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Some ideas:  \begin{itemize}  \item What is temperature? Is there a way of turning mechanical energy into a free energy? How do I invoke a heat bath?  %  \item Can I make a partition function (if I have an explicit $V$)?  %  \item Treat as absorbing boundary with drift, like Payam2.3.  %  \item If we can make free energy change zero, then $\langle e^{-\beta W}\rangle = 1$. With dissipative process.  %  \item The JE shouldn't depend on microscopic dynamics of the system, as long as they are microscopically reversible. Can I propose my own dynamics? E.g. the particle goes up or down the potential with some probability.  %  \item Interpretation of the {\it control parameter} $\lambda(t)$ in this context: it is the ``force'' that a particle in a absolute zero vacuum would experience in the potential. Real experiment \ra randomness.  %   \item The work parameter provides the distinction between work and heat flow (at least in Crooks' derivation \cite{http://adsabs.harvard.edu/abs/1998JSP....90.1481C}). (See also \citet{http://adsabs.harvard.edu/abs/1999PhRvE..60.2721C} and \citet{http://adsabs.harvard.edu/abs/1999PhDT........37C}.)   %   \item In the derivation of the JE, can we transform $\lambda(t) \ra \lambda(x)$ to make relevance to fixed potential stronger? If so, then smooth $V(x)$ can be steps in $H(t)$.   %   \item For a single particle in a monotonic potential, what counts as a macro/microstate. Is multiplicity always one?   %   \item Free energy is work the can be done. But this is interpretation, not definition.  \end{itemize}  Other notes: