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Both methods preserve the target equilibrium distribution by construction in linear settings, reduce correlation times without manual parameter tuning, and remain robust at finite timesteps. The AGLE selectively damps under-thermostatted spectral bands while maintaining exact fluctuation\u2013dissipation balance. The barostat suppresses resonances of traditional Parrinello\u2013Rahman schemes, adapts automatically to a target log-volume relaxation time, and, when combined with sparse Monte Carlo moves, guarantees exact sampling of the isothermal\u2013isobaric ensemble. Validation requires only linear-algebraic tests: all moment identities, autocorrelation functions, and volume statistics can be obtained without running interacting trajectories. Both schemes are black-box, require minimal tuning, and guarantee ensemble exactness at a finite timestep. These developments provide flexible building blocks for large-scale molecular simulations, unifying colored-noise thermostats with modern barostatting strategies.<\/jats:p>","DOI":"10.1063\/5.0303251","type":"journal-article","created":{"date-parts":[[2026,1,15]],"date-time":"2026-01-15T11:17:14Z","timestamp":1768475834000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":1,"title":["Adaptive colored-noise thermostats and piston barostats with exact\n                    <i>NPT<\/i>\n                    sampling"],"prefix":"10.1063","volume":"164","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6937-9950","authenticated-orcid":false,"given":"Francisco","family":"G\u00e1mez","sequence":"first","affiliation":[{"name":"Departamento de Qu\u00edmica F\u00edsica, Universidad Complutense de Madrid , 28040 Madrid,","place":["Spain"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2026,1,15]]},"reference":[{"key":"2026011506170752200_c1","volume-title":"Understanding Molecular Simulation","year":"2002","edition":"2"},{"key":"2026011506170752200_c2","volume-title":"Computer Simulation of Liquids","year":"2017","edition":"2"},{"key":"2026011506170752200_c3","volume-title":"Statistical Mechanics: Theory and Molecular Simulation","year":"2010"},{"key":"2026011506170752200_c4","doi-asserted-by":"publisher","first-page":"2384","DOI":"10.1063\/1.439486","volume":"72","year":"1980","journal-title":"J.\u00a0Chem. 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