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Thermodynamic Irreversibility from Inaccessible Endogenous Quantum Histories

This paper demonstrates that thermodynamic irreversibility in isolated finite systems arises not from the loss of microscopic information, but from the failure of hidden quantum histories to organize into coherent currents capable of restoring macroscopic order, a process that can be reversed only when dynamics are engineered to concentrate these return-oriented currents.

Original authors: Borhan Ahmadi

Published 2026-09-04

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Borhan Ahmadi

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

At the heart of physics lies a deep and enduring puzzle about time. On the smallest scales, the laws governing atoms and particles are perfectly reversible; if you were to film a single electron moving and play the movie backward, the motion would look just as natural and physically valid as the forward version. Yet, in our everyday world, time has a strict direction. Heat flows from hot to cold, eggs break but never un-break, and systems left alone tend to become more disordered. This one-way street is described by thermodynamics, specifically the concept of entropy, which measures disorder. For over a century, scientists have struggled to explain how this irreversible flow of time emerges from microscopic laws that do not care about direction. The standard explanation suggests that we simply lose track of the tiny details as things get bigger, but this paper challenges that view by asking a sharper question: if the microscopic information is never actually lost, why does it fail to organize itself to reverse the disorder?

The researchers, led by Borhan Ahmadi at the University of Gdańsk, investigated this by looking at a closed quantum system—a collection of particles isolated from the outside world, evolving according to the strict rules of quantum mechanics. In such a system, no information is ever truly destroyed; the microscopic state of every particle is preserved perfectly. However, when we observe the system, we usually only see a coarse, blurry picture, such as how many particles are in the left half versus the right half, rather than the exact position and momentum of every single one. This blurry picture is called a "thermodynamic record." The team wanted to understand what happens to the hidden, microscopic details that our record cannot see. Do these hidden details just sit there, or do they actively influence the future of the system?

To find out, the team developed a precise mathematical framework that separates the future behavior of the system into two parts. The first part is what you would predict if you only knew the current blurry record and assumed the hidden details were completely random. The second part is a correction term that accounts for the specific, hidden structure of the microscopic state. They discovered that the hidden structure is not passive. It generates "currents" that push the system's state forward. Crucially, they found that the prediction based solely on the blurry record cannot explain any immediate change in the system; the entire instantaneous motion comes from these hidden currents. This means that the direction in which the system moves—whether it becomes more disordered or more ordered—is determined entirely by how these hidden currents are organized by the underlying physics.

The study then tested this idea using computer simulations of different types of quantum chains, which are like rows of interacting particles. In one scenario, they used a "mixing" Hamiltonian, a set of rules that causes the particles to interact in a complex, chaotic way. In this case, the hidden currents were active and constantly changing the system, but they were scattered across many different frequencies, like a crowd of people shouting in different directions. Because the currents were so spread out, they canceled each other out on a large scale, and the system continued to become more disordered, with entropy rising steadily. The hidden information was present and active, but it failed to organize itself to reverse the trend.

In a second scenario, the researchers deliberately changed the rules of interaction to create a "commensurate" system, where the energy levels of the particles are tuned to match each other in a specific way. Here, the hidden currents did not scatter; instead, they synchronized. The microscopic details began to march in step, creating a powerful, coordinated flow that pushed the system back toward a state of low disorder. In this engineered setup, the system successfully reversed its thermodynamic history, returning to a state of high order without any information being lost or magically restored. The researchers measured this return and found that the system could indeed reconstruct a low-entropy macrostate, proving that the failure to reverse in the first case was not due to a lack of information, but a lack of organization.

The paper concludes that thermodynamic irreversibility is not the result of information being lost or destroyed. Instead, it is the result of hidden microscopic information failing to organize itself into a coherent flow that can restore order. In the mixing scenario, the information remains present but is too disorganized to drive a reversal. In the engineered scenario, the same information is perfectly organized to drive a reversal. This distinction holds true even in classical systems, suggesting a universal principle: the arrow of time is not fixed by the loss of data, but by the inability of that data to coordinate a return. The researchers also showed that while the entropy of the system generally increases, the hidden structure can remain dynamically active without ever causing a macroscopic return, a state they confirmed through rigorous tests of probability distributions.

This work clarifies a fundamental tension in physics by showing that the microscopic world never forgets, but it often fails to remember how to put things back together. The study does not claim that time travel is possible or that entropy can be reversed in any random system. Rather, it demonstrates that the conditions for reversal are specific and depend on how the microscopic details are arranged. By isolating the exact contribution of hidden structure, the team provided a clear picture of why some systems relax into disorder while others, under the right conditions, can reassemble themselves. The findings suggest that the "arrow of time" is a property of how information is organized, not a property of information being lost.

Technical Summary: Thermodynamic Irreversibility from Inaccessible Endogenous Quantum Histories

Problem Statement
The foundational tension in statistical mechanics lies in reconciling the preservation of fine-grained information under microscopic unitary dynamics with the emergence of a preferred thermodynamic arrow of time (entropy increase). While reversible laws permit entropy-lowering trajectories, isolated finite systems typically exhibit robust thermodynamic relaxation. The central question addressed is: Why does information hidden from a restricted thermodynamic record usually fail to reconstruct a low-entropy macrostate? Specifically, the paper investigates how microscopic structure, absent from the current macroscopic record, generates the instantaneous motion of that record and under what conditions this motion organizes into a thermodynamic return (entropy decrease) versus continued relaxation.

Methodology
The author analyzes a single isolated quantum system evolving under a fixed Hamiltonian, viewed through a fixed projective thermodynamic record. The methodology relies on an exact decomposition of the system's state and dynamics without invoking baths, stochastic interventions, or information-erasing mechanisms.

State Decomposition: The exact microscopic state $\rho_t$ is split into a thermodynamic representative $G[\rho_t]$ (uniform within each macrospace, preserving current record probabilities) and a residual $\chi_t$ containing all unresolved microscopic structure.
Finite-Step Propagation: The future macrodistribution $p(t+\tau)$ $p (t + τ)$ is derived exactly as the sum of two terms:
- $K(U)(\tau)p(t)$ : The evolution predicted solely from the current record (assuming the state is the macro-uniform representative).
- $r(t, \tau)$ : The exact correction driven by the unresolved residual $\chi_t$ .
Spectral Resolution: The author resolves the instantaneous currents between macrospaces spectrally. They decompose current power into contributions from energy gaps, distinguishing between transitions with unique gaps and those with degenerate gaps that can interfere coherently.
Ordering Tests: To distinguish between mere entropy generation and true thermodynamic return, the paper employs relative majorization (using generalized Lorenz curves) to test if the macrodistribution has left the class of multiplicity-preserving contractions.
Model Systems: The framework is tested on interacting hard-core and Bose–Hubbard chains, a 2D lattice, and number-conserving Floquet dynamics. Both "mixing" Hamiltonians (disordered spectra) and "engineered" Hamiltonians (commensurate spectra) are compared.

Key Contributions

Exact Finite-Step Decomposition: The paper establishes that for any finite time step, the record-only contribution to entropy change is second-order in time ( $O(\tau^2)$ ), meaning the instantaneous entropy rate is entirely driven by the hidden residual $\chi_t$ . This isolates the "hidden currents" as the sole source of instantaneous thermodynamic motion.
Spectral Organization of Return: It demonstrates that thermodynamic return is not merely the presence of hidden information, but the organization of that information. Transitions with identical energy gaps add coherently. The paper introduces a spectral metric ( $\Gamma_{spec}$ ) showing that engineered dynamics can concentrate current power into a few synchronized gap channels, whereas mixing dynamics spreads it over many frequencies.
Separation of Hidden Activity and Return: The author defines a regime where microscopic information remains dynamically active ( $\epsilon_{hist} > 0$ , indicating the record is not closed) yet fails to produce thermodynamic return ( $V_\pi = 0$ , indicating the distribution remains within the contraction order). This clarifies that hidden information does not automatically lead to entropy decrease.
Classical Counterpart: An exact classical measure-preserving counterpart is derived, showing that the finite-step contraction-residual structure is not uniquely quantum, though the specific short-time quadratic onset of transitions between orthogonal macrospaces is a quantum feature.

Results

Mixing vs. Engineered Dynamics: In mixing systems (e.g., interacting chains with non-degenerate gaps), the hidden currents are spread across many frequencies. The entropy rate remains positive, and no distributional return is detected, even though the hidden structure is dynamically active. In contrast, engineered commensurate controls concentrate current power into synchronized channels, allowing the hidden currents to overcome entropy-spreading contributions and reconstruct a low-entropy macrostate.
Entropy Rate vs. Distributional Order: The study confirms that a positive instantaneous entropy rate ( $\dot{S}_R > 0$ ) can persist even when the distribution leaves the strict relative-majorization contraction order, though a negative entropy rate requires leaving that order.
Dilute Limit Consistency: The models converge to the correct classical free-expansion entropy endpoint in the dilute limit, validating the thermodynamic consistency of the record-based entropy definition.
No Global Monotonicity: The results confirm that for finite systems, global monotonicity of record entropy is not guaranteed; return is possible if the microscopic dynamics organizes the currents appropriately.

Significance and Claims
The paper claims to resolve the dynamical question of how microscopic structure generates the instantaneous motion of a thermodynamic record. Its primary assertion is that thermodynamic irreversibility is not the loss of microscopic information, but the failure of that surviving information to organize currents that restore macroscopic order.

The author emphasizes that the "arrow of time" in this context is determined by the specific Hamiltonian's ability to organize the hidden currents relative to thermodynamic affinities. They do not claim a universal spectral criterion for irreversibility or global monotonicity for all times. Instead, they provide a precise, exact framework for distinguishing between mixing (entropy generation) and organized return within finite observation windows, demonstrating that the same thermodynamic record can exhibit relaxation or return depending entirely on the microscopic organization of the underlying dynamics. The work serves to sharpen the distinction between the definition of thermodynamic entropy and the explanation of its dynamical increase.

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