Statistical mechanics explores how the chaotic motion of countless tiny particles gives rise to the predictable laws governing heat, pressure, and phase transitions. This field bridges the gap between the microscopic world of atoms and the macroscopic reality we experience daily, offering deep insights into why materials behave the way they do.

On Gist.Science, we process every new preprint in this category as it appears on arXiv to make these complex findings accessible to everyone. For each paper, we provide both a plain-language explanation for the curious reader and a detailed technical summary for specialists, ensuring that groundbreaking research is never lost behind a wall of jargon.

Below are the latest papers in statistical mechanics, freshly curated and summarized to help you understand the cutting edge of this fascinating discipline.

🔢 mathematics

A Closer Look on the Influence of Constraints Upon the Optimization of the Nonadditive Entropic Functional SqS_{q}

This paper establishes the mathematical conditions for the existence and uniqueness of solutions when optimizing the nonadditive entropy SqS_q under a generalized energy constraint, proving that only specific constraint forms yield qq-exponential distributions while demonstrating that the linear constraint case (q′=1q'=1) preserves thermodynamic laws and effectively models complex systems ranging from many-body Hamiltonians to edge-of-chaos dynamics.

Leandro Lyra Braga Dognini, Constantino Tsallis2026-05-12
🔢 mathematics

An exact spacetime polymer gas for finite-temperature ZN\mathbb Z_N homological quantum code

This paper establishes an exact mapping between finite-temperature ZN\mathbb Z_N homological quantum codes and a (d+1)(d+1)-dimensional spacetime polymer gas with topological charges, utilizing this reformulation to derive rigorous low-temperature stability criteria, exact higher-form dualities, and connections to the plaquette random-cluster model.

Nafiz Ishtiaque, Shanto Chakroborty2026-05-12
🔬 condensed matter

Benchmarking a restricted Boltzmann machine on the Z2\mathbb{Z}_2 Bose-Hubbard chain in the adiabatic hard-core regime

This paper demonstrates that a shallow restricted Boltzmann machine, when used as a variational ansatz in variational Monte Carlo simulations, successfully reproduces the main adiabatic phase structure and captures symmetry-broken insulating configurations of the one-dimensional Z2\mathbb{Z}_2 Bose-Hubbard chain in the hard-core limit at half filling.

Gustavo Alejandro Avalos Valentín, Roman Josué Armenta Rico, Isaac Pérez Castillo2026-05-12
🔢 mathematics

Families of planar lattices with arbitrarily high TcT_{\rm c} for the ferromagnetic Ising model

This paper constructs families of periodic planar lattices, specifically Apollonian lattices, that achieve arbitrarily high critical temperatures for the ferromagnetic Ising model by demonstrating that TcT_{\rm c} scales logarithmically with the maximal coordination number and conjecturing this family to be optimal for such systems.

Davidson Noby Joseph, Connor M. Walsh, Igor Boettcher2026-05-12
🔬 condensed matter

Apparent double-TcT_c from a single BKT transition in anisotropic phase-only models

This paper demonstrates that apparent double-transition temperatures observed in transport experiments on anisotropic two-dimensional superconductors can arise as artifacts of finite-size and finite-current effects in a single BKT transition, implying that robust splittings observed in real materials like KTaO3_3 interfaces must stem from physics beyond this minimal anisotropic baseline.

Pei-Yuan Cai, Yi Zhou2026-05-12
🔬 condensed matter

Renormalization of Quantum Operations: Parity-Time Transition and Chaotic Flows

This paper extends the renormalization group framework to nonunitary quantum dynamics by demonstrating that the competition between decoherence and coherent evolution drives the flow toward chaotic behavior without fixed points, exemplified by a measurement-induced parity-time transition belonging to the one-dimensional Yang-Lee edge singularity universality class.

Atsushi Oyaizu, Hongchao Li, Masaya Nakagawa, Masahito Ueda2026-05-12