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In this paper, we study the thermodynamics and corrections of spherically symmetric BHs in models f(R)=R+\u03b1R2 and f(R)=R+2\u03b3R+8\u039b under the f(R) theory, which includes the electrodynamic field and the cosmological constant. Considering thermal fluctuations around equilibrium states, we find that, for both f(R) models, the corrected entropy is meaningful in the case of a negative cosmological constant (anti-de Sitter\u2013RN spacetime) with \u039b=\u22121. It is shown that when the BHs\u2019 horizon radius is small, thermal fluctuations have a more significant effect on the corrected entropy. Using the corrected entropy, we derive expressions for the relevant corrected thermodynamic quantities (such as Helmholtz free energy, internal energy, Gibbs free energy, and specific heat) and calculate the effects of the correction terms. The results indicate that the corrections to Helmholtz free energy and Gibbs free energy, caused by thermal fluctuations, are remarkable for small BHs. In addition, we explore the stability of BHs using specific heat. The study reveals that the corrected BH thermodynamics exhibit locally stable for both models, and corrected systems undergo a Hawking\u2013Page phase transition. Considering the requirement on the non-negative volume of BHs, we also investigate the constraint on the EH radius of BHs.<\/jats:p>","DOI":"10.3390\/e26100868","type":"journal-article","created":{"date-parts":[[2024,10,16]],"date-time":"2024-10-16T11:28:51Z","timestamp":1729078131000},"page":"868","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Corrected Thermodynamics of Black Holes in f(R) Gravity with Electrodynamic Field and Cosmological Constant"],"prefix":"10.3390","volume":"26","author":[{"given":"Mou","family":"Xu","sequence":"first","affiliation":[{"name":"Department of Physics, Liaoning Normal University, Dalian 116029, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yuying","family":"Zhang","sequence":"additional","affiliation":[{"name":"Department of Physics, Liaoning Normal University, Dalian 116029, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Liu","family":"Yang","sequence":"additional","affiliation":[{"name":"Department of Physics, Liaoning Normal University, Dalian 116029, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shining","family":"Yang","sequence":"additional","affiliation":[{"name":"Department of Physics, Liaoning Normal University, Dalian 116029, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jianbo","family":"Lu","sequence":"additional","affiliation":[{"name":"Department of Physics, Liaoning Normal University, Dalian 116029, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2024,10,15]]},"reference":[{"key":"ref_1","unstructured":"Weinberg, S. 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