{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:20:18Z","timestamp":1760149218197,"version":"build-2065373602"},"reference-count":21,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2023,7,14]],"date-time":"2023-07-14T00:00:00Z","timestamp":1689292800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"UANL-PAICYT","award":["IT1807-21","CB-167651"],"award-info":[{"award-number":["IT1807-21","CB-167651"]}]},{"DOI":"10.13039\/501100003141","name":"CONACYT","doi-asserted-by":"publisher","award":["IT1807-21","CB-167651"],"award-info":[{"award-number":["IT1807-21","CB-167651"]}],"id":[{"id":"10.13039\/501100003141","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Informatics"],"abstract":"<jats:p>The dichotomy in power consumption between digital and biological information processing systems is an intriguing open question related at its core with the necessity for a more thorough understanding of the thermodynamics of the logic of computing. To contribute in this regard, we put forward a model that implements the Boltzmann machine (BM) approach to computation through an electric substrate under thermal fluctuations and dissipation. The resulting network has precisely defined statistical properties, which are consistent with the data that are accessible to the BM. It is shown that by the proposed model, it is possible to design neural-inspired logic gates capable of universal Turing computation under similar thermal conditions to those found in biological neural networks and with information processing and storage electric potentials at comparable scales.<\/jats:p>","DOI":"10.3390\/informatics10030062","type":"journal-article","created":{"date-parts":[[2023,7,17]],"date-time":"2023-07-17T00:56:47Z","timestamp":1689555407000},"page":"62","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Biologically Plausible Boltzmann Machine"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9615-9088","authenticated-orcid":false,"given":"Arturo","family":"Berrones-Santos","sequence":"first","affiliation":[{"name":"Graduate Program in Systems Engineering and Doctorate in Mathematical Sciences, Autonomous University of Nuevo Le\u00f3n, Ciudad Universitaria, San Nicol\u00e1s de los Garza 66455, Nuevo Le\u00f3n, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6293-0305","authenticated-orcid":false,"given":"Franco","family":"Bagnoli","sequence":"additional","affiliation":[{"name":"Department of Physics and Astronomy and CSDC, INFN Sezione di Firenze, University of Florence, Via G. Sansone 1, 50019 Sesto Fiorentino, Italy"}]}],"member":"1968","published-online":{"date-parts":[[2023,7,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1038\/scientificamerican0785-48","article-title":"The fundamental physical limits of computation","volume":"253","author":"Bennett","year":"1985","journal-title":"Sci. Am."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1327","DOI":"10.1109\/TVLSI.2011.2157543","article-title":"Investigating the impact of logic and circuit implementation on full adder performance","volume":"20","author":"Purohit","year":"2011","journal-title":"IEEE Trans. Very Large Scale Integr. (VLSI) Syst."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1145\/3431282","article-title":"A vision to compute like nature: Thermodynamically","volume":"64","author":"Hylton","year":"2021","journal-title":"Commun. ACM"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1792","DOI":"10.1103\/PhysRevLett.35.1792","article-title":"Solvable model of a spin-glass","volume":"35","author":"Sherrington","year":"1975","journal-title":"Phys. Rev. Lett."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"013303","DOI":"10.1103\/PhysRevE.92.013303","article-title":"Comparing Monte Carlo methods for finding ground states of Ising spin glasses: Population annealing, simulated annealing, and parallel tempering","volume":"92","author":"Wang","year":"2015","journal-title":"Phys. Rev. E"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Huang, H. (2021). Statistical Mechanics of Neural Networks, Springer.","DOI":"10.1007\/978-981-16-7570-6"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1207\/s15516709cog0901_7","article-title":"A learning algorithm for Boltzmann machines","volume":"9","author":"Ackley","year":"1985","journal-title":"Cogn. Sci."},{"key":"ref_8","unstructured":"Goodfellow, I., Bengio, Y., and Courville, A. (2016). Deep Learning, MIT Press."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"054106","DOI":"10.1103\/PhysRevE.105.054106","article-title":"Numerical test of the replica-symmetric Hamiltonian for correlations of the critical state of spin glasses in a field","volume":"105","author":"Fernandez","year":"2022","journal-title":"Phys. Rev. E"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"620","DOI":"10.1103\/PhysRev.106.620","article-title":"Information theory and statistical mechanics","volume":"106","author":"Jaynes","year":"1957","journal-title":"Phys. Rev."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"477","DOI":"10.1007\/BF00709116","article-title":"The well-posed problem","volume":"3","author":"Jaynes","year":"1973","journal-title":"Found. Phys."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Jaynes, E.T. (1988). How Does the Brain Do Plausible Reasoning?, Springer.","DOI":"10.1007\/978-94-009-3049-0_1"},{"key":"ref_13","unstructured":"Laplace, P.S. (1998). Pierre-Simon Laplace Philosophical Essay on Probabilities: Translated from the Fifth French Edition of 1825 with Notes by the Translator, Springer."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1007\/BF01857727","article-title":"Conservative logic","volume":"21","author":"Fredkin","year":"1982","journal-title":"Int. J. Theor. Phys."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Daube, J.R., and Stead, S.M. (2009). Textbook of Clinical Neurophysiology, Oxford. [3rd ed.].","DOI":"10.1093\/med\/9780195385113.001.0001"},{"key":"ref_16","unstructured":"(2023, March 30). Available online: https:\/\/github.com\/ArturoBerronesSantos\/bioplausBM."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"014016","DOI":"10.1103\/PhysRevApplied.17.014016","article-title":"Hardware-aware in situ learning based on stochastic magnetic tunnel junctions","volume":"17","author":"Kaiser","year":"2022","journal-title":"Phys. Rev. Appl."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"5710","DOI":"10.1038\/s41467-021-26012-5","article-title":"Reconfigurable Stochastic neurons based on tin oxide\/MoS2 hetero-memristors for simulated annealing and the Boltzmann machine","volume":"12","author":"Yan","year":"2021","journal-title":"Nat. Commun."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"463","DOI":"10.1146\/annurev-neuro-062111-150403","article-title":"Decision-related activity in sensory neurons: Correlations among neurons and with behavior","volume":"35","author":"Nienborg","year":"2012","journal-title":"Annu. Rev. Neurosci."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"3912","DOI":"10.1016\/j.physa.2013.04.053","article-title":"Thermodynamic paths and stochastic order in open systems","volume":"392","author":"Lucia","year":"2013","journal-title":"Phys. A Stat. Mech. Appl."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1140\/epjb\/e2009-00161-0","article-title":"Maximum entropy principle and power-law tailed distributions","volume":"70","author":"Kaniadakis","year":"2009","journal-title":"Eur. Phys. J. B"}],"container-title":["Informatics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2227-9709\/10\/3\/62\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T20:12:19Z","timestamp":1760127139000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2227-9709\/10\/3\/62"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,7,14]]},"references-count":21,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2023,9]]}},"alternative-id":["informatics10030062"],"URL":"https:\/\/doi.org\/10.3390\/informatics10030062","relation":{},"ISSN":["2227-9709"],"issn-type":[{"type":"electronic","value":"2227-9709"}],"subject":[],"published":{"date-parts":[[2023,7,14]]}}}