Why Does Time Run Forward? A Quantum Proof Explains When Entropy Cannot Fall

The warm cup that poses a problem for quantum physics

Pour hot tea into cold water and the temperatures converge. Nobody expects the mixture, left alone, to separate itself into a hot layer and a cold one. That everyday asymmetry lies behind the thermodynamic arrow of time. Its governing rule, the second law of thermodynamics, has survived spectacular changes in physics. Yet the equations that describe individual quantum systems do not simply contain an instruction that says macroscopic entropy must rise.

In a paper published by the American Physical Society on November 3, 2026 (November 4 in Japan), four researchers associated with RIKEN, the University of Tokyo and the University of Osaka supplied a mathematically precise bridge. They defined what counts as thermal equilibrium in a quantum many-body system, which external controls count as macroscopic thermodynamic operations, and what entropy should mean at that scale. With those definitions, they derived two versions of the second law. It is an important result, but not a proof that all forms of time have been explained.

Why microscopic reversibility is not a minor technicality

A movie of a glass shattering looks natural when played forward and implausible in reverse. A movie of just a few idealized microscopic particles is different: many of their equations permit trajectories with time-reversed counterparts. Quantum dynamics is unitary for a closed system, preserving the information structure of the whole state even as observers see equilibration. How a world built from those rules produces reliable one-way behavior is not a superficial question.

The new work does not require quantum physics to cease being unitary. Instead, it asks which kinds of observations and interventions are relevant when a laboratory operator says that a system is at equilibrium and that a process is adiabatic. This distinction between every abstractly possible unitary transformation and controls an experimenter could describe in terms of a few bulk quantities is central to the result.

A century and a half of arguments about irreversibility

Thermodynamics grew alongside industrial attempts to understand engines, heat and work. Sadi Carnot analyzed heat-engine performance in the nineteenth century; Rudolf Clausius and William Thomson, later Lord Kelvin, helped formulate the second law. Ludwig Boltzmann then tried to explain thermal behavior using the statistics of innumerable microscopic constituents. His work transformed the question into one about which macroscopic states correspond to overwhelmingly many microscopic configurations.

The response was not unanimous. Josef Loschmidt objected that reversible mechanical equations permit reverse trajectories; Ernst Zermelo raised the problem of recurrence. Contemporary discussions of the time arrow still wrestle with probabilities, initial conditions and the choice of macroscopic description. The Japanese team does not declare that history over. It contributes a more specific quantum-mechanical theorem about equilibrium states and physically characterized operations in closed many-body systems.

The four researchers and the actual publication

The paper is titled “Second Law of Thermodynamics in Closed Quantum Many-Body Systems,” published in PRX Quantum, volume 7, article 043023. Its authors are Yuuya Chiba, Yasushi Yoneta, Ryusuke Hamazaki and Akira Shimizu. The institutions named in RIKEN’s announcement include the RIKEN Pioneering Research Institute, RIKEN Center for Quantum Computing, the University of Tokyo’s Institute for Photon Science and Technology, and the University of Osaka’s Center for Quantum Information and Quantum Biology.

The journal lists its publication date as November 3, while the Japanese-language joint announcement is dated November 4. Those dates are consistent across time zones. The announcement describes a theoretical derivation, not a report of a newly observed microscopic machine running backward or an experimental violation of thermodynamics.

A pure quantum state can still look like thermal equilibrium

Quantum theory calls a state “pure” when it is described as a single quantum state rather than a statistical mixture. The von Neumann entropy of the full pure state is zero. Yet extensive research on isolated quantum many-body systems has shown that certain pure states may look thermal when examined through ordinary macroscopic measurements. Thermodynamic entropy in those circumstances need not be zero.

This difference is not wordplay. If researchers identify thermodynamic entropy with the von Neumann entropy of the entire pure system, the familiar high-entropy equilibrium description disappears. And if all conceivable unitary operations are permitted, a pure state can in principle be transformed into another pure state, allowing work extraction that clashes with the usual equilibrium version of the second law. The team set out to resolve both difficulties without simply assuming the answer.

iMATE: defining equilibrium by what a large system reveals

Their first tool is a class of observables called additive quantities. Energy, particle number and total magnetization are familiar examples: dividing the system into pieces allows the corresponding contributions to be added to recover a bulk total. The researchers defined infinite-observable macroscopic thermal equilibrium, or iMATE, by requiring the expectations of all such additive observables, for the system and appropriate subsystems, to agree macroscopically with equilibrium values.

That definition includes qualifying pure quantum states. A state can retain mathematically rich microscopic information while agreeing with thermal equilibrium on the complete set of bulk quantities specified in the framework. Rather than choosing between a naive pure-state entropy and a thermodynamic description, the authors make explicit the level of description at which the comparison is meaningful.

Not every unitary transformation is a thermodynamic operation

A microscopic puppeteer imagined to control every particle individually could carry out transformations far removed from moving a piston or changing an external magnetic field. The authors restrict their thermodynamic operations to “macroscopic operations”: unitary evolution generated by Hamiltonians controlled through a finite number of external variables coupled to additive observables.

That is not a new law forbidding quantum operations in general. It is a precise model of what is meant by external, bulk-level adiabatic intervention. It also matters that “adiabatic” here refers to the thermodynamic absence of heat exchange, not automatically to the slow evolution meant by the quantum adiabatic theorem. The RIKEN announcement explicitly warns that the two uses of the word should not be confused.

First theorem: equilibrium is not a source of unlimited work

The paper first establishes a version of Planck’s principle. Start with a state satisfying iMATE, act through a cyclic macroscopic operation, and return the external control parameters to their starting values. Under the theorem’s duration condition, the system cannot yield an extensive amount of work—that is, work scaling macroscopically with its size.

This remains true even for qualifying pure quantum states. The apparent contradiction is resolved by recognizing that mathematically permitted operations on arbitrarily detailed quantum degrees of freedom are not necessarily macroscopic thermodynamic operations. The result is about a robust constraint on state transitions, not a claim that no microscopic fluctuation or infinitesimal energy change can ever occur.

Second theorem: an entropy measure that matches thermodynamics

The authors next construct what they call quantum macroscopic entropy density. Their definition uses spatial averaging of reduced quantum states over regions of fixed size and a von Neumann entropy constructed at that coarse-grained scale. For states satisfying iMATE, this new density agrees with thermodynamic entropy density even if the entire quantum system is pure.

They then consider a macroscopic operation followed by relaxation while external parameters are held fixed. Under the specified assumptions about relaxation, the quantum macroscopic entropy density cannot decrease. If the relaxed state is again thermal equilibrium, the statement reproduces the thermodynamic non-decrease law for adiabatic operations. “Increasing entropy” does not exclude equality: the precise mathematical claim is non-decrease.

The limitation that deserves a headline of its own

The strongest caveat is not hidden in the mathematics. The rigorous theorems apply to operations whose duration does not grow as the many-body system becomes larger. Real thermodynamic procedures sometimes scale in time with system size, including especially slow controls. RIKEN says that simply extending the present framework to longer-duration operations admits constructed counterexamples to the second law.

That does not mean scientists have operated a real heat engine that violates the second law. It means this particular mathematical model requires further conditions before a universal long-time statement can be claimed. Finding those conditions, and examining possible analogues with quantum simulators, is explicitly part of the group’s future program. A headline declaring that the ultimate origin of time has been solved would erase the paper’s most scientifically useful uncertainty.

Does this change the prospects for quantum computers?

Quantum computers and programmable quantum simulators offer environments in which many-body dynamics and controlled operations may be studied. A better account of how thermodynamic constraints emerge under restricted controls could eventually inform thinking about quantum devices, energy exchange and thermalization. The RIKEN release identifies quantum-system control as one potential direction.

No commercial quantum-computing performance improvement follows directly from this publication. The article is theoretical, and the proposed examination of longer-time cases is prospective. There is a considerable distance between proving a theorem in a carefully defined model, implementing a quantum-simulator test, and building a useful engineering system. Treating those steps as interchangeable would overstate the advance.

What the experimenter chooses to observe

In ordinary life we do not chart the motion of every molecule in a cooling cup. We look at a thermometer. We do not follow every spin in a magnet; we measure magnetization. Thermodynamics was built around that economy of observation long before quantum physics explained the constituents of matter. The new work makes those practical choices part of a rigorous quantum definition instead of leaving them implicit.

That is its intellectual achievement. It does not give time a birthplace, establish that all possible processes are irreversible, or remove the need to understand the universe’s low-entropy past. It shows, within a meaningful and explicitly limited set of quantum states and macroscopic interventions, why two central thermodynamic restrictions can hold without contradicting reversible microscopic dynamics. The cup of tea remains ordinary; the explanation beneath it has become more precise.