# Thermodynamics of LLM conformational space

[Read this page on the web](https://elsworth.phd/Formalisms/Thermodynamics-of-LLM-conformational-space)

Measure the constant heat capacity, $\Delta G$, of unfolding,
This can be done either by changing the temperature, or by changing the sequence. You can measure how many times you get a "misfold". So you measure for a specific sequence and then mutate it to measure how robust the mutation is to a "misfold". This can be used to measure the "stability of a LLM".

We can use the [[Personality Conformational Space sampling]]

$K_{eq}=\frac{Wrong}{Right}$ 

This is equilibrium thermodynamics, I just run the statistics at the end.

Calculate 

$$\Delta G_{eq}= -RT\ln (K) = -RT\ln \frac{Wrong}{Right}$$

$$\Delta G_{eq}=\Delta H-T\Delta S$$

We care about $\Delta H$ because this contains all the juicy information about "why" the information we are testing matters. Because $\Delta H$ is temperature invariant.

Now the question is what is the [[kinetics of a LLM response]] . What does that mean? 


# Stability
We can add denaturing (random insertion of text)
Or 
We can add stabilizing (relevant text to problem)

We can also $\uparrow T$ (destabilize) or $\downarrow T$ (stabilize) the prompt output. 


This all for the purpose of predicting:

$$Pr\left( {}^r\mathbb{I}_{target} \cap \mathcal{o}_{i,j} \not = \emptyset \hspace{0.1 cm  } |\hspace{0.1 cm  }  \mathcal{r}_{i}, \mathcal{P}_{j}\right)$$

As we are hoping to identify what pieces of information a language model will have access too and what the easiest/shortest method would be. 



We can combine methods of [[Mutation Types For Prompts]]

# Phase Separation
[[Phase separation of personalities]]

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