Sign conventions in Devoret Les Houches course on quantum fluctuations in electrical circuits In this article on p. 364 Devoret writes the "equations of motion" (using KCL) for the electric circuit shown on p. 363. He uses flux instead of voltages.
The sign convention he uses, as shown on p. 360 is strange for me since I was taught that, on passive elements, the direction of the voltage and the current should be the same. As Devoret's convention seems to be the opposite, the laws for the passive elements should hold with a sign opposite the usual one.
The next problem is that however I try to choose the directions of currents going into or coming from the node, I can't get the equations 2.14 and 2.15. Please explain how to derive those equations.
 A: Isn't it just a convention you have to choose once and for all. It's all about how to pass from Maxwell to lumped element circuits. Especially, I can choose the two different conventions (all quantities are vectorial in the following)
$$E=\pm\nabla V$$ 
since I didn't choose my field-to-potential rules yet. Usually one chooses to conform to the classical mechanics where force and potential go as $F=-\nabla V$ and choose then $E=-\nabla V$ alongside the usual Lorentz force $F=qE + v\times B$. 
Then integrate the definition above along a line, one has 
$$\int_{a}^{b}E\cdot dl=V\left(a\right)-V\left(b\right)$$
which is nothing more than the relation (2.1) in Devoret's lecture. Remark: Devoret clearly notes $v_{b}$ what I call $V\left(a\right)-V\left(b\right)$.
If one chooses (as Devoret) that $V\left(a\right) > V\left(b\right)$ (the voltage is positive by convention), one has that $E$ is opposed to $V=V\left(a\right)-V\left(b\right)$ from the relation $E=-\nabla V$. 
Finally, the definition of the current is given by the Ohm's law in circuits: $j=\sigma E$, and so the current is opposed to the voltage convention, as the electric field along the (lumped) element. 
A: Partial answer here about what the author means by flux:

We now introduce the flux $\phi_n$ of a node $n$ which is defined by the time integral of the voltage measured along the path connecting the node to the ground on the spanning tree. (Defined a few pages prior to 363.)

It then seems $\dot\phi$ is voltage as we would normally define it.
