arXiv subjects

Shlomo Segal

Publications and source records attributed to Shlomo Segal.

3 recordsLinked to original sources

arXiv2026

Channel selection at identically vanishing dissipation difference: isolating the frenetic sector of the overdamped path measure

Transition-state and Kramers-Langer theory determine reaction channel selection from data at a single point: the saddle. We show this is insufficient in a precise, constructive sense. Using the standard split of the Onsager-Machlup path weight into a time-antisymmetric part fixed by the entropy flux and a time-symmetric part, the frenesy, we first settle when a dissipation-based criterion can distinguish two forward histories at all: the entropy difference between two histories sharing endpoints equals beta times the circulation of the non-conservative force around the loop they enclose, and vanishes identically for every gradient flow. We then construct a two-channel gradient landscape whose channels share both endpoints, whose barrier heights are equal identically, and whose saddle Hessians are the same matrix. The entropy sector is switched off by construction, all local saddle-point theories predict 50:50 exactly, and the branching ratio isolates the frenetic sector. Langevin simulation gives P(+) = 0.4568 +/- 0.0012. We identify a covariant geometric contribution to pathway selection within the frenetic sector, (1/2) ln det(D_perp H_perp), show that the divergence-of-drift observable proposed for this role is not coordinate-invariant whereas this one is, and find that it reproduces the measured branching to within 0.5 sigma with no fitted parameters. Stiff spectator modes cancel identically, since selection depends only on a ratio of determinants. We also give a parameter-free prediction: a solenoidal force of strength epsilon must contribute exactly 2*beta*epsilon/pi to ln[P(+)/P(-)]. These results are an exactly controlled counterexample to the sufficiency of local saddle-point data for channel selection.

physics.chem-ph↗

arXiv2026

Geometric Dissipation Constraints in Stochastic Reaction Dynamics: A Variational Observable for Hidden Kinetic Structure in Energy Landscapes

We propose a geometric framework for characterizing hidden kinetic constraints in stochastic reaction dynamics. While free-energy barriers and entropy production provide global descriptors of thermodynamic behavior, they are largely insensitive to local geometric structure in configuration space that governs pathway selection. Starting from overdamped Langevin dynamics formulated as a gradient flow in Wasserstein space, we derive a variational functional whose leading-order asymptotic structure defines a local dissipation-geometry coupling observable. This quantity combines force-drift alignment with phase-space contraction induced by the divergence of the drift field, yielding a scalar field that reflects second-order geometric features of the underlying energy landscape. We demonstrate that this observable distinguishes kinetically distinct reaction channels that are degenerate under conventional free-energy analysis, as shown through numerical experiments on benchmark systems including the Muller-Brown potential, corrugated periodic landscapes, and the conformational transitions of Alanine Dipeptide. These experiments demonstrate robust separation of pathways and are consistent with a quadratic scaling behavior in the high-frequency homogenization regime. Our results suggest that stochastic reaction dynamics contain an additional geometric layer of kinetic control in molecular motion not captured by standard thermodynamic or reaction-coordinate descriptions.

cond-mat.stat-mech↗

arXiv2026

A Formal Physical Framework for the Origin of Life: Dissipation-Driven Selection of Evolving Replicators

The emergence of life from inanimate matter presents a thermodynamic challenge: the Second Law of Thermodynamics dictates a global trend towards disorder, yet life constitutes localized pockets of profound organization. This paper presents a formal physical framework for abiogenesis grounded in the statistical physics of non-equilibrium systems. We transition from the established connection between dissipation and process probability (e.g., Crooks Fluctuation Theorem) to a large-deviation framework for the likelihood of system histories. This formalism reveals a probabilistic bias towards histories with greater integrated dissipation. We then demonstrate how this bias leads to the selection of heredity. The core of our argument is a rigorous mathematical proposition showing that while simple autocatalysis leads to an exponential increase in dissipation, template-directed replication, via its capacity for mutation and adaptation (a process from which we derive an effective adaptation rate, alpha), unlocks a super-exponential growth pathway. This translates to a doubly-exponential amplification in the relative probability of its emergence over time, constituting an asymptotically dominant physical bias for its selection. This framework delineates a hierarchical transition from simple dissipative structures to information-bearing replicators, whose stability is contingent upon exceeding critical thresholds of fidelity, kinetic efficiency, and resource supply. We conclude by proposing a refined, quantitative, and falsifiable experiment, defining a precise mathematical signature for identifying the onset of evolutionary processes in synthetic chemical systems.

cond-mat.stat-mech↗