In the quantum world, a fact becomes objective when its value is imprinted on many independent fragments of the environment, like a notice posted on hundreds of bulletin boards across the city. Each copy alone adds no new information, but it changes the rules of the game for anyone trying to erase that information.
The authors considered a cloud of records entropy and divided it into blocks that cannot be controlled jointly. They found that erasing information at a fixed temperature costs a local controller more work than a global one. The difference is exactly equal to the energy of thermal motion of particles multiplied by a measure of statistical dependence between blocks. This extra cost is called the thermodynamic charge of factuality.
The magnitude of the charge depends on the access architecture. One person sees all the bulletin boards at once, while another sees only one. To erase a record, the second person must visit each board individually, and each extra step costs energy. Thus, redundancy of records becomes a measurable resource — work that can be calculated in joules. The study does not change quantum mechanics but points out the thermodynamic consequences of how access to information is structured.
as written by the authors arXiv:2608.05753v1
Objective facts in quantum Darwinism are values recorded redundantly in many independently accessible fragments of the environment. Redundancy does not create additional logical information, so its thermodynamic meaning has remained unclear. We show that it creates an exact work asymmetry between controllers with different access architectures. For a record cloud $$F$$ and a partition $$\mathcal{P}$$ into blocks that cannot be jointly controlled, the reversible isothermal erasure penalty relative to a global controller is $$k_{\mathrm{B}}T$$ times the partition total correlation. If the source event $$X$$ is supplied as catalytic classical side information, subtracting the corresponding penalty gives the source-loss law $$\mathcal{F}_{\mathcal{P}}^{T}=k_{\mathrm{B}}T\left[\sum_{B\in\mathcal{P}}I(X{:}F_B)-I(X{:}F)\right]$$. We call this the thermodynamic factuality charge. It ranges from $$-k_{\mathrm{B}}T H(X)$$ for perfect secret sharing to $$(|\mathcal{P}|-1)k_{\mathrm{B}}T H(X)$$ for perfect broadcast objectivity. Its normalized form defines a thermodynamic record number between $$0$$ and $$|\mathcal{P}|$$. We derive Landauer--Darwin bounds, endpoint-rigidity certificates, exact growth and partition-refinement laws, spectrum-broadcast saturation, and closed formulas for noisy classical and quantum collision models. The theory does not modify quantum mechanics or posit objective collapse; it identifies the thermodynamic resource generated by redundant records under restricted control.
The thermodynamic charge of factuality can take negative values: this corresponds to perfect secret sharing, where knowledge is distributed so that no single fragment reveals the whole picture.