Traveling Waves as Renormalization-Group Fixed Points without Universality Classes

Ko Okumura

Home/Archive/arXiv

arXiv · 2609.18984

Traveling Waves as Renormalization-Group Fixed Points without Universality Classes

Ko Okumura

View original source ↗Read source document ↗Export metadata ↓

Abstract

Traveling waves are fundamental asymptotic structures in nonlinear physical systems. While their connection to self-similarity is recognized, their renormalization-group (RG) status remains elusive. We extend a recently developed unified RG framework for nonlinear PDEs to traveling-wave solutions, using Burgers' and KdV equations as paradigmatic examples. By employing a logarithmic transformation, we map traveling waves onto asymptotically self-similar solutions, allowing for a systematic RG treatment. Our analysis reveals a striking departure from the standard RG paradigm: for traveling waves, scale invariance uniquely forces the field's scaling dimension to vanish (A=0). This vanishing dimension implies that the RG transformation rescales space and time while leaving the field magnitude unchanged. Consequently, all analytic perturbations become scale-invariant, eliminating the conventional classification into relevant and irrelevant structures. While classical shock-wave and soliton solutions emerge as stationary RG fixed points, the mechanism for universality class formation - the progressive elimination of irrelevant structures - is fundamentally absent. Traveling waves thus represent a unique class of RG fixed points without universality classes. This finding establishes a crucial distinction between these two concepts and provides a rigorous theoretical basis for why traveling waves exhibit strong memory of initial conditions and system parameters.

Explore related subjects

cond-mat.stat-mech

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Ko Okumura. 2026-08-17. Traveling Waves as Renormalization-Group Fixed Points without Universality Classes. https://arxiv.org/abs/2609.18984

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Information geometry of perturbed gradient flow systems on hypergraphs: A perspective towards nonequilibrium physics

This article serves to concisely review the link between gradient flow systems on hypergraphs and information geometry which has been established within the last five years. Gradient flow systems describe a wealth of physical phenomena and provide powerful analytical technquies which are based on the variational energy-dissipation principle. Modern nonequilbrium physics has complemented this classical principle with thermodynamic uncertaintly relations, speed limits, entropy production rate decompositions, and many more. In this article, we formulate these modern principles within the framework of perturbed gradient flow systems on hypergraphs. In particular, we discuss the geometry induced by the Bregman divergence, the physical implications of dual foliations, as well as the corresponding infinitesimal Riemannian geometry for gradient flow systems. Through the geometrical perspective, we are naturally led to new concepts such as moduli spaces for perturbed gradient flow systems and thermodynamical area which is crucial for understanding speed limits. We hope to encourage the readers working in either of the two fields to further expand on and foster the interaction between the two fields.

cond-mat.stat-mech↗

arXiv2026

Kinetic Interference in Translational Control: A Path-Measure Framework for Collision-Triggered Transcript Decay

I connect two literatures developed independently: the path-measure formulation of non-equilibrium statistical mechanics, where a trajectory action decomposes into a time-antisymmetric (entropic) and time-symmetric (frenetic) sector, and the stochastic modelling of ribosomal traffic on messenger RNA. The biological target is a proposed intervention -- antisense oligonucleotide (ASO) interference with wobble-uridine (U34) modification of transfer RNA -- whose intended effect is not to abolish translation but to perturb its timing, driving ribosome collisions and collision-triggered transcript decay preferentially on high-flux, codon-biased transcripts. Dynamical-activity and large-deviation analyses of generic lattice exclusion models -- notably the symmetric and totally asymmetric simple exclusion processes -- are well established. To my knowledge their formalization specifically for ribosomal traffic queues, translation elongation, and collision-triggered no-go decay remains unoccupied; this paper addresses that narrower gap, not the general one. Two claims here are load-bearing and untested. First, selectivity: transcripts whose loss is therapeutically desirable are separable, by vulnerable-codon-pair burden, from transcripts whose loss is toxic. Second, non-redundancy: the frenetic decomposition yields predictions, specific to ribosomal queueing and collision-triggered decay, not already obtainable from rate-level exclusion-process models or existing activity/large-deviation analyses of exclusion processes. This paper establishes neither. It specifies both as falsifiable tests with pre-registered decision rules, including outcomes under which the framework should be abandoned or narrowed. It is a research programme proposal, not a result. No new experimental, computational, or bioinformatic results are reported.

cond-mat.stat-mech↗

arXiv2026

Thermodynamic efficiency of communication channels

We identify a broad class of communication channels that captures common physical constraints in both artificial and natural systems and derive bounds on their thermodynamic cost. We find that the entropy production per channel use is bounded from below by the input-output mutual information, and their ratio -mutual information divided by entropy production- defines the thermodynamic efficiency. Unlike previous studies of energy-constrained communication channels, our analysis shows that thermodynamic costs must be assigned not only to the input symbols themselves, but also to transitions between successive symbols. As a result, maximizing thermodynamic efficiency favors a biased input that switches only rarely, rather than the capacity-achieving input. For the binary symmetric channel, this preference emerges through a pitchfork bifurcation that spontaneously breaks the symmetry of the channel. A minimal model of cellular sensing exhibits the same phenomenon.

cond-mat.stat-mech↗