deletions | additions       diff --git a/Distinguishing strings.tex b/Distinguishing strings.tex  index 5c6357e..780c520 100644  --- a/Distinguishing strings.tex  +++ b/Distinguishing strings.tex 
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Answers:  \begin{enumerate}  \item {\bf Note: from my (incomplete) derivation of Landauer's Principle in section~\ref{sec:LP}, I have decided that the following reasoning is wrong. But I don't quite know why! I leave the following here for now, but my conclusion is that it may not cost as much to write definite information if the prior bit-distribution is not flat.}\\  There must be some cost to {\it writing} information, because we are modifying blank DOF (bits) into new states, which necessarily deletes pre-existing information\footnote{Landauer's Principle (see Landauer (1961) for original work).}. This point seems to go unaddressed in the literature: writing information to an initially blank register increases the ``entropy'' (in the narrow sense of $S=-\sum_ip_i\log_2p_i$ for a very long string -- see section~\ref{sec:stringS}) of the register, and so there's no reason to {\it require }any dissipation. But here's why I think it must be there nonetheless. %  \begin{itemize}  \item We don't know {\it a priori} whether the writing process will result in a net increase or decrease of the string's ``entropy''. So, if we believe in cause-and-effect, and we accept that the end result is not known by the register until it has been realised, we should accept that heat dissipation takes place in the same way for each bit written. It is the result of physical processes, immutable by patterns in the outcome. 
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\item One might think that we are taking an initial random distribution of bits on the register and making it a determined distribution (reproducible if we re-run the measurements on the particle under scrutiny). But we really have no idea about whether the pre-existing string was random or generated by some other deterministic process. Put another way, if all we have is the bit-string, we can only ever estimate the probabilities and correlations of the string's generator; we can't reconstruct the process by which that sting was made (unless we know what the process was and whether it is logically reversible).  \end{itemize}  %  So even if the states are energy-degenerate, which can be arranged, the cost per bit written should be $kT\ln2$, regardless of the initial state of the register.\\   . {\bf Hold on this may be wrong!} Follow \citet{Piechocinska_2000} to derive LP from first principles. register.  \item In principle, there is no cost to reading information {\it unless} you want to remember it\footnote{Or deal with quantum mechanics.}. If this is the case, see point 1.