Hi Stephen P. King  

Cool. Go for it. 


[Roger Clough], [rclo...@verizon.net] 
1/17/2013  
"Forever is a long time, especially near the end." - Woody Allen 
----- Receiving the following content -----  
From: Stephen P. King  
Receiver: everything-list  
Time: 2013-01-16, 19:29:33 
Subject: Algorithmic Thermodynamics 


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, Mike Stay 
(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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