The second law of thermodynamics is one of the most enigmatic laws of physics. It states that the entropy of an isolated system does not decrease, but why this happens has been debated for over a hundred years. This work joins a line of research seeking explanations of irreversibility in quantum dynamics. Nearby are studies on thermal equilibrium, quantum chaos, and Maxwell's demon, but this paper proposes a direct mathematical mechanism: information erasure.
The author uses a lattice model with two types of fermions interacting on the same site. The evolution is split into steps: first particles of one type move, then the other. After each step, a local operation multiplies the states by random phases, which erases information about the particle distribution. The system then evolves backward in time, and because the interference has been destroyed, it cannot return to its original nonequilibrium state.
It is proven that after a cycle of 'forward evolution, information erasure, backward evolution,' the entropy of the system increases. Specifically, the entropies of the subsystems Sτ and Sυ, as well as the total entropy S, increase compared to their initial values. This means the system has moved closer to equilibrium. The process can be repeated, and with each step the system becomes more equilibrated until it reaches maximum entropy.
This work shows that the second law of thermodynamics can be derived from quantum mechanics and information theory without additional postulates. This places quantum mechanics at the foundation of statistical physics. Unlike neighboring works that rely on numerical simulations or the eigenstate thermalization hypothesis, this paper provides a rigorous mathematical proof for a specific model, which is a step toward a more general understanding.
It may be possible to generalize the proof to a broader class of systems, including those with long-range interactions and continuous spectra. It would be interesting to explore the connection between information erasure and entanglement or the complexity of quantum states. Also promising is studying how the rate of information erasure affects the speed of thermalization.
The result could influence fundamental questions in quantum statistical mechanics and the development of quantum technologies, where controlling irreversibility is important.
Test the information-erasure mechanism in experiments on quantum simulators. Generalize the proof to arbitrary Hamiltonians with nonintegrable dynamics.
This work is directly related to the problem of justifying the ergodic hypothesis and the origin of irreversibility in quantum systems. It offers a new perspective on the link between quantum information and thermodynamics, which could help resolve long-standing paradoxes such as Loschmidt's paradox.
This section is addressed to the author of the paper and their colleagues. Neighbouring works were found by meaning-based search across our archive, not by word overlap. We do not review: we show the field around the work.
What the work does
This paper presents a mathematical proof that an isolated quantum system in any non-equilibrium state inevitably evolves toward equilibrium. The author constructs a lattice model with two types of fermions and shows how local information-erasing operations destroy the interference needed for the system to return to its initial state. The result links the second law of thermodynamics to quantum information and provides a new justification for the ergodic hypothesis.
Where its strength is
The strength of this work lies in its direct mathematical mechanism: erasing information makes reverse evolution impossible, which rigorously proves entropy growth in a specific model. This sets it apart from approaches that rely on numerical simulations or the eigenstate thermalization hypothesis.
Where it could go next
Worth trying
Why this may matter
If the information-erasing mechanism can be extended to a broader class of quantum systems, it could provide a unified explanation of irreversibility, connecting thermodynamics, quantum information, and quantum chaos.
Nearby works in our archive
The archive is sparse around this work: the closest review is only 0.55, against a usual 0.64. It looks like few have drilled nearby.
The idea that information plays a key role in thermodynamics dates back to Maxwell's demon. In this work, information erasure is not a thought experiment but a mathematically rigorous operation.
Greg Egan's novel 'Schild's Ladder' explores quantum mechanics and information, but there is no direct parallel to this mechanism.