The Large Hadron Collider has spent more than a decade pushing the limits of known physics by smashing protons together at energies that once existed only in the first instants after the Big Bang. These collisions tear open the interior of the proton and expose the hidden landscape of quarks and gluons that normally remain confined. The immediate aftermath of each impact has the character of a microscopic firestorm. Dense fields of gluons multiply and interact with rising intensity. Quark pairs appear and vanish. Cascades spread outward in a rapid chain of branching processes. The interior of the proton enters a regime where the number of possible microstates grows sharply. Once the storm relaxes, the debris cools and stabilizes into a stream of ordinary hadrons that spread out into the detector. The early stage and the late stage have little in common when viewed through the lens of complexity, density or microscopic structure. The partonic phase is volatile and unpredictable while the hadronic phase appears comparatively calm and familiar. Yet both phases share a property that has become one of the most intriguing findings emerging from new analyses of LHC data.
In both stages, the entropy of the system remains the same. The number of accessible informational configurations in the initial cloud of quarks and gluons matches the number associated with the outgoing hadrons. This outcome has now been confirmed with a generalized dipole model developed by researchers at the Institute of Nuclear Physics of the Polish Academy of Sciences. The team, led by Prof. Krzysztof Kutak with contributions from Dr. Sandor Lokos and earlier work involving Dr. Pawel Caputa, compared a wide range of LHC multiplicity distributions with predictions derived from a new extension of the dipole picture. The result reveals a stable correspondence between the high energy parton evolution and the final state particle count, even across energy ranges spanning from 0.2 TeV up to the full 13 TeV capability of the collider.
The underlying issue goes far beyond fitting particle counts. Entropy is a measure that reflects the total number of microscopic configurations available to a system. In the context of proton collisions, this involves counting the variety of possible arrangements of the quark gluon cloud at the moment of maximum density and then counting the arrangements of the produced hadrons once the system cools. There is no obvious reason for these two values to coincide. The early partonic stage involves a proliferation of virtual gluons, soft emissions and complex cascade processes that expand the configuration space dramatically. The hadronic stage contains fewer degrees of freedom. It involves stable or semi stable composite particles that no longer replicate the turbulent internal landscape of the proton at high energy. The system has changed character, yet the entropy remains fixed. This is the central point that drives the interest in the new analysis.
Quantum mechanics imposes strict rules on the evolution of any closed system. One of these rules is the principle of unitarity. This requirement ensures that the sum of all possible quantum probabilities remains constant and that no information can vanish or appear spontaneously. When applied to proton collisions, unitarity places a constraint on how the partonic state evolves as it undergoes successive splittings. The LHC now provides enough data to check how strictly the system adheres to these rules. The new findings show that the informational content encoded in the initial parton distribution is carried forward into the final hadron distribution with no measurable deviation. In other words, the collision rearranges the system but does not erase its informational footprint. This requires a level of correlation between the earliest moments of the collision and the last step of hadronisation that few expected to observe so clearly in real data.
One reason this result attracts attention is the extreme non linearity of the gluon dominated phase. At high energies, the proton wavefunction contains a rapidly rising number of small x gluons. These gluons interact through branching and recombination processes governed by QCD evolution equations. The traditional models used to describe this include dipole based formalisms and the Balitsky Fadin Kuraev Lipatov framework. The new generalized dipole model incorporates an additional parameter tied to the conformal weight found in studies of quantum complexity. This adjustment allows the model to account for a broader set of subleading effects that become important when the number of produced hadrons is low or when the partonic evolution deviates from the simplest theoretical picture. When confronted with LHC measurements across experiments such as ALICE, ATLAS, CMS and LHCb, the generalized model reproduces the entropy pattern in a way that the older formulations could not.
The fact that the generalized model maps so closely to the observed data implies that the partonic system follows a highly constrained trajectory. Even when the proton interior becomes densely populated with gluons, the system evolves as if guided by constraints originating from quantum information theory rather than random fluctuations. The connection to Krylov complexity, introduced in the theoretical studies that preceded this work, adds weight to the idea that QCD at high energy shares structural features with other strongly interacting quantum systems. The parton cascade spreads through a space of operators in a manner that resembles the spread of complexity in quantum many body systems. Yet as the system approaches the cooling stage, the number of effective degrees of freedom drops sharply. Despite this change, the informational measure matches the early stage. The process seems to respect a deeper rule that maintains the informational load from start to finish.
Another piece of the puzzle comes from earlier work suggesting that the proton reaches a state of near maximal entanglement at high energy. This is based on the observation that the distribution of partonic microstates becomes almost uniform in the small x regime. The system begins to resemble a fully mixed state where every configuration is equally likely. In such a scenario, the entropy grows proportionally to the logarithm of the average multiplicity. The new study confirms that the hadron distributions follow the same pattern. It is this consistency that strengthens the interpretation that the outgoing hadrons carry a direct imprint of the initial quantum state of the proton. If the proton is maximally entangled before the collision, the debris field inherits that property after the collision.
There are several ways to interpret this unusual correspondence. One perspective is that the initial state partons are already carrying the full amount of entropy permitted by the system at the relevant energy. Because the partonic cascade cannot increase the entropy beyond this upper bound, the final hadrons reflect the same count. Another perspective is that the hadronisation process behaves as a form of reorganization rather than erasure. Instead of eliminating degrees of freedom, it redistributes them into composite particles whose multiplicity structure mirrors the original entanglement pattern. In both cases, the system preserves its original informational signature even when its internal composition undergoes radical change.
This prompts new lines of inquiry. Heavy ion collisions have long been studied for their potential to form quark gluon plasma, a state of matter that existed in the early universe. Proton proton collisions were not expected to exhibit any analogous conservation of informational structure. Yet the new findings show that even in the smallest systems, the informational flow remains intact. If this property holds under all high energy interactions, it may point toward a broader principle governing the behavior of quantum fields under extreme conditions. The proton may function as an information preserving object even when its constituents become strongly correlated and chaotic.
The implications extend into other areas of theoretical physics. The conversation surrounding black hole evaporation and the fate of information in gravitational collapse has anchored debates about the foundations of quantum theory for decades. In that context, unitarity is essential for resolving contradictions between general relativity and quantum mechanics. The new results from the LHC provide an example of unitarity in action within a system that is far more accessible to experiments. While proton collisions differ fundamentally from black holes, the underlying principle remains the same. The system evolves under strict informational constraints. It cannot erase what it started with.
The new experimental confirmation encourages additional tests. Once the LHC completes its next upgrade, the ALICE detector will have the capability to probe gluon densities in regions that have not yet been accessed. These regions may reveal new structures or deviations that do not appear at the current energy scale. If there is any stage where entropy begins to shift away from the observed correspondence, it is likely to appear in the densest part of the gluon field. This would provide a clear signal of new physics. Conversely, if the entropy match continues to hold, it would reinforce the idea that the informational structure of the proton is far more rigid than previously assumed.
Another opportunity comes from the Electron Ion Collider currently under construction at Brookhaven National Laboratory. Unlike proton proton collisions, electron proton collisions isolate the structure of a single proton without overlapping contributions from two complex systems. Electrons act as clean probes because they are elementary. By removing one of the proton wavefunctions from the equation, researchers can study how the internal entanglement evolves when subjected to a single pointlike interaction. If the entropy pattern matches the results from proton proton data, it would support the view that the proton’s informational characteristics are inherent rather than emergent. If it diverges, the deviation may highlight new interactions or hidden phases of quantum matter.
The theoretical community will also play a central role in exploring these questions. The generalized dipole model is only one step toward a more complete picture. Recombination, saturation and other non linear effects may require further refinement. The model’s connection to conformal symmetry and quantum complexity suggests that high energy QCD may share deeper mathematical structures with other fields that are not traditionally associated with particle physics. Understanding these links could uncover new insights into how information propagates in quantum systems that are far from equilibrium. It could also inform the development of future experiments designed to isolate specific aspects of the partonic evolution.
The persistence of the entropy signal across so many datasets and energy levels suggests a remarkable stability in the informational architecture of the proton. The chaotic appearance of the quark gluon phase does not reflect a genuine loss of order. Instead, it reflects a reorganization that maintains internal consistency with quantum constraints. The proton seems to behave as an object that carries a fixed informational charge even when its components are rearranged. The results now point to a scenario in which the most violent interactions produce patterns that are sharply defined at the level of probability distributions and multiplicity counts. These patterns survive the transition from the microscopic storm of the initial state to the cooled debris of the final state.
This observation invites a reconsideration of how complexity develops in high energy collisions. Traditional intuition suggests that the partonic cascade should increase complexity as the system moves through successive branchings. The new findings show that complexity grows only within the bounds allowed by the original entanglement structure. The outgoing hadrons display a complexity level that aligns with this constraint. The generalized dipole model captures this through its conformal weight parameter and the negative binomial structure of the predicted multiplicity distribution. The data confirm that the distribution is not arbitrary. It follows a specific pattern that agrees with an underlying mathematical structure governing the dynamics of the collision.
The consistency of the entropy across the two phases underscores the need for further work on the informational aspects of QCD. Quantum chromodynamics has traditionally been studied through the lens of scattering amplitudes, parton distributions and energy loss mechanisms. The new research indicates that information theory may provide a complementary framework for understanding the evolution of strongly interacting systems. The flow of information through the partonic cascade may be as important as the flow of energy and momentum. This opens a path toward a new conceptual language that links quantum field theory with quantum information in a way that has not yet been fully explored.
The future of this research will depend on the next generation of collider data. The LHC remains the only facility capable of exploring the highest energy regimes where the partonic saturation scale becomes relevant. The continued refinement of detectors and analysis techniques will provide greater resolution of multiplicity distributions and entropy patterns. If the correspondence between the two phases persists, it may become one of the most reliable signatures of the informational coherence of quantum systems at high energy. If it breaks, the deviation could signal the onset of a new regime or a new interaction that does not conform to the established pattern. Either outcome will sharpen our understanding of the proton and its role as a fundamental building block of matter.
For now, the most striking feature of the current results is the stability of the informational content across a process that completely transforms the internal structure of the system. The early stage consists of a dense, fluctuating mixture of quarks and gluons. The late stage consists of composite particles that no longer share that structure. Yet both reflect the same underlying entropy. The proton enters the collision in a state that is nearly maximally entangled. It leaves behind hadrons whose multiplicity distribution records the same degree of informational richness. The transformation is dramatic, but the informational weight remains constant. This is the pattern that emerges from the combined observational and theoretical work now being presented.
As research continues, the goal will be to identify which features of the process are universal and which are contingent on the specifics of the collision environment. Proton proton collisions produce a minimal system compared to heavy ion collisions, yet they show an informational signature that rivals far larger systems in its clarity. The machinery of QCD ensures that radiation, branching and recombination follow rules that never allow information to drift away. This structure makes the proton an object of considerable interest not only in particle physics but also in the broader study of quantum systems that evolve under strong constraints.
The new findings will fuel additional investigations into the relationship between quantum entanglement, complexity growth and particle production. The consistency between theory and experiment indicates that the proton is not a loosely organized cluster of quarks and gluons. It is a highly correlated quantum object that maintains its informational identity even when subjected to extreme disruption. The LHC has revealed that the flow of information through the collision is not random. It follows a path determined by the fundamental principles of quantum mechanics and the structure of the parton cascade. This insight lays the groundwork for a more refined understanding of the proton and the deeper rules that govern its behavior.
Source:
Kutak, K., & Lökös, S. (2025). Entropy and multiplicity of hadrons in the high energy limit within dipole cascade models. Physical Review D.
PDF available at: https://journals.aps.org/prd/abstract/10.1103/23wn-66np
