The Transition to Classical Statistical Physics

Lorenza Saitta, Attilio Giordana, Antoine Cornuéjols

Philippe Guillemant, C. Abid, Marc Médale

The experimental confirmation of Landauer principle and the emerging concept of a computational universe make it more and more crucial to understand the physical sense of information, as it has an intrinsic relation with observer knowledge that is often rejected as subjective. In this paper we propose an objective definition of phase information in a purely classical computational universe with quantized phase states, this quantization being imposed by our fundamental hypothesis that physical information has a finite and limited density, responsible for the irreversibility. We use a statistical study of results obtained by numerical simulations of a billiard to highlight an excessive and paradoxical loss of phase information that we solve by involving a classical to quantum transition. After discussing the pertinence of such a transition to clarify some problematic aspects of statistical physics, we conclude that a computational universe should automatically lose phase information through time in an irreversible way, which could be compensated by a gain of physical information due to observation and decoherence.

Peter Bongaarts

Jincheng Zhang

The concept of a photonic statistical topological transition (PSTT) introduces a novel framework in which the statistical properties of photons, quantified by higher‑order correlation functions g^(n), undergo topological changes that give rise to new quantum photonic phases. This paper presents a comprehensive theoretical analysis of PSTT, establishes the mathematical conditions under which topological invariants associated with photon statistics can change, and discusses the physical implications of such transitions. We demonstrate that the second‑order correlation function g^(2) can evolve from values characteristic of classical light (g^(2) > 1) to those of non‑classical light (g^(2) < 1) via a topologically protected transition, and we generalize the argument to higher‑order correlations. The potential for discovering new quantum light states, which may have applications in quantum information processing, precision measurement, and fundamental tests of quantum mechanics, is highlighted.

Angelo Plastino

The quantum–classical transition is one of the most frequently invoked concepts in modern physics. Yet the notion of classicality itself is far from unique. Depending on the physical context, classical behavior may be associated with decoherence, the semiclassical limit, thermodynamic averaging, suppression of correlations, emergence of collective order, or geometric simplification of statistical state space. These viewpoints are often presented as if they described a single phenomenon, although they emphasize different physical mechanisms and different operational criteria. In this article we examine the principal notions of classicality that appear across quantum theory, statistical physics, condensed matter physics, and information geometry. We compare the corresponding mechanisms of classical emergence and analyze the physical quantities commonly used to characterize them, including coherence, entanglement, fluctuations, correlation length, Fisher information, statistical complexity, and information-geometric curvature. We argue that many apparently distinct routes toward classical behavior share a common structural feature: a reduction of effective fluctuation freedom. From this perspective, classicality may be interpreted as an emergent regime in which the accessible fluctuation manifold becomes progressively constrained, stabilized, or geometrically simplified. This viewpoint naturally unifies decoherence, semiclassical localization, thermodynamic averaging, decorrelation, and collective organization within a common conceptual framework. Rather than representing a unique physical process, the quantum–classical transition appears as a family of related mechanisms through which complex quantum fluctuation structure gives rise to effective macroscopic classical behavior.

Hinata Yokoyama, Kengo Anzai, Dina Syverud-Lindland +2 more

We study a random unitary quantum circuit with only reset channels, which has high feasibility for real quantum devices. In particular, we investigate the many-body statistical physics properties, ``reset-induced'' entanglement phase transitions comparing the classical statistical picture in the large ``$d$'' limit of qudits. In the property of the reset-induced phase transition the parameter of qudit $d$ is essential. That is, the transition properties induced by the reset channel significantly depend on $d$. We numerically elucidate this statement employing efficient stabilizer circuit simulations for $d=2$. Specifically, critical fluctuations that grow with system size are observed near the transition point, and the finite-size scaling analyses yield data collapse consistent with a continuous mixed-state phase transition.} This behavior differs from expectations based on the classical statistical mapping in the large-$d$ limit.