# Bibliography

<!-- 9 October 2026 publication, PDF-reconciled conversion source. Mathematical macros used below:
\TV = \operatorname{TV}
\Dtr = \operatorname{D}
\tr = \operatorname{tr}
\id = \operatorname{id}
\dd = \,\mathrm d
\pTV = \operatorname{TV}
\pVar = \operatorname{Var}
\pLaw = \operatorname{Law}
\pGam = \Gamma
\pUnif = \mathsf U
-->

## Bibliography

<a id="bib-Rosenblatt1952"></a>

[1] M. Rosenblatt, Remarks on a Multivariate Transformation, *Ann. Math. Statist.* **23** (1952), 470–472. [doi:10.1214/aoms/1177729394](https://doi.org/10.1214/aoms/1177729394).

<a id="bib-Gross1975"></a>

[2] L. Gross, Logarithmic Sobolev Inequalities, *Amer. J. Math.* **97** (1975), 1061–1083. [doi:10.2307/2373688](https://doi.org/10.2307/2373688).

<a id="bib-LasotaYorke1973"></a>

[3] A. Lasota and J. A. Yorke, On the Existence of Invariant Measures for Piecewise Monotonic Transformations, *Trans. Amer. Math. Soc.* **186** (1973), 481–488. [doi:10.1090/S0002-9947-1973-0335758-1](https://doi.org/10.1090/S0002-9947-1973-0335758-1).

<a id="bib-Bennett1973"></a>

[4] C. H. Bennett, Logical Reversibility of Computation, *IBM J. Res. Dev.* **17** (1973), 525–532. [doi:10.1147/rd.176.0525](https://doi.org/10.1147/rd.176.0525).

<a id="bib-ValentiniWestman2005"></a>

[5] A. Valentini and H. Westman, Dynamical Origin of Quantum Probabilities, *Proc. R. Soc. A* **461** (2005), 253–272. [doi:10.1098/rspa.2004.1394](https://doi.org/10.1098/rspa.2004.1394). [arXiv:quant-ph/0403034](https://arxiv.org/abs/quant-ph/0403034).

<a id="bib-GoldsteinStruyve2007"></a>

[6] S. Goldstein and W. Struyve, On the Uniqueness of Quantum Equilibrium in Bohmian Mechanics, *J. Stat. Phys.* **128** (2007), 1197–1209. [doi:10.1007/s10955-007-9354-5](https://doi.org/10.1007/s10955-007-9354-5). [arXiv:0704.3070](https://arxiv.org/abs/0704.3070).

<a id="bib-DurrGoldsteinZanghi1992"></a>

[7] D. Dürr, S. Goldstein and N. Zanghì, Quantum Equilibrium and the Origin of Absolute Uncertainty, *J. Stat. Phys.* **67** (1992), 843–907. [doi:10.1007/BF01049004](https://doi.org/10.1007/BF01049004). [arXiv:quant-ph/0308039](https://arxiv.org/abs/quant-ph/0308039).

<a id="bib-DurrGoldsteinZanghi2004"></a>

[8] D. Dürr, S. Goldstein and N. Zanghì, Quantum Equilibrium and the Role of Operators as Observables in Quantum Theory, *J. Stat. Phys.* **116** (2004), 959–1055. [doi:10.1023/B:JOSS.0000037234.80916.d0](https://doi.org/10.1023/B:JOSS.0000037234.80916.d0). [arXiv:quant-ph/0308038](https://arxiv.org/abs/quant-ph/0308038).

<a id="bib-DurrEtAl2005Density"></a>

[9] D. Dürr, S. Goldstein, R. Tumulka and N. Zanghì, On the Role of Density Matrices in Bohmian Mechanics, *Found. Phys.* **35** (2005), 449–467. [doi:10.1007/s10701-004-1983-9](https://doi.org/10.1007/s10701-004-1983-9). [arXiv:quant-ph/0311127](https://arxiv.org/abs/quant-ph/0311127).

<a id="bib-DaviesLewis1970"></a>

[10] E. B. Davies and J. T. Lewis, An Operational Approach to Quantum Probability, *Commun. Math. Phys.* **17** (1970), 239–260. [doi:10.1007/BF01647093](https://doi.org/10.1007/BF01647093).

<a id="bib-Ozawa1984"></a>

[11] M. Ozawa, Quantum Measuring Processes of Continuous Observables, *J. Math. Phys.* **25** (1984), 79–87. [doi:10.1063/1.526000](https://doi.org/10.1063/1.526000).

<a id="bib-FuchsVanDeGraaf1999"></a>

[12] C. A. Fuchs and J. van de Graaf, Cryptographic Distinguishability Measures for Quantum-Mechanical States, *IEEE Trans. Inform. Theory* **45** (1999), 1216–1227. [doi:10.1109/18.761271](https://doi.org/10.1109/18.761271). [arXiv:quant-ph/9712042](https://arxiv.org/abs/quant-ph/9712042).

<a id="bib-RodgersReturn2026"></a>

[13] J. Rodgers, *Preparation-Return Holonomy and Equilibrium Uniqueness in Engineered Interacting Networks*, version 2, 4 October 2026, publication revision of the 7 September 2026 manuscript. [doi:10.5281/zenodo.23131064](https://doi.org/10.5281/zenodo.23131064).

<a id="bib-RodgersControl2026"></a>

[14] J. Rodgers, *Control Consistency and Born Equilibrium: Uniqueness from Local Potentials and Fixed Interactions*, version 2, revised preprint candidate, 4 October 2026. [doi:10.5281/zenodo.23131058](https://doi.org/10.5281/zenodo.23131058).

<a id="bib-RodgersP2"></a>

[15] J. Rodgers, *Effective Repeated Position Records with Retained Entropy and Calibrated Reset*, companion manuscript, 2026. [doi:10.5281/zenodo.23259558](https://doi.org/10.5281/zenodo.23259558).

<a id="bib-RodgersP3"></a>

[16] J. Rodgers, *Reference-Weighted Deterministic Quantum Flows with Singular Interactions and Retained Sources*, companion manuscript, 2026. [doi:10.5281/zenodo.23259569](https://doi.org/10.5281/zenodo.23259569).

<a id="bib-RodgersP4"></a>

[17] J. Rodgers, *Complete-Current Estimates for Coherent Quantum Sources and Continua*, companion manuscript, 2026. [doi:10.5281/zenodo.23259571](https://doi.org/10.5281/zenodo.23259571).