In one word: No
With a few more words:
The JVM does not keep any history on any object past its current state, except for very little information related to garbage collection and perhaps some method call metrics needed for the HotSpot optimizer. Doing otherwise would imply a huge processing and memory overhead. There is also the question of granularity; do you log field changes only? Every method call? Every CPU instruction during a method call? The JVM simply takes the easy way out and does none of the above.
You have to isolate the class and/or specific instance of that object and log any operation that you need on your own. You will probably have to do that manually - I have yet to find a bytecode instrumentation library that would allow me to insert logging code at runtime...
Alternatively, you might be able to use an instrumenting profiler, but be prepared for a huge performance drop when doing that.