State in Jetpack Compose

You can still use LiveData, RxJava Observables, Kotlin Flows to represent state in Jetpack Compose. All you have to do is use the respective extension functions. They convert the respective reactive object into a Jetpack Compose state.
For livedata you need the 'androidx.compose.runtime:runtime-livedata' artifact in your Gradle Dependencies.
For the rxJava you need the 'androidx.compose.runtime:runtime-rxjava2' artifact.
More info at https://developer.android.com/jetpack/androidx/releases/compose-runtime

How to use LiveData, RxJava, Flow in Jetpack Compose

The code of your composable functions may be executed multiple times due to multiple recomposition events. The block of code passed to the `remember` function will be called only during the first composition. This can be helpful if you need to maintain the same value across recompositions. 

What does remember {} do in Jetpack Compose

Jetpack Compose is a reactive UI framework. Compose will refresh your UI as soon as the value of a State object is updated. This tutorial shows you how to create state objects to use in your composable functions.