A new framework shows how lost information in quantum systems gives rise to macroscopic entropy and the arrow of time
In the macroscopic world, we see irreversible processes everywhere, heat flowing from hot to cold, gases mixing, systems decaying. Yet at the microscopic level, quantum mechanics is perfectly reversible, with its equations running equally well forwards and backwards in time. How then, does irreversibility emerge from fundamentally reversible dynamics?
A common explanation is coarse-graining, which simplifies a complex system by ignoring microscopic details and focusing only on large-scale behaviour. To make the micro–macro divide precise, however, one must first define what “macroscopic” means. Here it is given a quantitative inferential meaning: a state is macroscopic if it is perfectly inferable from the perspective of a specified measurement and prior. Central to this framework is a coarse-graining map built from the measurement and its optimal Bayesian recovery via the Petz map; macroscopic states are precisely its fixed points, turning macroscopicity into a sharp condition of perfect inferability. This construction is grounded in Bayesian retrodiction, which infers what a system likely was before it was measured, together with an observational deficit that quantifies how much information is lost in forming a macroscopic description.
States that are macroscopically inferable can be characterised in several equivalent ways, all tied to to a new measure of disorder called macroscopic entropy, which captures how irreversible, or “uninferable”, a macroscopic process appears from the observer’s perspective. This perspective is formalised through inferential reference frames, built from the combination of a prior and a measurement, which determine what an observer can and cannot recover about the underlying quantum state.
The researchers also develop a resource theory of microscopicity, treating macroscopic states as free and identifying the operations that cannot generate microscopic detail. This unifies and extends existing resource theories of coherence, athermality, and asymmetry. They further introduce observational discord, a new way to understand quantum correlations when observational power is limited, and provide conditions for when this discord vanishes.
Altogether, this work reframes macroscopic irreversibility as an information-theoretic phenomenon, grounded not in a fundamental dynamical asymmetry but in an inferential asymmetry arising from the observer’s limited perspective. It offers a unified way to understand coarse-graining, entropy, and the emergence of classical behaviour from quantum mechanics. It deepens our understanding of time’s direction and has implications for quantum computing, thermodynamics, and the study of quantum correlations in realistic, constrained settings.
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Focus on Quantum Entanglement: State of the Art and Open Questions guest edited by Anna Sanpera and Carlo Marconi (2025-2026)
