Severity: Warning
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Filename: drivers/Session_files_driver.php
Line Number: 177
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File: /var/www/html/index.php
Line: 316
Function: require_once
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Filename: Session/Session.php
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File: /var/www/html/index.php
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Function: require_once
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Message: Undefined array key "choices"
Filename: controllers/Detail.php
Line Number: 249
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File: /var/www/html/application/controllers/Detail.php
Line: 249
Function: _error_handler
File: /var/www/html/index.php
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Function: require_once
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Filename: controllers/Detail.php
Line Number: 249
Backtrace:
File: /var/www/html/application/controllers/Detail.php
Line: 249
Function: _error_handler
File: /var/www/html/index.php
Line: 316
Function: require_once
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Message: Trying to access array offset on value of type null
Filename: controllers/Detail.php
Line Number: 249
Backtrace:
File: /var/www/html/application/controllers/Detail.php
Line: 249
Function: _error_handler
File: /var/www/html/index.php
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Function: require_once
Severity: Warning
Message: Trying to access array offset on value of type null
Filename: controllers/Detail.php
Line Number: 249
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File: /var/www/html/application/controllers/Detail.php
Line: 249
Function: _error_handler
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Function: require_once
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Message: strpos(): Passing null to parameter #1 ($haystack) of type string is deprecated
Filename: models/Detail_model.php
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File: /var/www/html/application/models/Detail_model.php
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Function: strpos
File: /var/www/html/application/controllers/Detail.php
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Function: insertAPISummary
File: /var/www/html/index.php
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Function: require_once
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Message: str_replace(): Passing null to parameter #3 ($subject) of type array|string is deprecated
Filename: helpers/my_audit_helper.php
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File: /var/www/html/application/helpers/my_audit_helper.php
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Function: str_replace
File: /var/www/html/application/controllers/Detail.php
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Function: formatAIDetailSummary
File: /var/www/html/index.php
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Function: require_once
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Message: Undefined array key "choices"
Filename: controllers/Detail.php
Line Number: 256
Backtrace:
File: /var/www/html/application/controllers/Detail.php
Line: 256
Function: _error_handler
File: /var/www/html/index.php
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Function: require_once
Severity: Warning
Message: Trying to access array offset on value of type null
Filename: controllers/Detail.php
Line Number: 256
Backtrace:
File: /var/www/html/application/controllers/Detail.php
Line: 256
Function: _error_handler
File: /var/www/html/index.php
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Function: require_once
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Message: Trying to access array offset on value of type null
Filename: controllers/Detail.php
Line Number: 256
Backtrace:
File: /var/www/html/application/controllers/Detail.php
Line: 256
Function: _error_handler
File: /var/www/html/index.php
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Function: require_once
Severity: Warning
Message: Undefined array key "usage"
Filename: controllers/Detail.php
Line Number: 257
Backtrace:
File: /var/www/html/application/controllers/Detail.php
Line: 257
Function: _error_handler
File: /var/www/html/index.php
Line: 316
Function: require_once
Severity: Warning
Message: Trying to access array offset on value of type null
Filename: controllers/Detail.php
Line Number: 257
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File: /var/www/html/application/controllers/Detail.php
Line: 257
Function: _error_handler
File: /var/www/html/index.php
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Function: require_once
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Message: Undefined array key "usage"
Filename: controllers/Detail.php
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Backtrace:
File: /var/www/html/application/controllers/Detail.php
Line: 258
Function: _error_handler
File: /var/www/html/index.php
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Function: require_once
Severity: Warning
Message: Trying to access array offset on value of type null
Filename: controllers/Detail.php
Line Number: 258
Backtrace:
File: /var/www/html/application/controllers/Detail.php
Line: 258
Function: _error_handler
File: /var/www/html/index.php
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Function: require_once
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Message: Undefined array key "usage"
Filename: controllers/Detail.php
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File: /var/www/html/application/controllers/Detail.php
Line: 259
Function: _error_handler
File: /var/www/html/index.php
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Message: Trying to access array offset on value of type null
Filename: controllers/Detail.php
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File: /var/www/html/application/controllers/Detail.php
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Function: _error_handler
File: /var/www/html/index.php
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Function: require_once
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Message: Undefined array key "usage"
Filename: controllers/Detail.php
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File: /var/www/html/application/controllers/Detail.php
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Function: _error_handler
File: /var/www/html/index.php
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Message: Trying to access array offset on value of type null
Filename: controllers/Detail.php
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File: /var/www/html/application/controllers/Detail.php
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Function: _error_handler
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Filename: controllers/Detail.php
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File: /var/www/html/application/controllers/Detail.php
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Function: _error_handler
File: /var/www/html/index.php
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Function: require_once
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Message: file_get_contents(https://...@gmail.com&api_key=61f08fa0b96a73de8c900d749fcb997acc09): Failed to open stream: HTTP request failed! HTTP/1.1 429 Too Many Requests
Filename: helpers/my_audit_helper.php
Line Number: 143
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File: /var/www/html/application/helpers/my_audit_helper.php
Line: 143
Function: file_get_contents
File: /var/www/html/application/helpers/my_audit_helper.php
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Function: simplexml_load_file_from_url
File: /var/www/html/application/helpers/my_audit_helper.php
Line: 3098
Function: getPubMedXML
File: /var/www/html/application/controllers/Detail.php
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Function: pubMedSearch_Global
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Function: pubMedGetRelatedKeyword
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Filename: helpers/my_audit_helper.php
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File: /var/www/html/application/helpers/my_audit_helper.php
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Function: _error_handler
File: /var/www/html/application/controllers/Detail.php
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File: /var/www/html/application/controllers/Detail.php
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Function: pubMedGetRelatedKeyword
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Function: require_once
Increasing interest in the thermodynamics of small and/or isolated systems, in combination with recent observations of negative temperatures of atoms in ultracold optical lattices, has stimulated the need for estimating the conventional, canonical temperature T of systems in equilibrium with heat baths using eigenstate-specific temperatures (ESTs). Four distinct ESTs-continuous canonical, discrete canonical, continuous microcanonical, and discrete microcanonical-are accordingly derived for two-level paramagnetic spin lattices (PSLs) in external magnetic fields. At large N, the four ESTs are intensive, equal to T, and obey all four laws of thermodynamics. In contrast, for N < 1000, the ESTs of most PSL eigenstates are non-intensive, differ from T, and violate each of the thermodynamic laws. Hence, in spite of their similarities to T at large N, the ESTs are not true thermodynamic temperatures. Even so, each of the ESTs manifests a unique functional dependence on energy which clearly specifies the magnitude and direction of their deviation from T; the ESTs are thus good temperature estimators for small PSLs. The thermodynamic uncertainty relation is obeyed only by the ESTs of small canonical PSLs; it is violated by large canonical PSLs and by microcanonical PSLs of any size. The ESTs of population-inverted eigenstates are negative (positive) when calculated using Boltzmann (Gibbs) entropies; the thermodynamic implications of these entropically induced differences in sign are discussed in light of adiabatic invariance of the entropies. Potential applications of the four ESTs to nanothermometers and to systems with long-range interactions are discussed.
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http://dx.doi.org/10.1063/1.5012914 | DOI Listing |
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