I've had my Galaxy Note 4 AT&T model for a little over a month now. I got it pre-owned, but even so it works great, almost as if brand new. With the exception of the battery life.
I've noticed drain ever since I first powered the phone on. Going through the initial setup and then just experimenting around with the interface for about 25-30 minutes led to 26% of battery lost. The screen brightness was 25%, and there was not even a SIM card in the phone at the time, so it could not be attributed to any cell connectivity. Also I can't blame any apps that were installed, as there were no apps installed by me yet. In fact, after disabling about half of the built in bloatware I knew I would never use, I still didn't see any battery improvement.
Since then, just to give you an idea, it drains an average of 10% overnight, and this is with the app tray cleared, screen off, and airplane mode on (Wi-Fi off too). Now, I know this phone is four years old and perhaps the processor and other components require more power than they used to, but that can't be normal.
I also did a video streaming battery test. At almost no brightness and no other background apps running, I got almost exactly 2h30 of streaming YouTube videos in HD. In contrast, a fellow YouTuber got 6h23 with the brightness at max.
I know this is not the battery. The battery that came with the phone that I know is genuine Samsung, a brand new battery ordered directly from Samsung, and a third battery (that I'm not sure if it's genuine Samsung) all have the same drain problem. Also note that none of the batteries do anything crazy, like "jump" percentages or die unexpectedly before the phone reaches 1%; the drainage is pretty consistent and always goes from 100% to 0%. It's just that this happens too rapidly.
I've gone into the Battery section of Settings multiple times once the battery has gone below 20% from a 100% charge, and it always says that the screen is the thing taking the most power (around 10-12%), then the Android System following with about half of what the screen was using, then Cell Standby and Android System tied at around 2-3%. Underneath that, any apps I was using are listed, at 1%. In total, the whole listing doesn't even nearly add up to 100%; not sure if that's normal either. I typically use the phone with 30% screen brightness unless outside, and the "Auto Adjust Screen Tone" setting is always on.
I've been able to narrow the problem down to the Micro SD card reader part. I've had a 128 GB Sandisk Ultra in the phone since I got it. But I've also used this same card in my previous phone (a Samsung Galaxy Luna), and there were no battery issues at all. I also don't use it as an integral part of the phone's functionality (I don't store apps on it), it is only used to hold my music library and the photos/videos I take with the phone's camera.
I tried once to remove the SD card, put it in my PC and fully reformat it using the official SD reformat tool, then put it back in the phone (obviously I backed up the files). This briefly fixed the battery drain, but after a few days it went right back to the way it was.
As another experiment, I removed the SD card and charged the phone to 100%, and didn't put the card back in. Running the phone with no SD card so far has given the greatest success I've had with solving the issue; I got more than double the amount of time on a charge.
The only thing I can think of is that the Note 4, in its official spec sheet, only can accept up to a 64 GB card, and I'm using it with a 128 GB. But other people on forums don't seem to be having battery issues. I've also seen suggestions to update the firmware, but I do not use my phone under a major carrier's service, so updating is not an option. It seems to be running the latest firmware anyway: it's on 6.0.1. Some have suggested to try the Greenify app; this seemed to help a little at first but that could have been placebo. Ultimately I uninstalled it after a week.
I suppose I could just carry around extra batteries everywhere I go, or keep removing the SD card when I'm not listening to music or filming, but it's so small that I wouldn't want to risk losing or corrupting it. I'm willing to live with this because the Note 4 is such a nice phone in every other regard, but does anyone have any other suggestions before I give up? I would even consider rooting and installing a custom ROM, but I would like for this to be my absolute last resort if at all possible. Let me know if you have any more questions; I'll be sure to give more information.