Is it feasible to have a vehicle powered by fuel that the vehicle produces within its self? This vehicle can be a land vehicle or an air vehicle if you want. It must be capable of transporting at least one person.
Requirments
Must be self-contained within the vehicle Must be powerful enough to move the vehicle at 10km per hour Must not rely on outside resources such as oil or natural gas
Edits Can have a closed loop inside the vehicle if wanted
According to your last sentence (before Addition), the answer is: no!
You describe a perpetual motion machine which shall produce something (usually energy, in your case especialy fuel) from nothing. That’s not possible, it would break more than one law of physics. If we take the last sentence word by word, even solar power is not allowed as it uses an external resource (sunlight). You could try it with some reactor-engines, but even those need external materials from time to time (and are bulky and not really suitable for a vehicle).
Even if you accept external energy (sunlight for example) but want to stay with fuel you would need a technology which allows you to transfer energy to matter (like star trek replicators). This technology doesn't exist and we don't know if it ever will.
If we want to stay with self-produced fuel, but accept external energy and harvestable (regrowing) ressources, btl-technology comes to my mind. The technology to transfer biomass (wood, straw, nearly everything from plants) to usable fuel is still in development and not efficient by any means at the moment, but if our technological know-how advances further we could reach the point where this would be A.) usable and B.) could get small enough to fit on a truck or something equally big. You won't have a vehicle with long distances between stops to reload material, but it would work and should meet your requirements.
(Little hint: if you don't stick to fuel it gets much easier, you just need a steam-engine. 'Fuel' is whatever is capable of burning and the only other thing you need to replenish often is water.)
Thorium Reactor
A company called Laser Power Systems are planning a car running on a compact thorium reactor, claiming that just 8 grams of thorium could power a thorium turbine car for a century. This estimate has been criticised - this feat would require no less than 80 grams!
We are, however, quite far from making this come true. We don't have any actual working thorium reactors yet, and the first ones are likely to be far too large for a car (though in theory, they can be made far smaller than traditional nuclear reactors. And then, of course, there is the need for shielding against radioactivity, where 1 cm of lead is required to just cut gamma radiation in half. Still, it is feasible with future technology.
A steamboat fits the bill. You can cut the ships own structure to feed the furnace. This will move you over 10km/h and will last as long as there are superfluous parts in the ship's structure (i.e.: the ship can move without its roof).
Don't be mad at me. You wanted the vehicle to produce its own fuel. This is a self-destructive process for the vehicle. Otherwise you would be in violation of Thermo's 2nd and we would have to give you a ticket for it.
Nuclear Battery
Whilst not actually generating the energy itself, a nuclear battery generates a constant trickle of energy for many years. This could in turn charge capacitors in the vehicle which would allow it to drive until the capacitors ran flat and then have to wait for them to recharge.
A tiny white-hole inside your car.
https://en.m.wikipedia.org/wiki/White_hole
While the consequences of white hole existance will likely throw most of our understanding of the natural laws in chaos, I doubt the general public would notice. We are causing time travel on a quantum level already and have theories that Black Holes break the conservation of information and energy and the world is still spinning so I guess a white-hole energy reactor wouldnt be much of a problem.
White holes are the theoretical opposite of a Black Hole. You cant enter them while matter and energy can only come out. So use one in your vehicle to generate the energy you need in any way you please.
Another alternative would be almost as magical: if you can control quantum fluctuations around a tiny Black Hole/kugelblitz you can control the amount of energy released per second (which is important as without it a Black Hole weighing 1 kilo would evaporate almost instantly in the form of a big radiation explosion). This allows you to power your vehicle for incredible amounts of time. You do have to make new BH's every now and then as its likely not possible to feed a BH that small even with light, which is weird in the case of a Kugelblitz which is a BH created by so much light energy in one tiny region of space it collapses in on itself.
Zero Point Energy
This in itself would not be exactly be self contained energy as I believe it draws energy from the quantum plane, but it would be close enough. That's at least what I know. More information here.
Consider a hydrogen modulated self regulating nuclear power module. It's purposely designed to be small, self contained, and self regulating. That means it doesn't need control rods or anything complex like current reactors do. As power output increases, the Uranium Hydride decomposes into Uranium and Hydrogen. It then loses its neutron absorption capability, and the reactor power drops on its own. It reaches equilibrium where the reaction is just moderated enough to keep going, with few moving parts. It is impossible for this design to meltdown, and will run for many years.
Current designs are about a couple meters in length, but could probably be made smaller. The fuel is not weapon grade, so tampering with it to get the Uranium would not yield bomb-making capability. The coolant is liquid bismuth, potassium, or lead, surrounding the reactor. This makes it very durable. If it falls off a truck for example, the case cracks, the metal leaks out and solidifies, making it hard to leak radioactive material. And for those concerned with safety of hydrogen in the reactor, it also works with Uranium Nitride and others, but Hydride is the most efficient.
This is all very viable with current technology, and is being actively developed (see Gen4 Energy for an example of a current design for a commercial reactor). Only approval by the Atomic Energy Commission is in the way of making these a reality.
As for performance, the original patent filing was for a reactor 1.5 meters in length, about 18-20 tons, and generates 27 megawatts of electrical energy. Even if you were to scale that down by a factor of 10, you'd still have a vehicle that could travel at any speed really, and you'd still have a ton of leftover power to add energy weapons, or whatever other electric or heat powered devices you need.
All the other answers are fantastic, but they're mostly ways to harvest a single resource, but there's a little considered aspect of the twin nuclear technologies which is criminally undersold IMO
That is that Fission reactors can produce fusionable materials, and that fusion reactors can produce fissionable materials
We don't have quite the technology to have an entirely-closed nuclear lifespan yet in the real world, but it is definitely a future feasibility, which means with a fictional efficiency improvement you could have a main reactor, which produces fuel to feed a supplementary reactor, which produces fuel for the main reactor, ad infinitum.
There would still be mass loss, from energy harvesting and byproducts (helium etc,) so you could have refuelling timelines tuned basically around the needs of the story depending on what specific tech you go with, but it would actually mean actually producing your own fuel onboard cyclically
https://iopscience.iop.org/article/10.1088/0029-5515/51/10/103011
Assume that a hydrogen fusion power generator is developed sometime in the future, the goal of massive research programs.
Assume that smaller and smaller fusion power generators are developed over time.
So there will be fusion power generators that can fit into gigantic super ships, or maybe even smaller ships, And maybe spaceships, and maybe locomotives, and maybe cars, and maybe airplanes.
And maybe those fusion power generators will power electric motors to drive those vehicles.
Or maybe those fusion power generators will power fuel production plants which make chemical fuel for engines for the vehicle. Vehicles operating on Earth could take water, or water vapor in the air, and use electricity to split it into hydrogen and oxygen, and store the hydrogen and oxygen. And when enough is stored up the vehicle will be able to burn the hydrogen and oxygen, producing water vapor and energy to power motors such as internal combustion engines or steam turbines. If the water vapor is saved it can be split into hydrogen and oxygen over and over again.
And any decent sized tank of hydrogen for the fusion generator would contain enough hydrogen to last for years, decades, centuries, or millennia.
So whether this type of vehicle used the power of the fusion generator to power electric motors, or used it to produce hydrogen and oxygen to fuel chemical motors, it couldn't operate eternally but could be made self contained as far as fuel sources were concerned for years, decades, centuries, or millennia, assuming there were no mechanical problems.
