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arxiv: 2606.06184 · v1 · pith:FSYLA2HSnew · submitted 2026-06-04 · ❄️ cond-mat.stat-mech · cond-mat.mes-hall

The mesoscopic foundations of non equilibrium thermodynamics and the arrow of time in the Dual Model of Liquids

Fabio Peluso This is my paper

Pith reviewed 2026-06-27 23:13 UTC · model grok-4.3

classification ❄️ cond-mat.stat-mech cond-mat.mes-hall
keywords Dual Model of Liquidsmesoscopic scaletime arrownon-equilibrium thermodynamicslattice excitationsmolecular clustersirreversibilityliquids
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The pith

The Dual Model of Liquids identifies a mesoscopic time arrow through interactions between solidlike aggregates and lattice excitations.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes that interactions in the Dual Model of Liquids between solidlike molecule aggregates and lattice excitations link the macroscopic behavior of normal liquids to mesoscopic physical processes. This connection serves as a foundation for non-equilibrium thermodynamics. The duality further allows identification of a time arrow at the mesoscopic scale, where quanta of elastic energy interacting with molecular clusters create a privileged direction. This direction influences time-dependent and dissipative macroscopic processes, although the interaction itself stays temporally reversible. A reader would care because it explains how irreversibility emerges in liquids from reversible microscopic rules.

Core claim

The interaction in the Dual Model of Liquids between the solidlike molecule aggregates and the lattice excitations is appropriate to represent the link between the behaviour at macroscopic scale of normal liquids and the physical processes characterizing those systems at mesoscopic scale. The duality allows identifying a time arrow on the mesoscopic scale in liquids. The interaction of quanta of elastic energy with the molecular clusters introduces a privileged direction, which is relevant in time dependent and dissipative macroscopic processes, although the interaction remains temporally reversible.

What carries the argument

The Dual Model of Liquids, specifically the interaction between solidlike molecule aggregates and lattice excitations, which connects macroscopic liquid behavior to mesoscopic processes and introduces a privileged time direction.

If this is right

  • The model grounds non-equilibrium thermodynamics in mesoscopic liquid dynamics.
  • A time arrow emerges at the mesoscopic scale due to elastic energy quanta interacting with clusters.
  • This arrow affects dissipative and time-dependent processes at larger scales.
  • The underlying interaction remains reversible despite the directionality.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • This suggests potential applications in modeling irreversible processes in other condensed matter systems.
  • Simulations of liquid flows could test for the predicted privileged direction under varying conditions.
  • Connections may exist to broader questions of time asymmetry in statistical mechanics.

Load-bearing premise

The interaction between solidlike molecule aggregates and lattice excitations in the Dual Model of Liquids accurately represents the connection from mesoscopic processes to macroscopic liquid behavior.

What would settle it

A simulation or experiment demonstrating that elastic energy quanta interactions with molecular clusters produce no privileged direction in time-dependent liquid processes would falsify the claim of a mesoscopic time arrow.

Figures

Figures reproduced from arXiv: 2606.06184 by Fabio Peluso.

Figure 3
Figure 3. Figure 3: Therefore, the perturbations travelling i [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 1
Figure 1. Figure 1: The mean free-flight of a wave-packet betw [PITH_FULL_IMAGE:figures/full_fig_p009_1.png] view at source ↗
Figure 1
Figure 1. Figure 1: p R (a) R p hi vp h2 hr hi h2 p R (b) R p vp hr p thwp pp k wp fp Ehh    21  [PITH_FULL_IMAGE:figures/full_fig_p056_1.png] view at source ↗
Figure 5
Figure 5. Figure 5: p  R p R hi vp h hr  p R R p vp h hr  p  R R p vp h hr  [PITH_FULL_IMAGE:figures/full_fig_p060_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: a T0 T0 12 b Th Tc Jq T ext 1 2 C2 C1 [PITH_FULL_IMAGE:figures/full_fig_p061_6.png] view at source ↗
Figure 1
Figure 1. Figure 1: The acquired momentum and energy increase [PITH_FULL_IMAGE:figures/full_fig_p062_1.png] view at source ↗
Figure 8
Figure 8. Figure 8: h Jp Jq R   z [PITH_FULL_IMAGE:figures/full_fig_p063_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: System at equilibrium System out of equilibrium Jp Jq [PITH_FULL_IMAGE:figures/full_fig_p064_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: VA V’A<VA VB VB>V’B x y Layer 2 V2 V2>V1 Layer1 V1 Liquid Particle A Liquid Particle B grad V grad T [PITH_FULL_IMAGE:figures/full_fig_p065_10.png] view at source ↗
read the original abstract

This manuscripts has two goals. The first goal is to show that the interaction in the Dual Model of Liquids between the solidlike molecule aggregates and the lattice excitations is appropriate to represent the link between the behaviour at macroscopic scale of normal liquids and the physical processes characterizing those systems at mesoscopic scale. The second goal is to show that the duality allows identifying a time arrow on the mesoscopic scale in liquids. The interaction of quanta of elastic energy with the molecular clusters introduces a privileged direction, which is relevant in time dependent and dissipative macroscopic processes, although the interaction remains temporally reversible

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 0 minor

Summary. The manuscript claims two results within the Dual Model of Liquids: first, that the interaction between solidlike molecule aggregates and lattice excitations provides an appropriate link between macroscopic behavior of normal liquids and mesoscopic processes; second, that the duality identifies a mesoscopic time arrow because the interaction of elastic-energy quanta with molecular clusters introduces a privileged direction relevant to dissipative processes, even though the underlying interaction remains temporally reversible.

Significance. If the claims were supported by explicit derivations mapping the dual-model dynamics to an emergent time asymmetry, the work could contribute a mesoscopic perspective on non-equilibrium thermodynamics and the arrow of time. As presented, however, the assertions are made without derivations, symmetry-breaking terms, or verifiable mappings, so the potential significance cannot be realized.

major comments (2)
  1. [Abstract] Abstract: the two goals are stated, yet the text supplies no derivations, Hamiltonian, equations, or explicit mechanism showing how reversible elastic-quanta interactions with molecular clusters produce a privileged direction or time arrow.
  2. [Abstract] Abstract (time-arrow claim): the statement that the interaction 'introduces a privileged direction... although the interaction remains temporally reversible' is asserted without a symmetry-breaking term, explicit mapping from the dual-model dynamics, or independent benchmark, rendering the central claim unverifiable.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript. The work is conceptual in nature, identifying links within the established Dual Model of Liquids rather than deriving new dynamical equations. We respond point by point to the major comments below.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the two goals are stated, yet the text supplies no derivations, Hamiltonian, equations, or explicit mechanism showing how reversible elastic-quanta interactions with molecular clusters produce a privileged direction or time arrow.

    Authors: The manuscript's objectives are to demonstrate the conceptual appropriateness of the solidlike aggregates-lattice excitations interaction for connecting macroscopic liquid behavior to mesoscopic processes, and to identify the emergent time arrow from the duality. These are achieved by reference to the structure of the Dual Model (detailed in prior literature) without introducing new Hamiltonians here, as the focus is on the interpretive link rather than re-derivation. The mechanism is the interaction's role in dissipative contexts, which supplies the privileged direction while remaining reversible at the fundamental level. revision: no

  2. Referee: [Abstract] Abstract (time-arrow claim): the statement that the interaction 'introduces a privileged direction... although the interaction remains temporally reversible' is asserted without a symmetry-breaking term, explicit mapping from the dual-model dynamics, or independent benchmark, rendering the central claim unverifiable.

    Authors: The privileged direction is not imposed by an added symmetry-breaking term but arises intrinsically from the mesoscopic duality: the reversible elastic-quanta interaction couples to molecular clusters in a manner that aligns with the directionality of dissipative macroscopic processes. This constitutes the explicit mapping provided by the model structure itself. While a fully formal dynamical derivation would strengthen the presentation, the current identification is verifiable within the Dual Model framework and does not require new benchmarks beyond the model's established consistency with liquid phenomenology. revision: no

Circularity Check

1 steps flagged

Time arrow asserted as property of Dual Model duality without independent derivation

specific steps
  1. self definitional [Abstract (second goal)]
    "the duality allows identifying a time arrow on the mesoscopic scale in liquids. The interaction of quanta of elastic energy with the molecular clusters introduces a privileged direction, which is relevant in time dependent and dissipative macroscopic processes, although the interaction remains temporally reversible"

    The privileged direction (time arrow) is claimed to be introduced by the interaction, but the interaction and duality are defined within the Dual Model of Liquids; the arrow is therefore identified by construction as a feature of the model rather than derived from external equations, benchmarks, or symmetry analysis.

full rationale

The paper's second goal and central claim state that the duality in the Dual Model of Liquids allows identifying a mesoscopic time arrow via elastic quanta interacting with molecular clusters. This is presented as following directly from the model's defined interaction, which is asserted to introduce a privileged direction relevant to dissipative processes (while remaining reversible). No explicit mapping, symmetry-breaking term, or derivation from the model's Hamiltonian or equations is supplied in the abstract or goals; the result therefore reduces to a restatement of the model's own assumptions rather than an independent derivation. This matches the self-definitional pattern exactly.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

Review performed on abstract only; ledger therefore limited to elements explicitly named as foundational in the abstract text.

axioms (1)
  • domain assumption The interaction in the Dual Model of Liquids between the solidlike molecule aggregates and the lattice excitations is appropriate to represent the link between macroscopic and mesoscopic scales.
    Presented as the first goal of the manuscript.
invented entities (1)
  • Dual Model of Liquids no independent evidence
    purpose: Framework that links macroscopic liquid behavior to mesoscopic processes and identifies a time arrow
    The model is invoked for both stated goals; no independent evidence outside the model is supplied.

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