2067
> 
> 
>  Algorithmic Thermodynamics
> 
> John C. Baez
> <http://arxiv.org/find/math-ph,math/1/au:+Baez_J/0/1/0/all/0/1>,Mike
> Stay <http://arxiv.org/find/math-ph,math/1/au:+Stay_M/0/1/0/all/0/1>
> (Submitted on 11 Oct 2010)
> 
>    Algorithmic entropy can be seen as a special case of entropy as
>    studied in statistical mechanics. This viewpoint allows us to apply
>    many techniques developed for use in thermodynamics to the subject
>    of algorithmic information theory. In particular, suppose we fix a
>    universal prefix-free Turing machine and let X be the set of
>    programs that halt for this machine. Then we can regard X as a set
>    of 'microstates', and treat any function on X as an 'observable'.
>    For any collection of observables, we can study the Gibbs ensemble
>    that maximizes entropy subject to constraints on expected values of
>    these observables. We illustrate this by taking the log runtime,
>    length, and output of a program as observables analogous to the
>    energy E, volume V and number of molecules N in a container of gas.
>    The conjugate variables of these observables allow us to define
>    quantities which we call the 'algorithmic temperature' T,
>    'algorithmic pressure' P and algorithmic potential' mu, since they
>    are analogous to the temperature, pressure and chemical potential.
>    We derive an analogue of the fundamental thermodynamic relation dE =
>    T dS - P d V + mu dN, and use it to study thermodynamic cycles
>    analogous to those for heat engines. We also investigate the values
>    of T, P and mu for which the partition function converges. At some
>    points on the boundary of this domain of convergence, the partition
>    function becomes uncomputable. Indeed, at these points the partition
>    function itself has nontrivial algorithmic entropy.
> 
> 
>     Now to discuss how this is useful to define a local notion of a
> measure for COMP.
> 
> -- 
> Onward!
> 
> Stephen
> 
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