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We provide an error estimate of the difference of physical observable induced by the variation of bath correlation function, based on diagrammatic and combinatorial arguments. This gives a mathematically rigorous justification of the result in \\cite{mascherpa2017open}.<\/jats:p>","DOI":"10.22331\/q-2025-10-28-1896","type":"journal-article","created":{"date-parts":[[2025,10,28]],"date-time":"2025-10-28T15:23:23Z","timestamp":1761665003000},"page":"1896","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":3,"title":["Error Bounds for Open Quantum Systems with Harmonic Bosonic Bath"],"prefix":"10.22331","volume":"9","author":[{"ORCID":"https:\/\/orcid.org\/0009-0008-7753-0030","authenticated-orcid":false,"given":"Kaizhao","family":"Liu","sequence":"first","affiliation":[{"name":"Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Ave, Cambridge MA 02139, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6255-5165","authenticated-orcid":false,"given":"Jianfeng","family":"Lu","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Department of Physics, Department of Chemistry, Duke University, Box 90320, Durham NC 27708, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"9598","published-online":{"date-parts":[[2025,10,28]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"Massimiliano Esposito, Upendra Harbola, and Shaul Mukamel. ``Nonequilibrium fluctuations, fluctuation theorems, and counting statistics in quantum systems''. 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