I've looked at this answer, and it states how:

Under the new memory model, when thread A writes to a volatile variable V, and thread B reads from V, any variable values that were visible to A at the time that V was written are guaranteed now to be visible to B.

Therefore, given the example:

public class Main {
    static int value = -1;
    static volatile boolean read;

    public static void main(String[] args) {
        Thread a = new Thread(() -> {
            value = 1;
            read = true;
        });

        Thread b = new Thread(() -> {
            while (!read);

            System.out.println("Value: " + value);
        });

        a.start();
        b.start();
    }
}

Is the change to value (from -1 to 1) guaranteed to be visible to thread b despite the non-volatility of value (only read)?

If so, given a bunch of changes that are performed with the intention of being visible to another thread, is there any purpose in making any variable changed other than the last one volatile?

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Yes, the change to value is guaranteed to be visible to thread b.

JLS 17.4.4. Synchronization Order says:

  • A write to a volatile variable v (§8.3.1.4) synchronizes-with all subsequent reads of v by any thread (where "subsequent" is defined according to the synchronization order).

JLS 17.4.5. Happens-before Order says:

Two actions can be ordered by a happens-before relationship. If one action happens-before another, then the first is visible to and ordered before the second.

If we have two actions x and y, we write hb(x, y) to indicate that x happens-before y.

  • If x and y are actions of the same thread and x comes before y in program order, then hb(x, y).

  • There is a happens-before edge from the end of a constructor of an object to the start of a finalizer (§12.6) for that object.

  • If an action x synchronizes-with a following action y, then we also have hb(x, y).

  • If hb(x, y) and hb(y, z), then hb(x, z).

Bullet 1 says that value = 1 happens-before read = true.
Bullet 3 says that read = true happens-before !read.
Bullet 1 says that !read happens-before "Value: " + value.
Bullet 4 says that value = 1 happens-before "Value: " + value.