What is a "transient" state?

Question

I was analyzing this source code of the Ising model. I found the term "transient state".

I also found the term in this text:

There are two absorbing states in this Markov chain because once either Jane or Eddie wins, the game is over, and the die is not rolled again. That the winner’s side of the die remains up forever is reflected in the value of unity along the diagonal and the value of zero in the nondiagonal elements for states 1 and 2. Also note that one of the 10 sides must be up, and so the sum of all the elements in each row of M_die must be unity. We multiply the matrix M_die on the left-hand side by a unit row vector VT with a 1 in the state the die is in before it is rolled. For the game to start the initial vector must be in the transient state, that is, it must be in state 3.

And, in this text:

What is a "transient" state or value or result in the Ising model?

Answer 1

The excerpt that you gave us defines a steady state as one in which the state is not changing ($\frac{\textrm{d}\rho}{\textrm{d}t} = 0$) and a transient state in which the state is changing ($\frac{\textrm{d}\rho}{\textrm{d}t} \ne 0$).

This makes sense because before the word "transient" was used in this scientific context, it was a word used in the English language meaning "unsteady" or "changing". The word has been used in one form or another since the late 16th century, with its roots coming from the Latin-based prefix "trans" which means to go across or switch (in this case the state is switching its form over time).

Answer 2

Transient state can be defined as a state in which $\frac{\text{d} \rho}{\text{dt}} \neq 0$, which, in an Ising Model MCMC (or any step-based) simulation, could be translated to $\frac{\text{d} M}{\text{dt}} \neq 0$ with $M$ the magnetization of the system.

In a simulation, fluctuations are going to be happening inevitably. The non-transient states are the ones where the system has converged to a steady state.