The white Belts biggest problem is that they panic. They tense every muscle in their body and keep them tensed until they fatigue. You need to learn to relax all your muscles except the ones you need, when you need them. You need to get comfortable in the different positions, and understand what is at risk in those positions so you can focus on that and not keep your entire body tensed.
I totally agree with this. Everyone does it. The one thing that helped me overcome this was rolling with new guys that started training a few months after me. Since I had a few months experience on them and knowledge of basic positions and control, I was able to realize what I was doing wrong by observing them. That way, I overcame my beginner jitters early on, and it also helped the newer guys overcome theirs more quickly.
Since then, I have joined the Marines, so my fitness level over the past year, compared to when i was a white and even new blue belt, is light-years from what it was. I have learned so many strength, endurance, and stamina focused workouts that have really benefitted my game tremendously. I recommend Crossfit-type workouts, but honestly, my favorite, is just make-it-up-as-you-go workouts.
It usually always consists of running. Run for warmup, between your workouts, after your workouts, and sometimes during. It usually lasts for about 45 min to 2 hours. The key is to never repeat the same routine twice. (obviously, over time, odds are you might, but just as long as you don't repeat the same workout everyday). This keeps your body guessing. If your body gets in rythym and can predict peaks of your workout, then your heartrate, endurance, and stamina will instinctively adjust themselves to perform at certain times, causing you to possibly crash at a critical moment, when you need strength.
Sorry, I went on a little long with that. Just a thought: IMHO....Jiu-Jitsu is more mental than physical. The second you stop thinking about what you are doing, you start to exert more energy than is required. Have fun and keep it up. Safe rolling!!