Food webs and energy pyramids are basic middle school science. Literally all life requires an energy source to continue to function. This is because life is essentially an energy transfer system where by kinetic (light, motion, sound, heat, etc) and potential energy (chemical) are transfered back and forth. This system requires a constant input of new outside energy.
Or a store of old energy that has not yet been depleted. On Earth, crustal chemosynthetic bacteria and archaea that live in basalt have some pretty exotic metabolic pathways, and in some cases have access to stores of energy that are substantial enough to possibly stretch past the lifetime of the surface biosphere. (It is not clear if the reactions involved can be sustained for long once the Earth is no longer capable of supporting surface water, and plate tectonics, however.) In other real locations (e.g. Io for a dramatic case), tides and related orbital processes can produce heating over long enough periods to be relevant for life.
This doesn't even begin to get into fantasy world issues. If souls are a renewable resource, then the torturing of souls may also be a renewable energy resource, for an example that might even be relevant to stock DF. Remnant energy from the creation of the world(s) may manifest in many ways.
If the god(s) have access to other realms, the concept of the "world" as being a closed system may be seriously inadequate. To somewhat mangle a classic D&D take on things, if powerful entities can tap into the potential difference between the positive energy plane, the prime material plane, and the negative energy plane, reserves of energy that dwarf that of fusion may be available. To use an unnecessarily dwarven take on things, what about a small Stirling engine, with a tiny portal to the Elemental Plane of Fire as the heat source, and a tiny portal to the Elemental Plane of Ice as the heat sink; said engine turns a prayer wheel, which provides psychic energy that allows a god to perform "miracles", which may include acts that seemingly reverse local entropy gradients, create or destroy matter or energy, and in extreme cases violate causality.
Consider, for a moment, a legend from our world; the amount of energy necessary to manifest "ex nihilo", from nothing, enough bread and fish to feed 5,000 men plus an unknown number of women and children. To heavily over-simplify a minimum number, let's figure on 1/3 of daily minimum calorie requirements ("one meal") for the stated men alone; that's 1,800 kcal (UN standard) / 3 * 5,000 = 3,000,000 kcal ~ 1.2 x 10^10 joules. This is pretty close to the energy released by the explosion of 3 tons of TNT, and we've been consistently using the smaller numbers in our Fermi estimation; the number could be easily be several times that within the context of the legend, and the energy needed to actually create the mass of the food by direct application of m = E/c^2 would be dramatically higher yet (1). Still, even with the utter minimum number, it'd represent a heck of a fireball if that energy was being used by someone more warlike
It is even possible that what is perceived as the "world" is merely a simulation, with somewhat arbitrary and possibly whimsical parameters set without regard to conventional physical law, by incomprehensible entities operating several tropic and conceptual levels above reality as can ordinarily be perceived...
ETA:
(1) Assuming again we need 1,800 / 3 = 600 kcal; barley bread is 282 kcal / 100 g; tilapia (Galilaea tilapia is one likely fish given the setting) without skin, bones, and pin bones is 128 kcal / 100 g; usable ratio of edible fish to starting fish mass is between 30% and 37% (call it 1/3) and we want a 5/2 ratio. So that's 428 kcal of bread = 152 g, plus 171 kcal of edible fish = 134 g of edible fish * 3 = 402 g of total fish. So, roughly 550 g of food * 5,000 men = 2,750 kg of food * 9.0 * 10^16 joules/kg ~ 2.5 * 10^20 joules. For comparison, this is well over 1,000 times the energy of the largest nuclear bomb ever detonated; over 300 times the energy released by the eruption of Krakatoa; about 5 times the energy released in an entire day by a hurricane (note that only 1/400 or so of that is the obvious wind, most of the energy is used in producing rain); or about 24 minutes worth of the total solar energy striking the entire earth. Swords into plowshares is harder than it looks