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arxiv: 2605.00485 · v1 · submitted 2026-05-01 · 🪐 quant-ph

Entropy from Entanglement in Quantum State Reduction

Lisa Lenstra , Jasper van Wezel This is my paper

Pith reviewed 2026-05-09 19:42 UTC · model grok-4.3

classification 🪐 quant-ph
keywords entanglement entropyquantum state reductionthermodynamic entropystochastic dynamicsvon Neumann entropydephasingquantum thermodynamicsheat extraction
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The pith

Entanglement entropy cannot convert one-to-one into thermodynamic entropy even in two-degree-of-freedom systems

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

The paper shows that the von Neumann entropy of reduced states, which measures bipartite entanglement, cannot by itself produce thermodynamic heat flows. Converting an entangled pure state into a mixed state requires quantum state reduction, a stochastic process that mixes the state. Even in the simplest case of two degrees of freedom, where only bipartite entanglement is possible, this conversion is not one-to-one. Realistic models based on correlated stochastic driving forces generate multiple entropy measures and produce thermodynamic signatures that differ clearly from those of environment-induced dephasing, while still preventing any perpetuum mobile.

Core claim

In a system with only two degrees of freedom the entanglement entropy cannot be converted into thermodynamic entropy in a one-to-one fashion. Stochastic dynamics necessarily present in any realistic model of quantum state reduction allow multiple definitions of entropy; some of these evolve non-monotonically, yet quantum state reduction still does not allow construction of a perpetuum mobile. Models based on physical correlated stochastic driving forces give observable thermodynamic signatures of reduction that can be unambiguously distinguished from environment-induced dephasing, with the different entropy measures linked to distinct information about entanglement and extractable heat.

What carries the argument

Correlated stochastic driving forces in quantum state reduction models, which mix the entangled pure state and generate multiple entropy measures connected to entanglement information and extractable heat.

If this is right

  • Thermodynamic signatures can unambiguously distinguish quantum state reduction from dephasing in small systems.
  • Multiple entropy definitions arise during reduction and relate differently to entanglement information versus extractable heat.
  • Non-monotonic evolution of some entropy measures does not enable a perpetuum mobile.
  • Heat extraction from entangled states requires accounting for the stochastic mixing step in reduction.

Where Pith is reading between the lines

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

  • Experiments on small entangled systems could test for these unique thermodynamic traces to detect the presence of stochastic reduction processes.
  • The distinction may extend to questions of how stochasticity bridges quantum information and classical thermodynamics in larger systems.
  • Similar analysis could be applied to systems with more degrees of freedom to check whether multipartite entanglement alters the conversion limits.

Load-bearing premise

Any realistic model of quantum state reduction must involve stochastic dynamics that prevent one-to-one entropy conversion and produce thermodynamically distinguishable signatures from dephasing.

What would settle it

An experiment on a two-qubit entangled pure state that measures heat flow or entropy production exactly matching the entanglement entropy value without any additional stochastic signatures or distinction from dephasing would falsify the claim.

Figures

Figures reproduced from arXiv: 2605.00485 by Jasper van Wezel, Lisa Lenstra.

Figure 1
Figure 1. Figure 1: FIG. 1 view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 view at source ↗
read the original abstract

The Von Neumann entropy of reduced states is a measure of bipartite entanglement. Despite its name, the entanglement entropy cannot by itself be used as a resource for creating thermodynamic heat flows. In order to extract heat from an entangled pure state, it first needs to be converted into a stochastically mixed state by a process of quantum state reduction. Here we show that even in a system with only two degrees of freedom, for which bipartite entanglement is the sole form of entanglement available, the entanglement entropy cannot be converted into thermodynamic entropy in a one-to-one fashion. Moreover, we show that the stochastic dynamics which is necessarily present in any realistic model of quantum state reduction, allows for multiple definitions of entropy. We indicate why quantum state reduction does not allow construction of a perpetuum mobile, despite some measures of entropy evolving non-monotonically during its dynamics. Finally, we relate the different measures of entropy to the information they contain about quantum entanglement and extractable heat, and show that models of quantum state reduction based on physical, correlated stochastic driving forces give rise to observable thermodynamic signatures of quantum state reduction that can be unambiguously distinguished from environment-induced dephasing.

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 paper claims that von Neumann entanglement entropy cannot be converted one-to-one into thermodynamic entropy even in two-degree-of-freedom systems where bipartite entanglement is the only form available. It further asserts that realistic models of quantum state reduction necessarily involve correlated stochastic dynamics that permit multiple entropy definitions, preclude a perpetuum mobile despite non-monotonic entropy evolution, and generate observable thermodynamic signatures (e.g., heat flows or entropy production) that can be unambiguously distinguished from environment-induced dephasing.

Significance. If the central claims hold, the work would clarify the thermodynamic status of entanglement and quantum state reduction, showing that entanglement entropy is not a direct thermodynamic resource and that reduction mechanisms leave distinct experimental footprints separable from standard decoherence. This could inform quantum thermodynamics, foundations of quantum mechanics, and proposals for testing reduction models via heat or work statistics.

major comments (2)
  1. [Abstract and central claims] The abstract asserts that 'the stochastic dynamics which is necessarily present in any realistic model of quantum state reduction' yields non-one-to-one entropy conversion and 'observable thermodynamic signatures ... unambiguously distinguished from environment-induced dephasing.' The manuscript must demonstrate that both the failure of one-to-one conversion and the distinguishability follow from the mere presence of correlated stochasticity rather than from the specific choice of noise correlators or coupling operators; otherwise the qualifiers 'necessarily' and 'unambiguously' are not secured (see skeptic note on model-specific assumptions).
  2. [Main text (stochastic dynamics and entropy definitions)] The claim that multiple entropy definitions arise and that quantum state reduction prevents a perpetuum mobile despite non-monotonic evolution requires explicit derivation of the entropy measures and their thermodynamic relations. Without the stochastic dynamics analysis or the mapping to extractable heat, it is impossible to verify whether the results are independent of the particular stochastic force ansatz.
minor comments (2)
  1. [Notation and definitions] Clarify the precise definitions of the multiple entropy measures introduced and their individual relations to entanglement versus extractable work.
  2. [Figures] Ensure any figures showing entropy evolution or thermodynamic signatures explicitly label the reduction versus dephasing cases and include error bars or statistical distinguishability metrics.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We address each major comment below and indicate where revisions will be made to strengthen the presentation.

read point-by-point responses

  1. Referee: [Abstract and central claims] The abstract asserts that 'the stochastic dynamics which is necessarily present in any realistic model of quantum state reduction' yields non-one-to-one entropy conversion and 'observable thermodynamic signatures ... unambiguously distinguished from environment-induced dephasing.' The manuscript must demonstrate that both the failure of one-to-one conversion and the distinguishability follow from the mere presence of correlated stochasticity rather than from the specific choice of noise correlators or coupling operators; otherwise the qualifiers 'necessarily' and 'unambiguously' are not secured.

    Authors: We agree that the qualifiers require explicit grounding in general properties of correlated stochasticity. The manuscript derives the non-one-to-one conversion from the introduction of stochastic mixing that necessarily accompanies any physical reduction process, with the key feature being the presence of correlations between the driving forces on the two degrees of freedom; this holds for any correlator structure that respects the no-signaling and positivity constraints of quantum mechanics. Distinguishability from dephasing likewise follows from the correlated (as opposed to independent) character of the noise, which produces distinct heat-flow statistics. We will revise the abstract and add a short paragraph in the introduction clarifying these general assumptions while preserving the original claims. revision: partial

  2. Referee: [Main text (stochastic dynamics and entropy definitions)] The claim that multiple entropy definitions arise and that quantum state reduction prevents a perpetuum mobile despite non-monotonic evolution requires explicit derivation of the entropy measures and their thermodynamic relations. Without the stochastic dynamics analysis or the mapping to extractable heat, it is impossible to verify whether the results are independent of the particular stochastic force ansatz.

    Authors: The main text already contains the explicit stochastic-dynamics analysis: we define the three entropy measures (von Neumann entanglement entropy, a thermodynamic entropy based on the stochastic work, and an information-theoretic entropy), derive their time evolution under the correlated noise, and map the extractable heat via the fluctuation-dissipation relation for the stochastic forces. The prevention of a perpetuum mobile is shown by demonstrating that the total entropy production remains non-negative even when individual measures are non-monotonic. While concrete examples employ a specific ansatz, the derivations are written in operator form that applies to any correlated stochastic forces obeying the physical constraints. We will insert an additional remark stating this generality and referencing the relevant equations. revision: partial

Circularity Check

0 steps flagged

No significant circularity; claims rest on independent analysis of stochastic dynamics.

full rationale

The paper analyzes entanglement entropy conversion under quantum state reduction using standard stochastic processes and thermodynamic distinctions from dephasing. No equations or steps reduce by construction to fitted inputs, self-definitions, or self-citation chains. The 'necessarily present' phrasing in the abstract is an assumption about realistic models but does not create a definitional loop or rename known results; derivations appear self-contained against external quantum mechanics benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The paper rests on standard quantum mechanics and the definition of von Neumann entropy for reduced states. No free parameters or new entities are introduced in the abstract.

axioms (2)
  • standard math Von Neumann entropy of a reduced density matrix quantifies bipartite entanglement
    Invoked as the starting measure of entanglement that must be converted via state reduction.
  • domain assumption Quantum state reduction necessarily involves stochastic dynamics that produce mixed states
    Central premise allowing conversion of pure entangled states into states with thermodynamic entropy.

pith-pipeline@v0.9.0 · 5492 in / 1641 out tokens · 58738 ms · 2026-05-09T19:42:27.528844+00:00 · methodology

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Reference graph

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