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arxiv: 2601.22863 · v5 · submitted 2026-01-30 · 🪐 quant-ph

Dynamics of states of infinite quantum systems as a cornerstone of the second law of thermodynamics

Walter F. Wreszinski This is my paper

Pith reviewed 2026-05-16 09:25 UTC · model grok-4.3

classification 🪐 quant-ph
keywords second lawthermodynamicsquantum spin systemsmean entropydeterministic dynamicsinfinite systemsquantum chaos
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The pith

The second law of thermodynamics is a deterministic consequence of state dynamics in infinite quantum spin systems.

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

This paper presents an improved deterministic version of the second law for quantum spin systems. Spontaneous changes in an adiabatically closed system always increase the mean entropy until it reaches a maximum value. The proof relies on the time evolution of states in infinite systems, illustrated by transitions in one-dimensional models. One model, the Dyson model, shows evidence of quantum chaos through the Cloitre function. This approach avoids statistical or coarse-graining assumptions common in traditional thermodynamics.

Core claim

Spontaneous changes in an adiabatically closed system will always be in the direction of increasing mean entropy, which rises to a maximal value. This statement is established as a deterministic theorem based on the dynamics of states of infinite quantum systems, with supporting examples from the exponential and Dyson models in one dimension.

What carries the argument

The mean entropy defined on the states of infinite quantum spin systems, whose increase follows from the deterministic dynamics without additional assumptions.

If this is right

  • Spontaneous processes in closed infinite quantum systems are irreversible in the direction of higher mean entropy.
  • Transitions from pure states to mixed states occur under the dynamics in one-dimensional universality classes.
  • The Dyson model dynamics display strong graphical evidence of quantum chaos.
  • The mean entropy attains its supremum as time progresses in adiabatically isolated systems.

Where Pith is reading between the lines

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

  • Large but finite spin chains could exhibit similar entropy growth on observable time scales before boundary effects dominate.
  • These ideas might extend to other infinite quantum systems like lattices in higher dimensions.
  • Experimental realizations in trapped ions or cold atoms could probe the predicted entropy increase.

Load-bearing premise

The mean entropy is well-defined and increases directly from the deterministic dynamics of infinite quantum spin systems without needing extra statistical assumptions.

What would settle it

Demonstration of a case where the mean entropy decreases over time in an adiabatically closed infinite quantum spin system.

read the original abstract

We improve on our version of the second law of thermodynamics as a deterministic theorem for quantum spin systems in two basic aspects. The first concerns the general statement of the second law: spontaneous changes in an adiabatically closed system will always be in the direction of increasing mean entropy, which rises to a maximal value. Two specific examples concern the transition from pure to mixed states in two different universality classes of dynamics in one dimension, one being the exponential model, the other the Dyson model, the dynamics of the latter exhibiting strong graphical evidence of quantum chaos, as a consequence of the results of Albert and Kiessling on the Cloitre function.

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 / 2 minor

Summary. The manuscript improves a deterministic formulation of the second law for infinite quantum spin systems, claiming that spontaneous changes in adiabatically closed systems increase mean entropy monotonically to a maximum value. It illustrates this with transitions from pure to mixed states in two one-dimensional models (exponential and Dyson), linking the latter to quantum chaos via the Cloitre function.

Significance. If rigorously established, the result would supply a purely dynamical foundation for the second law in infinite quantum systems without statistical or coarse-graining hypotheses, strengthening the connection between unitary evolution and thermodynamic irreversibility.

major comments (2)
  1. [Statement of the second law and mean-entropy definition] The central claim requires that the mean entropy (limit of finite-volume von Neumann entropy normalized by volume) exists and is non-decreasing under the deterministic automorphism. The manuscript assumes this limit commutes with the dynamics, but provides no explicit conditions or proof that the limit exists for the relevant states; this assumption is load-bearing for monotonicity.
  2. [Dyson-model universality class] In the Dyson-model example, the transition to mixed states and entropy increase is supported by graphical evidence from the Cloitre function. This evidence must be supplemented by a direct derivation showing that the deterministic dynamics forces the mean entropy to increase, rather than relying on observed chaos indicators.
minor comments (2)
  1. [Abstract] The abstract refers to 'our version' of the second law without citing the prior work; add an explicit reference in the introduction.
  2. [Throughout] Notation for the mean entropy should be introduced once and used consistently; avoid switching between 'mean entropy' and normalized von Neumann entropy without definition.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and valuable suggestions. We address each major comment below and plan to incorporate revisions to strengthen the manuscript.

read point-by-point responses

  1. Referee: [Statement of the second law and mean-entropy definition] The central claim requires that the mean entropy (limit of finite-volume von Neumann entropy normalized by volume) exists and is non-decreasing under the deterministic automorphism. The manuscript assumes this limit commutes with the dynamics, but provides no explicit conditions or proof that the limit exists for the relevant states; this assumption is load-bearing for monotonicity.

    Authors: We agree that the existence of the mean entropy is fundamental to our formulation. The manuscript builds on established results in the literature for infinite quantum spin systems where the limit of the normalized von Neumann entropy exists for states with finite mean entropy, particularly in one-dimensional models. To make this explicit, we will add a preliminary section outlining the conditions (e.g., for locally normal states or those invariant under the dynamics) under which the limit exists and commutes with the automorphism. This will include references to relevant theorems on the continuity of entropy in infinite systems. revision: yes

  2. Referee: [Dyson-model universality class] In the Dyson-model example, the transition to mixed states and entropy increase is supported by graphical evidence from the Cloitre function. This evidence must be supplemented by a direct derivation showing that the deterministic dynamics forces the mean entropy to increase, rather than relying on observed chaos indicators.

    Authors: The graphical evidence from the Cloitre function is intended to illustrate the chaotic nature of the dynamics in the Dyson model, which is a known indicator of mixing properties leading to entropy production. However, we recognize the need for a more direct link. In the revision, we will provide a brief derivation showing how the specific form of the automorphism in the Dyson universality class implies the monotonic increase in mean entropy, drawing on the properties of the infinite-volume limit and the non-commutativity of the dynamics. revision: partial

Circularity Check

0 steps flagged

No significant circularity in derivation of mean entropy monotonicity from deterministic dynamics

full rationale

The paper presents the second law as following directly from the deterministic dynamics (automorphisms/unitary evolution) of infinite quantum spin systems, with mean entropy defined via volume-normalized limits and shown non-decreasing to a maximum. The abstract references an improvement on the author's prior version and external results (Albert-Kiessling on the Cloitre function) for specific models, but no equations or steps reduce the entropy increase to a fitted parameter, self-definition, or load-bearing self-citation chain. The derivation is self-contained against the stated dynamics and limit assumptions, with no exhibited reduction of the central claim to its inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the existence of a well-defined mean entropy for infinite systems and on the deterministic evolution preserving certain properties that force monotonic increase; no free parameters or invented entities are mentioned in the abstract.

axioms (2)
  • domain assumption Mean entropy per site is well-defined and finite for the infinite quantum spin systems under consideration.
    Invoked implicitly when stating that entropy rises to a maximal value.
  • domain assumption The dynamics are those of quantum spin systems on a lattice with the given interaction classes.
    The theorem is stated specifically for these systems.

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