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Every single thought you have has a physical process behind it. Ideas are collaborations between neurons and groups of neurons to model the world.

An idea can be as simple as a small line at a 32 degree angle, in an image. The neurons responsible for detecting lines at precisely that angle have no concept of what a line is. They respond to a specific pattern of stimulus from other cells, and emit their own responses when that stimulus fits the pattern.

Knowing what pattern to respond to is a form of memory.

There is a specialized "memory region" (it does considerably more than that) in the center of your brain called the hippocampus which doesn't "store all your data", so much as a significant portion of its neurons are dedicated to coordinating activity in the rest of your brain so that you can learn, remember, and abstract ideas. It emits signals which propagate through most of the brain and signify whether or not information is in the past, present, or future.

Memory as we commonly discuss it is a simulation of the past. It's a rough approximate replay of coordinated activity pulsing through the brain. When your mind wanders, and when you sleep the hippocampus recruits other areas of your brain to replay past events. There seem to be two primary reasons for this:

1. To abstract/compress/refine the data. A little chaos is "injected" into the data by "loosening restrictions", which in statistical terms helps to avoid overfitting and promote generalization. Basically your brain wants to learn general patterns and ideas rather than extremely situationally specific ones. This is the heart of abstraction
2. To encourage individual neurons and networks to reinforce and remember ideas

Over time connections which enable/facilitate the recall/replay of patterns degrade if they aren't replayed. We don't remember everything forever, we barely even process most of the information our senses receive.

To answer your question then... volatile. However the rate of information decay is going to vary directly with the rate of physical decay, with special importance placed (for non procedural memory) on the hippocampus (edit: and part of the prefrontal cortex), but there is a lot of memory all over the brain.

For example, the bilionaires that freeze their brans in hope of future tech being able to clone their minds. Once a brain loses all it's electrical impulses, can your "mind" survive that? Is our brain like RAM on our PCs that lose everything once shutoff or like a SSD?

The rate of information decay is going to vary directly with the rate of physical decay, with special importance placed (for non procedural memory) on the hippocampus (edit: and part of the prefrontal cortex), but there is a lot of memory all over the brain.

Which means that the extent to which the neurons are damaged/destroyed is going to determine the extent to which function is lost. Function and memory are the same thing.

Think of it this way: it's impossible to imagine throwing a ball without using regions of your brain responsible for actually throwing a ball. When you remember throwing a ball the neurons involved in throwing that ball are active.

If you damage the region responsible for remembering the sequence of events that led to you throwing the ball, and/or the regions involved in ball throwing, you won't be able to run the "I threw a ball one time" program.

Regarding freezing and thawing: I don't know but I imagine ice crystals would create some very serious issues.

Based on his answer it would actually be persistent- assuming there was a method of flash freeze/storage perfected in which literally zero of the tissue was damaged or altered…. This is interesting, i to have wondered if memories were physically there in our brain or simply ‘stored’ or ‘running’ in our brain via electric impulses that would all be ‘wiped’ should the brain shut down and start up again.

In the case where we use unobtanium to perfectly freeze and preserve the brain without damage then yeah. The electrical impulses aren't the important part. Neurons use those impulses to quickly signal themselves to signal other neurons chemically, or that a sufficiently stimulating signal/pattern has been received.

Memories aren't persistent in a normally functioning healthy brain which hasn't been scifi frozen in time.

Memory isn't my field of expertise, but one idea that should help you think about this question is that "electrical activity" in the brain isn't like electricity in computers, it isn't free electrons flowing along metal wires. It's electrochemical. Potential differences are built up by separated concentrations of ions in solution (e.g. Na+, Ca2+, Cl-). If you freeze the brain, presumably all those ions stay where they are in the frozen solution, so voltages persist and would still be there when thawed. It's like if you were to freeze a battery -- after you thawed it, wouldn't it still have a charge? So, ignoring any damage that freezing/thawing would have on the brain, based on our current understanding, I believe the mind would persist.

You might then wonder, even if it's not exactly electrical, what if all "electrochemical activity" were turned off? Perhaps by having all the ion concentrations equilibrate until there were no more potential differences? And to that, I don't think there is a solid answer, the neural mechanisms of memory are still hotly debated. People have observed memory engrams (i.e. a biological change associated with the formation of a new memory) in the form of "temporary" brain activity, while others have observed more stable changes in things like new synapses. An old idea is that short-term memory could stored by "activity" and long-term memory stored by these more stable changes, and if that were the case, then shutting off all brain activity would eliminate short-term memory but wouldn't affect long-term. But that's not a consensus view, so I don't think we can answer this yet.

This was really interesting to read, thanks. It would make sense that there would be great utility behind the brain’s constant replaying and abstraction of past events, as it attempts to squeeze every last bit of relevance and meaning from each experience.

I think this idea also exemplifies the difference between knowledge and wisdom; a young person may know a lot of things, but an older person has had time to generalize their knowledge and experiences, allowing for a broader perspective and the ability to draw more disparate and meaningful connections.

To your last point, is this why people with Alzheimer’s remember things from when they are a kid, but not who their children are?

I suppose not, since both of those examples would be considered long-term memories. Though there are other ways to categorize memories though, like episodic memory, or semantic memory. I don't think we can conclusively say why some memories are affected in disease and others aren't, but there is an idea that some neurodegenerative diseases (like Alzheimer's disease) don't progress evenly throughout the brain, and might start in a specific area and progress into other areas later. So if there are some areas of the brain that are more important for certain types of memories, and the disease develops there first, then those will be the first memories affected. For example, if a disease starts in the hippocampus, which is particularly important for place memory, then maybe the first noticeable memory problems would be increasingly forgetting where things are.