{"doi":"10.30538/oms2020.0136","title":"Towards understanding the mathematics of the \\(2^{nd}\\) law of thermodynamics","abstract":"<jats:p>In this paper, the mathematical formulation of \\(2^{nd}\\) law of thermodynamics has been explained, and the mathematical formulation of \\(1^{st}\\) law has been revisited from this noble perspective. It is not claimed that the \\(2^{nd}\\) law of thermodynamics is a redundant of the \\(1^{st}\\) law, rather I shown here how we can extract the mathematical formulation of the \\(2^{nd}\\) law from the mathematical formulation of the \\(1^{st}\\) law of thermodynamics. The Clausius statement of the \\(2^{nd}\\) law of thermodynamics is, it is impossible to construct a device whose sole effect is the transfer of heat from a cool reservoir to a hot reservoir. An alternative statement of the law is, \"All spontaneous processes are irreversible\" or, \"the entropy of an isolated system always increases\". Having strong experimental evidences, this empirical law is obvious, which tells us the arrow of time and the direction of spontaneous changes.</jats:p>","journal":"Open Journal of Mathematical Sciences","year":2020,"id":28220,"datarank":0.0,"base_score":0.0,"endowment":0.0,"self_citation_contribution":0.0,"citation_network_contribution":0.0,"self_endowment_contribution":0.0,"citer_contribution":0.0,"corpus_percentile":null,"corpus_rank":null,"citation_count":0,"citer_count":0,"citers_with_citation_signal":0,"citers_with_endowment":0,"datacite_reuse_total":0,"is_dataset":false,"is_dataset_confidence":null,"is_data_producer":false,"deposit_databanks":null,"is_oa":false,"file_count":0,"downloads":0,"has_version_chain":false,"published_date":null,"fair_score":null,"fair_percentile":null,"algorithm_id":"datarank_citation_only_1hop_v6","ranking_scope":"data_only","authors":[{"id":158629,"name":"Md. Shafiqul Islam","orcid":null,"position":1,"is_corresponding":false}],"reference_count":0,"raw_metadata":{"has_enrichment":true,"base_score":0.0,"endowment":0.0,"datacite_reuse_total":0,"file_count":0,"downloads":0,"views":0,"has_version_chain":false,"is_dataset":false,"is_oa":false,"pmid":"24523987","pmcid":null,"openalex_id":"https://openalex.org/W3124981253","authors":[],"funders":[],"total_grants":0,"fwci":0.0,"citation_percentile":0.18198847,"influential_citations":0,"citation_trend":[],"oa_status":"gold","license":"cc-by","oa_locations":[{"url":"https://doi.org/10.30538/oms2020.0136","host_type":"journal"},{"url":"https://doi.org/10.30538/oms2020.0136","host_type":"GOLD"},{"url":"https://doi.org/10.30538/oms2020.0136","host_type":"publisher"},{"url":"http://doi.org/10.30538/oms2020.0136","host_type":"journal"},{"url":"https://doaj.org/article/4d02c039d4a449b7ad7a387fc6f207e3","host_type":"repository"}],"fields_of_study":["Advanced Thermodynamics and Statistical Mechanics","Statistical Mechanics and Entropy","Phase Equilibria and Thermodynamics","Chemistry","Mathematics"],"mesh_terms":[],"keywords":["Second law of thermodynamics","Laws of thermodynamics","Thermodynamics","Non-equilibrium thermodynamics","Entropy (arrow of time)","On the Equilibrium of Heterogeneous Substances","First law of thermodynamics","Law","Extended irreversible thermodynamics","First law","Mathematics","Statistical physics","Physics"],"sdg_mappings":[{"sdg_number":0,"sdg_label":"Peace, Justice and strong institutions"}],"linked_datasets":[],"clinical_trials":[],"software_tools":[],"database_accessions":[],"source":"live","citation_network_status":"fetched"},"created_at":"2026-06-08T20:55:54.972697Z","pmid":null,"pmcid":null,"fwci":null,"citation_percentile":null,"influential_citations":0,"oa_status":null,"license":null,"views":0,"total_file_size_bytes":0,"version_count":0,"fair_f":null,"fair_a":null,"fair_i":null,"fair_r":null,"fair_zscore":null,"fair_rationale":null,"fair_model":null,"fair_agent_version":null,"fair_fulltext_source":null,"fair_has_llm":null,"fair_computed_at":null,"clinical_trials":[],"software_tools":[],"db_accessions":[],"linked_datasets":[],"topics":[]}