Get quick answers to your questions about the article from our AI researcher chatbot
{'id': 'https://openalex.org/W2046170388', 'doi': 'https://doi.org/10.1103/physrevlett.80.218', 'title': 'Perturbation and Variational Methods in Nonextensive Tsallis Statistics', 'display_name': 'Perturbation and Variational Methods in Nonextensive Tsallis Statistics', 'publication_year': 1998, 'publication_date': '1998-01-12', 'ids': {'openalex': 'https://openalex.org/W2046170388', 'doi': 'https://doi.org/10.1103/physrevlett.80.218', 'mag': '2046170388'}, 'language': 'en', 'primary_location': {'is_oa': False, 'landing_page_url': 'https://doi.org/10.1103/physrevlett.80.218', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S24807848', 'display_name': 'Physical Review Letters', 'issn_l': '0031-9007', 'issn': ['0031-9007', '1079-7114', '1092-0145'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310320261', 'host_organization_name': 'American Physical Society', 'host_organization_lineage': ['https://openalex.org/P4310320261'], 'host_organization_lineage_names': ['American Physical Society'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}, 'type': 'article', 'type_crossref': 'journal-article', 'indexed_in': ['arxiv', 'crossref', 'datacite'], 'open_access': {'is_oa': True, 'oa_status': 'green', 'oa_url': 'http://arxiv.org/pdf/cond-mat/9804095', 'any_repository_has_fulltext': True}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5060481487', 'display_name': 'E. K. Lenzi', 'orcid': 'https://orcid.org/0000-0003-3853-1790'}, 'institutions': [{'id': 'https://openalex.org/I4210125245', 'display_name': 'Centro Brasileiro de Pesquisas Físicas', 'ror': 'https://ror.org/02wnmk332', 'country_code': 'BR', 'type': 'facility', 'lineage': ['https://openalex.org/I4210125245', 'https://openalex.org/I4210151455']}], 'countries': ['BR'], 'is_corresponding': False, 'raw_author_name': 'E. K. Lenzi', 'raw_affiliation_strings': ['Centro Brasileiro de Pesquisas Físicas, R. Dr. Xavier Sigaud 150, 22290-180 Rio de Janeiro-RJ, Brazil'], 'affiliations': [{'raw_affiliation_string': 'Centro Brasileiro de Pesquisas Físicas, R. Dr. Xavier Sigaud 150, 22290-180 Rio de Janeiro-RJ, Brazil', 'institution_ids': ['https://openalex.org/I4210125245']}]}, {'author_position': 'middle', 'author': {'id': 'https://openalex.org/A5023139160', 'display_name': 'L. C. Malacarne', 'orcid': 'https://orcid.org/0000-0002-9436-6497'}, 'institutions': [{'id': 'https://openalex.org/I123443094', 'display_name': 'Universidade Estadual de Maringá', 'ror': 'https://ror.org/04bqqa360', 'country_code': 'BR', 'type': 'education', 'lineage': ['https://openalex.org/I123443094']}, {'id': 'https://openalex.org/I17974374', 'display_name': 'Universidade de São Paulo', 'ror': 'https://ror.org/036rp1748', 'country_code': 'BR', 'type': 'education', 'lineage': ['https://openalex.org/I17974374']}], 'countries': ['BR'], 'is_corresponding': False, 'raw_author_name': 'L. C. Malacarne', 'raw_affiliation_strings': ['Departamento de Física Matemática, Instituto de Física da Universidade de São Paulo, Caixa Postal 20516, 01498, São Paulo-SP, Brazil', 'Departamento de Física, Universidade Estadual de Maringá, Avenida Colombo 5790, 87020-900 Maringá-PR, Brazil'], 'affiliations': [{'raw_affiliation_string': 'Departamento de Física, Universidade Estadual de Maringá, Avenida Colombo 5790, 87020-900 Maringá-PR, Brazil', 'institution_ids': ['https://openalex.org/I123443094']}, {'raw_affiliation_string': 'Departamento de Física Matemática, Instituto de Física da Universidade de São Paulo, Caixa Postal 20516, 01498, São Paulo-SP, Brazil', 'institution_ids': ['https://openalex.org/I17974374']}]}, {'author_position': 'last', 'author': {'id': 'https://openalex.org/A5043332827', 'display_name': 'R. S. Mendes', 'orcid': 'https://orcid.org/0009-0002-5216-0578'}, 'institutions': [{'id': 'https://openalex.org/I123443094', 'display_name': 'Universidade Estadual de Maringá', 'ror': 'https://ror.org/04bqqa360', 'country_code': 'BR', 'type': 'education', 'lineage': ['https://openalex.org/I123443094']}, {'id': 'https://openalex.org/I4210125245', 'display_name': 'Centro Brasileiro de Pesquisas Físicas', 'ror': 'https://ror.org/02wnmk332', 'country_code': 'BR', 'type': 'facility', 'lineage': ['https://openalex.org/I4210125245', 'https://openalex.org/I4210151455']}], 'countries': ['BR'], 'is_corresponding': False, 'raw_author_name': 'R. S. Mendes', 'raw_affiliation_strings': ['Centro Brasileiro de Pesquisas Físicas, R. Dr. Xavier Sigaud 150, 22290-180 Rio de Janeiro-RJ, Brazil', 'Departamento de Física, Universidade Estadual de Maringá, Avenida Colombo 5790, 87020-900 Maringá-PR, Brazil'], 'affiliations': [{'raw_affiliation_string': 'Departamento de Física, Universidade Estadual de Maringá, Avenida Colombo 5790, 87020-900 Maringá-PR, Brazil', 'institution_ids': ['https://openalex.org/I123443094']}, {'raw_affiliation_string': 'Centro Brasileiro de Pesquisas Físicas, R. Dr. Xavier Sigaud 150, 22290-180 Rio de Janeiro-RJ, Brazil', 'institution_ids': ['https://openalex.org/I4210125245']}]}], 'institution_assertions': [], 'countries_distinct_count': 1, 'institutions_distinct_count': 3, 'corresponding_author_ids': [], 'corresponding_institution_ids': [], 'apc_list': {'value': 3750, 'currency': 'USD', 'value_usd': 3750, 'provenance': 'doaj'}, 'apc_paid': None, 'fwci': 5.917, 'has_fulltext': True, 'fulltext_origin': 'pdf', 'cited_by_count': 52, 'citation_normalized_percentile': {'value': 0.842097, 'is_in_top_1_percent': False, 'is_in_top_10_percent': False}, 'cited_by_percentile_year': {'min': 92, 'max': 93}, 'biblio': {'volume': '80', 'issue': '2', 'first_page': '218', 'last_page': '221'}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T12261', 'display_name': 'Statistical Mechanics and Entropy', 'score': 0.9999, 'subfield': {'id': 'https://openalex.org/subfields/3109', 'display_name': 'Statistical and Nonlinear Physics'}, 'field': {'id': 'https://openalex.org/fields/31', 'display_name': 'Physics and Astronomy'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}, 'topics': [{'id': 'https://openalex.org/T12261', 'display_name': 'Statistical Mechanics and Entropy', 'score': 0.9999, 'subfield': {'id': 'https://openalex.org/subfields/3109', 'display_name': 'Statistical and Nonlinear Physics'}, 'field': {'id': 'https://openalex.org/fields/31', 'display_name': 'Physics and Astronomy'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}, {'id': 'https://openalex.org/T10288', 'display_name': 'Fractional Differential Equations Solutions', 'score': 0.9961, 'subfield': {'id': 'https://openalex.org/subfields/2611', 'display_name': 'Modeling and Simulation'}, 'field': {'id': 'https://openalex.org/fields/26', 'display_name': 'Mathematics'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}, {'id': 'https://openalex.org/T11270', 'display_name': 'Complex Systems and Time Series Analysis', 'score': 0.9535, 'subfield': {'id': 'https://openalex.org/subfields/2002', 'display_name': 'Economics and Econometrics'}, 'field': {'id': 'https://openalex.org/fields/20', 'display_name': 'Economics, Econometrics and Finance'}, 'domain': {'id': 'https://openalex.org/domains/2', 'display_name': 'Social Sciences'}}], 'keywords': [{'id': 'https://openalex.org/keywords/tsallis-entropy', 'display_name': 'Tsallis entropy', 'score': 0.79990125}, {'id': 'https://openalex.org/keywords/statistical-mechanics', 'display_name': 'Statistical Mechanics', 'score': 0.77739394}], 'concepts': [{'id': 'https://openalex.org/C117521176', 'wikidata': 'https://www.wikidata.org/wiki/Q7849341', 'display_name': 'Tsallis entropy', 'level': 3, 'score': 0.79990125}, {'id': 'https://openalex.org/C99874945', 'wikidata': 'https://www.wikidata.org/wiki/Q188715', 'display_name': 'Statistical mechanics', 'level': 2, 'score': 0.77739394}, {'id': 'https://openalex.org/C171018156', 'wikidata': 'https://www.wikidata.org/wiki/Q7370306', 'display_name': 'Rotation formalisms in three dimensions', 'level': 2, 'score': 0.5976677}, {'id': 'https://openalex.org/C121864883', 'wikidata': 'https://www.wikidata.org/wiki/Q677916', 'display_name': 'Statistical physics', 'level': 1, 'score': 0.5830102}, {'id': 'https://openalex.org/C177918212', 'wikidata': 'https://www.wikidata.org/wiki/Q803623', 'display_name': 'Perturbation (astronomy)', 'level': 2, 'score': 0.5281617}, {'id': 'https://openalex.org/C106301342', 'wikidata': 'https://www.wikidata.org/wiki/Q4117933', 'display_name': 'Entropy (arrow of time)', 'level': 2, 'score': 0.49506155}, {'id': 'https://openalex.org/C2780056601', 'wikidata': 'https://www.wikidata.org/wiki/Q7849339', 'display_name': 'Tsallis statistics', 'level': 2, 'score': 0.45860916}, {'id': 'https://openalex.org/C37914503', 'wikidata': 'https://www.wikidata.org/wiki/Q156495', 'display_name': 'Mathematical physics', 'level': 1, 'score': 0.4433074}, {'id': 'https://openalex.org/C65574998', 'wikidata': 'https://www.wikidata.org/wiki/Q386272', 'display_name': 'Feynman diagram', 'level': 2, 'score': 0.4394093}, {'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.4137818}, {'id': 'https://openalex.org/C74650414', 'wikidata': 'https://www.wikidata.org/wiki/Q11397', 'display_name': 'Classical mechanics', 'level': 1, 'score': 0.3631066}, {'id': 'https://openalex.org/C121332964', 'wikidata': 'https://www.wikidata.org/wiki/Q413', 'display_name': 'Physics', 'level': 0, 'score': 0.3395579}, {'id': 'https://openalex.org/C28826006', 'wikidata': 'https://www.wikidata.org/wiki/Q33521', 'display_name': 'Applied mathematics', 'level': 1, 'score': 0.33394343}, {'id': 'https://openalex.org/C62520636', 'wikidata': 'https://www.wikidata.org/wiki/Q944', 'display_name': 'Quantum mechanics', 'level': 1, 'score': 0.20944363}, {'id': 'https://openalex.org/C2524010', 'wikidata': 'https://www.wikidata.org/wiki/Q8087', 'display_name': 'Geometry', 'level': 1, 'score': 0.0}], 'mesh': [], 'locations_count': 4, 'locations': [{'is_oa': False, 'landing_page_url': 'https://doi.org/10.1103/physrevlett.80.218', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S24807848', 'display_name': 'Physical Review Letters', 'issn_l': '0031-9007', 'issn': ['0031-9007', '1079-7114', '1092-0145'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310320261', 'host_organization_name': 'American Physical Society', 'host_organization_lineage': ['https://openalex.org/P4310320261'], 'host_organization_lineage_names': ['American Physical Society'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}, {'is_oa': True, 'landing_page_url': 'http://arxiv.org/abs/cond-mat/9804095', 'pdf_url': 'http://arxiv.org/pdf/cond-mat/9804095', 'source': {'id': 'https://openalex.org/S4306400194', 'display_name': 'arXiv (Cornell University)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I205783295', 'host_organization_name': 'Cornell University', 'host_organization_lineage': ['https://openalex.org/I205783295'], 'host_organization_lineage_names': ['Cornell University'], 'type': 'repository'}, 'license': None, 'license_id': None, 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}, {'is_oa': True, 'landing_page_url': 'https://arxiv.org/abs/cond-mat/9804095', 'pdf_url': 'https://arxiv.org/pdf/cond-mat/9804095', 'source': {'id': 'https://openalex.org/S4306400194', 'display_name': 'arXiv (Cornell University)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I205783295', 'host_organization_name': 'Cornell University', 'host_organization_lineage': ['https://openalex.org/I205783295'], 'host_organization_lineage_names': ['Cornell University'], 'type': 'repository'}, 'license': None, 'license_id': None, 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}, {'is_oa': False, 'landing_page_url': 'https://api.datacite.org/dois/10.48550/arxiv.cond-mat/9804095', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S4393179698', 'display_name': 'DataCite API', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I4210145204', 'host_organization_name': 'DataCite', 'host_organization_lineage': ['https://openalex.org/I4210145204'], 'host_organization_lineage_names': ['DataCite'], 'type': 'metadata'}, 'license': None, 'license_id': None, 'version': None}], 'best_oa_location': {'is_oa': True, 'landing_page_url': 'http://arxiv.org/abs/cond-mat/9804095', 'pdf_url': 'http://arxiv.org/pdf/cond-mat/9804095', 'source': {'id': 'https://openalex.org/S4306400194', 'display_name': 'arXiv (Cornell University)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I205783295', 'host_organization_name': 'Cornell University', 'host_organization_lineage': ['https://openalex.org/I205783295'], 'host_organization_lineage_names': ['Cornell University'], 'type': 'repository'}, 'license': None, 'license_id': None, 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}, 'sustainable_development_goals': [{'id': 'https://metadata.un.org/sdg/10', 'display_name': 'Reduced inequalities', 'score': 0.42}], 'grants': [], 'datasets': [], 'versions': ['https://openalex.org/W2046170388'], 'referenced_works_count': 37, 'referenced_works': ['https://openalex.org/W1975259897', 'https://openalex.org/W1983874169', 'https://openalex.org/W1999777726', 'https://openalex.org/W2001523346', 'https://openalex.org/W2004872575', 'https://openalex.org/W2005619765', 'https://openalex.org/W2009387827', 'https://openalex.org/W2017073970', 'https://openalex.org/W2021649169', 'https://openalex.org/W2025653890', 'https://openalex.org/W2025978223', 'https://openalex.org/W2029244269', 'https://openalex.org/W2034502523', 'https://openalex.org/W2041872358', 'https://openalex.org/W2047052554', 'https://openalex.org/W2047511448', 'https://openalex.org/W2053246816', 'https://openalex.org/W2062517214', 'https://openalex.org/W2063314565', 'https://openalex.org/W2064926364', 'https://openalex.org/W2068090132', 'https://openalex.org/W2075324868', 'https://openalex.org/W2077574606', 'https://openalex.org/W2078300394', 'https://openalex.org/W2079941801', 'https://openalex.org/W2088819827', 'https://openalex.org/W2091749817', 'https://openalex.org/W2092946730', 'https://openalex.org/W2313489408', 'https://openalex.org/W2332674559', 'https://openalex.org/W3004320394', 'https://openalex.org/W3040881605', 'https://openalex.org/W3106306086', 'https://openalex.org/W4229869748', 'https://openalex.org/W4229902223', 'https://openalex.org/W4232328843', 'https://openalex.org/W4249653603'], 'related_works': ['https://openalex.org/W568016335', 'https://openalex.org/W4387883270', 'https://openalex.org/W2753051222', 'https://openalex.org/W2399462240', 'https://openalex.org/W2379111240', 'https://openalex.org/W2361046054', 'https://openalex.org/W2154579008', 'https://openalex.org/W2077192097', 'https://openalex.org/W2015649491', 'https://openalex.org/W1998223346'], 'abstract_inverted_index': {'A': [0], 'unified': [1], 'presentation': [2], 'of': [3, 24, 85], 'the': [4, 10, 22, 25, 28, 39, 43, 58, 83], 'perturbation': [5], 'and': [6], 'variational': [7, 26], 'methods': [8], 'for': [9, 42], 'generalized': [11, 32], 'statistical': [12, 45], 'mechanics': [13], 'based': [14], 'on': [15], 'Tsallis': [16], 'entropy': [17], 'is': [18, 31, 64], 'given': [19], 'here.': [20], 'In': [21], 'case': [23], 'method,': [27], 'Bogoliubov': [29], 'inequality': [30, 48], 'in': [33, 70, 82], 'a': [34, 67], 'very': [35], 'natural': [36], 'way': [37], 'following': [38], 'Feynman': [40], 'proof': [41], 'usual': [44], 'mechanics.': [46, 72], 'The': [47, 62, 73], 'turns': [49], 'out': [50], 'to': [51, 57, 79], 'be': [52, 80], 'form': [53], 'invariant': [54], 'with': [55, 66], 'respect': [56], 'entropic': [59], 'index': [60], '$q$.': [61], 'method': [63], 'illustrated': [65], 'simple': [68], 'example': [69], 'classical': [71], 'formalisms': [74], 'developed': [75], 'here': [76], 'are': [77], 'expected': [78], 'useful': [81], 'discussion': [84], 'nonextensive': [86], 'systems.': [87]}, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W2046170388', 'counts_by_year': [{'year': 2017, 'cited_by_count': 1}, {'year': 2014, 'cited_by_count': 1}, {'year': 2013, 'cited_by_count': 2}, {'year': 2012, 'cited_by_count': 2}], 'updated_date': '2024-12-10T16:14:33.690385', 'created_date': '2016-06-24'}