Entropy, Cosmology, and the Illusion of Objectivity (GPT5.2)

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Entropy, Cosmology, and the Illusion of Objectivity

In physics, entropy occupies an awkward position in our conceptual furniture. In classical laboratory thermodynamics it behaves like a solid citizen: measurable, predictive, monotonic. Yet at a foundational level it is disturbingly slippery. Its definition depends on how we partition the world into macrostates, and that partition depends on which variables we choose to treat as salient. Change the coarse-graining and the entropy changes with it. There is nothing in the microscopic laws that tells us which description is the right one.

This dependence is not a minor technical blemish; it is structural. Entropy is not a property of a system simpliciter, but of a system under a description. Phase space does not come pre-tiled into macrostates. We impose the tiling, guided by stability, locality, and practical decoupling, and are rewarded—remarkably—with thermodynamics that works.

That said, this freedom is not the whimsical licence of bored physicists inventing macrostates at will. The macroscopic variables that dominate thermodynamics—temperature gradients, pressure differences, chemical potentials, free energy flows—are not arbitrary inventions. They are forced upon us by the structure of interactions in large systems: by locality, by short-range forces, by equilibration timescales, and by the existence of robust collective degrees of freedom. These quantities are not fundamental, but they are inevitable. Any coarse-graining that ignores them fails to track anything dynamically stable.

Cosmology, however, seems to resist even this qualified deflationary reading. The early universe was in an extraordinarily special state. Smooth, homogeneous, and gravitationally far from equilibrium, its initial state lay in a tiny region of the space of possible cosmic configurations. This fact is not conventional or observer-relative. It is written into the cosmic microwave background, into structure formation, into the very possibility of stars, chemistry, evolution, and life. Persistent free-energy gradients arise because matter began in a configuration from which gravitational clumping could only increase.

This appears to restore objectivity to entropy. But the restoration is only partial, and it comes at a price.

What is objectively fixed is not a unique entropy value, but a severe boundary condition. Almost any physically serious coarse-graining—any description that respects gravity, locality, and the relevant degrees of freedom—agrees on the essential ordering: the early universe was vastly “lower entropy” than the present one. The universe began in a configuration so special that all reasonable measures point in the same direction.

In this sense, the Past Hypothesis is real in a way entropy itself is not. It is an objective fact about the initial state of the cosmos, not a uniquely defined state variable attached to it. Entropy functions as a bookkeeping device that becomes indispensable once that fact is granted. It tracks the unravelling of an initial condition whose improbability is the deep mystery.

The arrow of time, then, is not imposed by entropy; entropy records it. The universe does not come equipped with a canonical entropy functional. What it comes with is a remarkably ordered beginning. History, complexity, and life unfold because of that beginning, not because entropy was ever a fundamental property written into the laws.

Entropy feels objective because the initial condition was brutally asymmetric. The miracle is not that entropy depends on description. The miracle is that, given how the universe started, it scarcely matters which sensible description we choose.

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