Document Structure

MicroLaTeX

A MicroLaTeX document starts with title line and a tag line. The tag line has the form \tags{tag1, tag2, ...}. The first tag is obligatory and has the form USERNAME:Unique-identifier. The identifier is generated automatically from the title.

\title{Notes on Entropy}

\tags{jxxcarlson:notes-on-entropy}

Here is a slightly larger example:

\title{Notes on Entropy}

\tags{jxxcarlson:notes-on-entropy, shannon}

\contents

\section{Entropy in physics}

A single spin has states $U$ and $D$ (up and down). 
An $N$-spin system s a sequence of $N$ spins, e.g.,

$$
UUDUDD
$$

Suppose that there are $N_U$ spins in
state $U$ and $N_D$ in state $D$.  We call
$(N_U, N_D)$ a \emph{macrostate} of the system.
A macrostate generally consists many \emph{microstates}, e.g.,

\begin{code}
UUUDDD
UUDUDD
UDUUDD
DUUUDD
...
DDDUUU
\end{code}

for the macrostate $(3,3)$.  If $s$ is a macrostate,
let $\Omega(s)$ be the number of microstates belonging
to it.  Then

\begin{definition}
The entropy of the macrostate $s$ is $\log\Omega(s)$.
\end{defintion}

...

\section{Shannon Entropy}

The structure of this larger example will be familiar to LaTeX users. Nonetheless, there are some differences of syntax and features:

  • MicroLaTeX is block-structured. Blocks must have a blank line above and below. Displayed mathematical text is a block, where the double dollar signs occupy lines of their own. Any \begin .. \end pair is also a block.

  • The \contents macro automatially generates the table of contents, provided that there are at least two sections.

  • Note that the \tags macro in this case defines an additional tag, shannon. Such tags are useful in searches. A search on shannon will retrieve this document.

NOTE. On export, MicroLaTeX is translated to standard LaTeX.

L0

| title
Notes on Entropy

[tags jxxcarlson:notes-on-entropy]

Below is a longer example. L0 is also block-structured, where blocks consist of contiguous non-empty lines bounded above and below by a blank line. There are four kinds of blocks:

  • Paragraphs
  • Ordinary blocks
  • Verbatim blocks
  • Special blocks

An ordinary block is a header of the form | NAME followed by its body. The title and contents blocks are ordinary. A verbatim block has a header of the form || NAME. The code block is a verbatim block, as are the equation and aligned blocks, corresponding to the LaTeX equation and align blocks. A block which starts with the single line $$ as in the example below, correponds to the $$ ... $$ construct in LaTeX. It is a special block.

| title
Notes on Entropy

[tags jxxcarlson:notes-on-entropy, shannon]

| contents

| section
Entropy in physics

A single spin has states $U$ and $D$ (up and down). 
An $N$-spin system s a sequence of $N$ spins, e.g.,

$$
UUDUDD


Suppose that there are $N_U$ spins in
state $U$ and $N_D$ in state $D$.  We call
$(N_U, N_D)$ a [emph macrostate] of the system.
A macrostate generally consists many [emph microstates], e.g.,

|| code
UUUDDD
UUDUDD
UDUUDD
DUUUDD
...
DDDUUU


for the macrostate $(3,3)$.  If $s$ is a macrostate,
let $\Omega(s)$ be the number of microstates belonging
to it.  Then

| definition
The entropy of the macrostate $s$ is $\log\Omega(s)$.

...

| section
Shannon Entropy

As with LaTeX, one has section, subsection, and subsubsection blocks. One can also say | section 1, | section 2, etc.

NOTE. On export, L0 is translated to standard LaTeX.

XMarkdown

The minimal structure of an XMarkdown document is similar to that of an L0 document. The rest of the text can be normal Markdown, or can be XMarkdown, i.e., Markdown + some extensions.

| title
Notes on Entropy

@[tags jxxcarlson:notes-on-entropy]

Below is a longer XMarkdown documents. 

| title
Notes on Entropy

@[tags jxxcarlson:xmarkdown-test, shannonx]

| contents

# Entropy in physics

A single spin has states $U$ and $D$ (up and down). 
An $N$-spin system is a sequence of $N$ spins, e.g.,

$$
UUDUDD
$$

Suppose that there are $N_U$ spins in
state $U$ and $N_D$ in state $D$.  We call
$(N_U, N_D)$ a *macrostate* of the system.
A macrostate generally consists many @[emph microstates], e.g.,

|| code
UUUDDD
UUDUDD
UDUUDD
DUUUDD
...
DDDUUU


for the macrostate $(3,3)$.  If $s$ is a macrostate,
let $\Omega(s)$ be the number of microstates belonging
to it.  Then

| definition
The entropy of the macrostate $s$ is $\log\Omega(s)$.

...

# Shannon Entropy

In an XMarkdown document, you can use most of standard Markdown, e.g., sections and subsections with #, ##, etc., backticks for inline code, triple backticks for blocks of code, *italic text* **bold text**, and dashes for bullet lists. For numbered lists, we use a leading dot:

. Bread

. Wine

. Cheese

Note that you can freely "borrow" L0 syntax in XMarkdown, e.g, displayed mathematical text, the definition and code blocks, etc.

NOTE. On export, XMarkdown is translated to standard LaTeX.