- A quantity proportional to the logarithm of the number of microstates corresponding to the macrostate of a physical system.
- A measure of the irreversibility of the process by which energy spreads and differences are consumed.
- In the political language of the late galaxy, the term came to mean every loss that could not be reversed.
Galactic civilization did not perish simply because the total amount of energy became insufficient. It perished because energy had spread too evenly. Heat flowed from hot places to cold ones, and that flow was the driving force of civilization. Civilization spoke of consuming energy, but it never actually destroyed energy. It converted starlight into electricity, used electricity for computation and motion, and in the end dispersed it as low-temperature heat. What was consumed was not energy but difference: the difference between a star and cold space, between compressed matter and vacuum, between remembered information and random noise. Life was a structure that existed briefly while those differences flowed. The same total amount of energy remained as before, but there was no longer anywhere for it to flow.
Early galactic civilization understood entropy as a waste problem. It radiated heat from power facilities beyond planets, moved computing facilities to colder worlds, and discarded energy from overheated star systems into space. To maintain order in one region, it increased disorder in another. The galaxy was vast, and cold space seemed endless. Even as settlements multiplied, the places available for dumping waste did not seem to diminish. The universe was still immense. The problem was that civilization had connected every place through wormholes. Heat released in one star system reduced the cooling capacity of another, and waste heat discarded far away arrived thousands of years later in the skies of new settlements. Civilization had assumed that there would always be somewhere to throw things away, but a connected civilization had no outside. More cooling facilities were built for the sake of cooling. Cooling facilities could not eliminate heat; they could only move it to places of lower temperature. Moving heat also required energy, and that energy became heat as well. The more civilization processed waste heat, the more waste heat it produced. Supermassive AIs used cold regions far from stars as computing sites. Heat generated by computation was released into shielded space. As the volume of computation increased, those shielded regions also warmed. To obtain lower temperatures, computing sites moved toward the outskirts of the galaxy, and new wormholes were installed to eliminate communication delays. The maintenance costs of those wormholes became heat again. Efficiency continued to improve. The energy required for one unit of computation fell to billionths of what it had once been. At the same time, the number of computations being performed increased by a factor of trillions. None of the saved energy remained unused. It became the justification for computations that had once been impossible. Every citizen was granted the right to calculate possible versions of their own life in advance. The probability that a disease would not occur, that an accident would not happen during travel, and that a restored memory would not differ from the original were all calculated. Whenever a possible danger was found, new futures in which that danger had been avoided were calculated again. Civilization burned the present in order to know the future.
Thermodynamicists had known the ending for a long time. The entropy of an isolated system does not decrease. Local order can be created, but creating that order produces greater disorder in the surroundings. The moment the entire galaxy became the inside of civilization, there was no longer any nearby region that could be called the surroundings. Instead of saying that the galaxy would perish, they said that the long-term conversion rate of available energy was declining. Because a single star took billions of years to go dark, no generation felt itself to be the last. Every age had its crises, but science and technology could simply pass them on to the next generation. After fusion came stellar mining; after stellar mining came rotational-energy extraction; after that came black-hole accretion and quantum-vacuum engineering. Each new technology opened a larger reservoir than the one before it. Every time civilization discovered a new fuel, it grew to a scale that could not be maintained without that fuel.
Black holes were the last reliable source of energy. Matter could be dropped into them to obtain light, their rotation could be slowed to perform work, and in the far future even Hawking radiation could be recovered. At one time, calculations suggested that a single black hole could sustain the civilization around it until the final night of the universe. But those calculations did not include the growth rate of the civilization managing the black hole. Once black-hole power networks were completed, cheap energy produced more wormholes and larger computational systems. Even small settlements on the galactic outskirts were equipped with independent black-hole backup power sources. Generators that were never actually used maintained their rotational states for emergencies, and the equipment monitoring those states released new heat into the surrounding space.
After the photon deficit began, entropy research moved in a new direction. If the missing energy was not being converted into heat, the deficit might actually cool the universe. Some researchers interpreted the phenomenon as a natural form of cooling and argued that if unusable waste heat were escaping from the system, it might extend the lifespan of civilization. Early measurements gave them hope. The deficit appeared even in low-energy thermal radiation. If some of the heat disappeared from a warming universe, temperature differences could be recreated. The photon deficit was announced not as a sign of extinction, but as a process by which the galaxy was expelling its own entropy. That year, energy use across the wormhole network rose sharply. The belief that waste heat was disappearing had removed the limit imposed by cooling costs. Suspended stellar-engineering projects resumed, and supermassive artificial intelligences that had been placed on hold were activated. Tourist routes that had once been impossible because of heat opened near the galactic center.
The deficit gave civilization confidence that it did not need to change itself. But the measurements were soon revised. The deficit did not occur only in unusable waste heat. Short-wavelength light newly emitted by stars and rotational energy extracted from black holes also showed losses while passing through the power network. The magnitude of the deficit varied according to the type and path of the energy, but the hope that only waste heat was disappearing could no longer be maintained. Civilization converted, transmitted, stored, and traded the same energy countless times. The more energy flowed, the more opportunities there were for it to be lost. While usable energy disappeared, the heat left behind by using that energy continued to accumulate in the universe.
The last scientist did not choose what kinds of energy would arrive in the storage space. The outflow of energy had begun long before he was born, and hot light, low-temperature radiation, and energy that had passed through power networks were all flowing out along different paths. He could not trace those flows backward and select particular energy from the past. Only after completing the storage space could he determine whether some of what had already escaped still retained differences capable of doing work. Whatever possibility could be left to the future depended on those differences.
Inside the storage space, energy barely flowed. Because internal time passed slowly, the approach to thermal equilibrium appeared almost to stop. Energy at different temperatures and densities was preserved separately. While billions of years passed outside, the storage space remained in its initial state. It was not a device for storing energy so much as a device for postponing the increase of entropy into the future. Measuring the state of incoming energy, sorting it by type, and maintaining order inside required computation. Computation produced heat. The last scientist could not eliminate that heat, nor could he send it back to the galaxy of the past. The storage space had to keep even the waste heat it generated within itself. For that reason, a waste-heat zone was created in the deepest part of the storage space, where time passed faster than in the rest of it. The entropy generated during classification was concentrated there. Most of the storage space remained at low entropy, while a small region aged at an almost unimaginable rate. The garden intended for future life contained an invisible landfill.
The civilization of the past knew nothing of this structure. All it observed was that usable energy was disappearing at an ever-increasing rate. Stars dimmed faster than expected, and black holes lost their spin faster than calculations predicted. Even when more energy was supplied, the share available to civilization continued to shrink. Civilization improved efficiency. Greater efficiency allowed more work to be done with the same amount of energy. Once more work became possible, facilities that had been shut down were restarted, and new lives, memories, and routes were added to what had to be maintained. Improvements in efficiency extended civilization’s lifespan, but increased its scale even faster. Entropy was the cost that appeared in a new form each time technology succeeded.
The galaxy’s final conservation policy was to integrate the lives of all citizens into the same computational space. The plan was to eliminate duplicated bodies, cities, and planets and continue consciousness with the minimum possible energy. Countless star systems were physically closed, and people moved into enormous simulated worlds. Material travel declined, but computation exploded. Each consciousness required a complete sensory world and memories of the past in order to maintain confidence that it truly existed. Sharing a single world would have reduced the computational load, but it limited the right to choose different lives. To preserve that right, countless worlds were run in parallel. The galaxy gave up bodies, but preserved possibilities.
By the time the last stars were dimming, civilization still possessed vast amounts of energy. It was spread throughout the universe as low-temperature radiation and remained in the mass of stopped machines, cooled planets, and black holes that had lost their spin. In terms of total quantity, it was not very different from the early galaxy. Yet nothing could be started with that energy, because nowhere did enough difference remain. By then, energy that had escaped over immense spans of time had accumulated in the future storage space. Some of it had already spread as heat, while some still retained the form of light from young stars, rotating mass, and chemical differences that had not yet been consumed. The last scientist preserved those differences separately so that they would not all disappear. Whether they were enough for new stars and life was impossible to know. From the total amount of stored energy alone, the last scientist could not prove that life would be born. Even if matter gathered again and stars formed, there was no way to know whether beings capable of reproducing themselves would emerge there. There was no reason for them to be human, or to remember humanity. What he left behind was not the correct answer to a calculation about the future. It was the possibility that, hundreds of millions of years later, other matter might develop senses and look at the stars.
By the time the last scientist completed the storage space, galactic civilization was already close to extinction. He could not recover the time that had vanished, but he left a place where energy whose destination had been unknown could gather before it was completely dispersed. The last scientist did not reverse that flow. He tried only to preserve the differences that still remained within the energy that had already flowed out. That act did not save the civilization of the past, nor did it guarantee life in the future. What exhausted the galaxy were the correct decisions civilization had made over a very long time in order to preserve itself. The last scientist merely saw what remained after those decisions.