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Any civilization requires consuming useful energy (see below). If one assumes that there still is a civilization after a billion years, where did the energy come from that was used until that time?

Collecting energy from the sun and other sources that last billions of years

Energy for millions of generations / billions of years could come from several sources.

The sun is expected to maintain roughly the same output for at least many hundreds of millions of years, probably several billion years. As long as the earth maintains its orbit and weather patterns, the sun would deposit many thousand times more energy on the earth's surface than is consumed by current civilizations. It could be harnessed directly or indirectly via biomass, wind or water.

Tidal forces caused by the moon are also expected to change little in strength over millions of years and could also serve as energy for long periods. The moon moves slowly away from the earth, its distance would be expected to increase by about 10% in a billion years due to tidal forces.

Geothermal energy from nuclear decays of radioactive elements in the earth is also expected to be only slowly reduced over the course of billions of years.

Current ways to collect these forms and turn them into useful energy are more expensive than harnessing energy from conventional sources, but not more than a factor of 2 to 10. There has been progress to make using these sources easier, and as long as materials employed can be recycled increasing knowledge will make it ever easier to collect this energy. Continuing civilizations on this planet are certainly possible from an energy perspective using these sources.

Energy collected in this way is still more expensive than currently available sources. Having abundant and easily harnessable sources of useful energy is critical to maintaining a high population density, if only for food production and distribution. Sudden reductions in population density risk causing the loss of knowledge making them irreversible. It is thus an essential task now to develop ways to make harnessing these renewable sources easy enough to maintain a large population. Stretching the other sources discussed below will extend the time available for this task.

Nuclear fusion: could last, but it is safer to assume it will be more expensive than solar

If it ever becomes feasible, energy harnessed from nuclear fusion might last for millions of years at current usage if lithium can be won from the sea or billions of years if fusion using only deuterium would become possible. Harnessing nuclear fusion for energy consumption - if it turns out to be possible - with currently conceivable technologies seems likely more expensive than energy now produced. It might turn out cheaper. Until proven otherwise it is safer - and therefore mandatory - to assume that it will be more expensive than collecting energy from the sun.

As knowledge increases better approaches might be found. The cost of energy harnessed in the future in this way (or in other ways) might therefore eventually prove to be lower, maybe even much lower. Other ways to harness useful energy might yet be found. But it is not certain that any of this will happen. A lasting civilization can not continuously gamble on uncertain outcomes in matters that endanger its survival. It is therefore mandatory to be cautionary and to assume that fusion power for energy consumption will be more expensive than collecting energy from the sun.
That our civilization must not rely on the emergence of fusion power wouldn't necessarily mean stopping all research now. But it would be safer to spend scarce resources on developing ways making collecting energy from the sun easier and leave the development of fusion power to later generations if they so choose. Fusion power is a nice ambition for future generations, it has no room in plans to make our current civilization last.

Nuclear fission: cheap thrill for a few generations at the cost of reducing future possibilities

Energy from nuclear fission has no role for civilizations lasting for millions of generations, as for energy production viable fuels would only last for a few tens of generations even with the best technologies. Such fuels would better be saved for applications where their use becomes indispensable (e.g., travel to other solar systems, if possible, must be expected to require very high energy density fuel sources). Consuming fission fuels now because they are relatively somewhat cheaper than lasting sources seems irresponsible in the light of reduced options of future generations.

Moreover, the use of nuclear technology is taking an irresponsible gamble on future capabilities with the disposal of nuclear waste. This waste could become an existential threat if there ever were a reversal in technical or economic capabilities.

The use of fossil sources is a brief event in the history of life on any planet

Fossil fuel sources such as coal, oil and gas and their variants seem limited in quantity and their combustion products, mainly CO2, seem to significantly alter the atmosphere, changing living conditions. If civilization continues their use will be a very brief event in history. Continued consumption despite of the knowledge of the limits and effects will be seen as irresponsible and must be stopped both to maintain viable living conditions in the short term and options for future generations in the long term.

Sources yet unknown

Physicists describe four fundamental interactions that can give rise to useful energy. New discoveries might open up other sources of harnessing energy differences. Reality might have more in store than physics has been able to describe up to now. Regardless of how likely one thinks that this is, the same precautionary argument as for nuclear fusion applies: a lasting civilization can not gamble on uncertain developments. Nice for future generations if this comes about. Until it is certain, one must make do with sources we know for sure are possible and will last.

Why use energy at all?

Any civilization, no matter how advanced, will require consumption of useful energy.

The second law of thermodynamics (if it describes reality correctly in this), demands that processing of information requires the equalization of energy differences. If conscious awareness requires the processing of information, as it would seems to, then the utilization of energy for other reasons will compete with existence of sentinent, self aware beings.
(That is unless there is a fundamental flaw in the way we perceive basic physics. No theory can never be proven correct, but thermodynamics has certainly proven very useful in many ways. As beating the "second law" would generate infinite profits, many attempts have been made. It seems unlikely that any will succeed in the future, so it should be assumed that any civilization, conscious awareness and happiness all require the consumption of useful energy)

Energy consumption

Energy is of course never consumed, only transformed from one type to another. The 'first law of thermodynamics' suggests that the amount of energy in the universe is a constant. But useful energy is consumed when energy differences are equalized, entropy rises. Which is meant in the colloquial "energy consumption".