{"id":52634,"date":"2024-09-10T11:31:03","date_gmt":"2024-09-10T03:31:03","guid":{"rendered":"https:\/\/swarma.org\/?p=52634"},"modified":"2024-09-10T11:31:03","modified_gmt":"2024-09-10T03:31:03","slug":"%e4%bb%8e%e7%a2%b0%e7%a2%b0%e8%bd%a6%e8%b0%88%e8%b5%b7%ef%bc%9a%e6%8b%93%e5%b1%95%e7%88%b1%e5%9b%a0%e6%96%af%e5%9d%a6%e5%85%b3%e7%b3%bb%ef%bc%8c%e5%b1%95%e7%a4%ba%e6%9b%b4%e5%a4%9a%e7%90%86%e8%ae%ba","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=52634","title":{"rendered":"\u4ece\u78b0\u78b0\u8f66\u8c08\u8d77\uff1a\u62d3\u5c55\u7231\u56e0\u65af\u5766\u5173\u7cfb\uff0c\u5c55\u793a\u66f4\u591a\u7406\u8bba\u53d1\u73b0"},"content":{"rendered":"
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\u904d\u5386\u6027\u662f\u5e73\u8861\u6001\u7edf\u8ba1\u7269\u7406\u7684\u552f\u4e00\u5047\u8bbe\uff0c\u5373\u4e00\u4e2a\u89c2\u6d4b\u91cf\u7684\u65f6\u95f4\u5e73\u5747\u7b49\u4e8e\u5b83\u7684\u7cfb\u7efc\u5e73\u5747<\/span><\/strong>\u3002\u7136\u800c\u5bf9\u4e8e\u8fd9\u4e2a\u7b80\u5355\u7684\u8868\u8ff0\uff0c\u65e0\u8bba\u7406\u8bba\u8fd8\u662f\u5b9e\u9a8c\u90fd\u96be\u4ee5\u76f4\u63a5\u8bc1\u5b9e\uff0c\u5982\u540c\u4eba\u4eec\u65e0\u6cd5\u5bfb\u89c5\u4e00\u4e2a\u7c92\u5b50\u662f\u5426\u8bbf\u95ee\u4e86\u4e00\u4e2a\u7b49\u80fd\u9762\u4e0a\u7684\u6240\u6709\u5730\u65b9<\/span>\uff08\u76f8\u683c\uff09<\/span>\u90a3\u6837\uff0c\u786e\u5b9a\u5176\u6ee1\u8db3\u4e86\u5404\u6001\u5386\u7ecf\u3002<\/span><\/p>\n


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\u5982\u679c\u4e00\u4e2a\u7b49\u80fd\u9762\u4e0a\u5b58\u5728\u65e0\u9650\u6df1\u52bf\u9631\u6216\u8005\u65e0\u9650\u9ad8\u52bf\u5792<\/span>\uff08\u56fe4\uff09<\/span>\uff0c\u90a3\u4e48\u7c92\u5b50\u4ece\u67d0\u4e00\u521d\u59cb\u4f4d\u7f6e\u51fa\u53d1\uff0c\u5b83\u5c06\u4e0d\u53ef\u80fd\u8bbf\u95ee\u6240\u6709\u7684\u5730\u65b9\uff0c\u79f0\u4e4b\u4e3a\u5f3a\u904d\u5386\u6027\u7834\u7f3a<\/strong>\u3002\u53e6\u5916\u7684\u60c5\u5f62\u662f\uff0c\u867d\u7136\u7b49\u80fd\u9762\u662f\u5149\u6ed1\u7684\uff0c\u4f46\u662f\u7531\u4e8e\u7cfb\u7edf\u4e0e\u5176\u73af\u5883\u53d1\u751f\u4e0d\u5f7b\u5e95\u8017\u6563\uff0c\u4ee5\u81f4\u4e8e\u7cfb\u7edf\u5bf9\u5b83\u7684\u521d\u59cb\u51c6\u5907\u8fd8\u4fdd\u7559\u7740\u90e8\u5206\u8bb0\u5fc6\uff0c\u4f53\u73b0\u5728\u89c2\u6d4b\u91cf\u7684\u5173\u8054\u51fd\u6570\u6e10\u8fdb\u4e0d\u4e3a\u96f6\uff0c\u79f0\u4e4b\u4e3a\u5f31\u904d\u5386\u6027\u7834\u7f3a<\/strong>\uff0c\u7cfbGER\u9762\u4e34\u7684\u6311\u6218[3,6]\u3002<\/span><\/p>\n


<\/p>\n

\u8fc4\u4eca\uff0c\u4e00\u4e9b\u904d\u5386\u6027\u6761\u4ef6\u88ab\u63d0\u51fa\u4e86\uff0c\u5e38\u89c1\u7684\u6709\u4e24\u4e2a\u3002\u5176\u4e00\uff0c\u8f9b\u6b23<\/span>\uff08Khinchin\uff09<\/span>\u5b9a\u7406\uff0c\u5373\u89c2\u6d4b\u91cf\u5173\u8054\u51fd\u6570\u968f\u7740\u4e24\u65f6\u95f4\u5dee\u7684\u589e\u52a0\u800c\u6e10\u8fdb\u6d88\u5931\u3002\u610f\u5473\u7740\u7cfb\u7edf\u5f53\u524d\u7684\u72b6\u6001\u4e0e\u5176\u5148\u524d\u7684\u51c6\u5907\u65e0\u5173\uff0c\u7cfb\u7edf\u9700\u8981\u8bbf\u95ee\u7b49\u80fd\u9762\u4e0a\u7684\u6240\u6709\u5730\u65b9\u3002\u5176\u4e8c\uff0c\u628a\u89c2\u6d4b\u91cf\u7684\u6709\u9650\u65f6\u95f4\u5e73\u5747\u770b\u4f5c\u4e00\u4e2a\u968f\u673a\u53d8\u91cf\uff0c\u8ba1\u7b97\u5b83\u7684\u65b9\u5dee\u3002\u5982\u679c\u957f\u65f6\u95f4\u540e\uff0c\u8fd9\u4e2a\u65b9\u5dee\u7b49\u4e8e\u96f6\uff0c\u5c31\u8868\u793a\u89c2\u6d4b\u91cf\u7684\u65f6\u95f4\u5e73\u5747\u4e3a\u4e00\u5b9a\u503c\uff0c\u800c\u89c2\u6d4b\u91cf\u7684\u7cfb\u7efc\u5e73\u5747\u5f80\u5f80\u662f\u5728\u4e00\u4e2a\u5b9a\u6001\u5206\u5e03\u5bc6\u5ea6\u51fd\u6570\u4e0b\u6c42\u5f97\u7684\uff0c\u5e94\u8be5\u4e5f\u662f\u4e00\u4e2a\u5e38\u91cf\u3002\u6240\u4ee5\uff0c\u89c2\u6d4b\u91cf\u7684\u65f6\u95f4\u5e73\u5747\u8d8b\u4e8e\u5b9a\u5e38\u662f\u904d\u5386\u6027\u6210\u7acb\u7684\u5fc5\u8981\u6761\u4ef6\u3002\u4f5c\u4e3aGER\u7684\u5e94\u7528\uff0c\u6211\u4eec\u8ba8\u8bba\u4e86\u904d\u5386\u6027\u5f31\u7834\u7f3a\u6761\u4ef6\u548c\u975e\u5f39\u78b0\u649e\u9897\u7c92\u7269\u4ecb\u8d28\u4e2d\u7684\u5e03\u6717\u8fd0\u52a8\u3002<\/span>\u53d1\u73b0\u8f9b\u6b23\uff08Khinchin\uff09\u5b9a\u7406\u5373VCF\u6e10\u8fdb\u6d88\u5931\u4ee5\u53ca\u89c2\u6d4b\u91cf\u65f6\u95f4\u5e73\u5747\u7684\u5206\u5e03\u6536\u655b\u7684\u6761\u4ef6\uff0c\u5747\u4e0d\u80fd\u4fdd\u8bc1\u65f6\u95f4\u5e73\u5747\u7b49\u4e8e\u7cfb\u7efc\u5e73\u5747\u3002<\/span><\/strong><\/span>\u5982\u6240\u5468\u77e5\uff0c\u7406\u8bba\u4e0a\u7528\u7cfb\u7efc\u5e73\u5747\uff0c\u5b9e\u9a8c\u4e0a\u7528\u65f6\u95f4\u5e73\u5747<\/span>\uff08\u5373\u5728\u4e00\u6761\u8f68\u8ff9\u4e0a\u6253\u5361\u8bb0\u5f55\uff09<\/span>\u3002\u540e\u8005\u662f\u8fd1\u5e74\u6765\u53d1\u5c55\u8d77\u6765\u7684\u5355\u7c92\u5b50\u5f84\u8ff9\u6280\u672f[7]\uff0c\u5176\u91cd\u8981\u6027\u5728\u4e8e\u7528\u8f83\u5c0f\u7684\u5355\u8f68\u8ff9\u4ee3\u4ef7\u6765\u5f97\u77e5\u7cfb\u7efc\u523b\u753b\u7684\u7269\u6027\u884c\u4e3a\u3002<\/span><\/p>\n


<\/p>\n

\u603b\u7ed3\u8d77\u6765\uff0c\u6211\u4eec\u5bf9\u7231\u56e0\u65af\u5766\u5173\u7cfb\u7ed3\u6784\u4e0a\u7684\u63a2\u8ba8\u548c\u5f62\u5f0f\u4e0a\u7684\u63a8\u5e7f\uff0c\u76ee\u524d\u5f97\u5230\u7684\u6bd4\u8f83\u91cd\u8981\u53d1\u73b0\u6709\uff1a<\/span><\/section>\n
(1) \u57fa\u4e8e\u7559\u6570\u5b9a\u7406\uff0c\u63ed\u793a\u901f\u5ea6\u5173\u8054\u51fd\u6570\u7684\u62c9\u666e\u62c9\u65af\u53d8\u6362\u5728\u5750\u6807\u539f\u70b9\u5b58\u5728\u6781\u70b9[6]\uff1b<\/span><\/section>\n
(2) \u5728\u5e7f\u4e49\u6717\u4e4b\u4e07\u65b9\u7a0b\u7684\u6846\u67b6\u4e0b\uff0c\u4ea7\u751f\u5f39\u9053\u6269\u6563\u7684\u6839\u6e90\u7cfb\u566a\u58f0\u7684\u4f4e\u9891\u7f3a\u5931[8]\uff1b<\/span><\/section>\n
(3) \u904d\u5386\u6027\u7684\u5f31\u7834\u7f3a\u5bfc\u81f4\u7cfb\u7edf\u975e\u70ed\u5316\uff1b<\/span><\/section>\n
(4) \u5bf9\u4e8e\u51b7\u5374\u73af\u5883\uff0c\u9664\u4e86\u8d85\u6162\u6269\u6563\u4e4b\u5916\uff0c\u5e7f\u4e49\u7231\u56e0\u65af\u5766\u5173\u7cfb\u6536\u655b[3]\uff1b<\/span><\/section>\n

(5) \u4e3a\u4f7f\u7231\u56e0\u65af\u5766\u5173\u7cfb\u5f97\u4ee5\u5e94\u7528\uff0c\u7cfb\u7edf\u9700\u7ecf\u8fc7\u4e00\u4e2a\u6709\u6548\u904d\u5386\u6027\u65f6\u95f4\u7684\u6f14\u5316[7]\u3002<\/span><\/p>\n


<\/p>\n

\n
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*\u56fd\u5bb6\u81ea\u7136\u79d1\u5b66\u57fa\u91d1\u59d4\u5458\u4f1a\u7406\u8bba\u7269\u7406\u4e13\u6b3e\u201c\u7406\u8bba\u7269\u7406\u6587\u5316\u4f20\u64ad\u201d\u8d44\u52a9\u9879\u76ee(12347212)\u3002<\/span><\/p>\n

** jdbao@bnu.edu.cn<\/span><\/p>\n<\/section>\n<\/section>\n<\/blockquote>\n


<\/p>\n

\u4e3b\u8981\u53c2\u8003\u6587\u732e<\/span><\/strong><\/span><\/p>\n

[1] R. P. Feynman\uff0cR.B. Leighton\uff0cM. Sands\u8457. \u8d39\u6069\u66fc\u7269\u7406\u5b66\u8bb2\u4e49\u2022\u7b2c1\u5377[M]. \u4e0a\u6d77\u79d1\u5b66\u6280\u672f<\/span>\u51fa\u7248\u793e\uff0c2005.<\/span><\/p>\n

[2] A. S. Bodrova, A. V. Chechkin, A. G. Cherstvy, and R. Metzler, Ultraslow scaled Brownian motion[J], <\/span>New J. Phys. 17, 063038 (2015).<\/span><\/p>\n

[3] J. D. Bao and X. R. Wang, Generalized Einstein relation for aging processes[J], Communications Physics 7\uff0c249 (2024). https:\/\/doi.org\/10.1038\/s42005-024-01791-7 \u201c\u8001\u5316\u8fc7\u7a0b\u7684\u5e7f\u4e49\u7231\u56e0\u65af\u5766\u5173\u7cfb\u201d.<\/span><\/p>\n

[4] \u5305\u666f\u4e1c. \u7269\u542b\u5999\u7406\u2014\u2014\u50cf\u8d39\u6069\u66fc\u90a3\u6837\u673a\u667a\u5730\u6559\u4e0e\u5b66[M]. \u6e05\u534e\u5927\u5b66\u51fa\u7248\u793e, 2018.<\/span><\/p>\n

[5] J. D. Bao, Y. Z. Zhuo, F. A. Oliveira, and P. Hanggi, Intermediate dynamics between Newton and Langevin, Phys. Rev. E 74 , 061111 (2006). \u201c\u725b\u987f\u548c\u6717\u4e4b\u4e07\u4e4b\u95f4\u7684\u52a8\u529b\u5b66\u201d<\/span><\/p>\n

[6] J. D. Bao. Generalized Einstein relations and conditions for anomalous relaxation[J], Phys. Rev. E 100, 052149 (2019) \u201c\u5e7f\u4e49\u7231\u56e0\u65af\u5766\u5173\u7cfb\u548c\u53cd\u5e38\u9a70\u8c6b\u201d .<\/span><\/p>\n

[7] J. D. Bao, X. R. Wang, and W. M. Liu, Ergodic time scale and transitive dynamics in single-particle <\/span>tracking[J], Phys. Rev. E 103, 032136 (2021). \u201c\u904d\u5386\u6027\u65f6\u95f4\u5c3a\u5ea6\u548c\u5355\u7c92\u5b50\u5f84\u8ff9\u6f14\u53d8\u52a8\u529b\u5b66\u201d.<\/span><\/p>\n

[8] J. D. Bao and Y. Z. Zhuo, Ballistic Diffusion Induced by a Thermal Brodband Noise, Phys. Rev. Lett. 91, 138104 (2003). \u201c\u70ed\u5bbd\u5e26\u566a\u58f0\u8bf1\u53d1\u5f39\u9053\u6269\u6563\u201d<\/span><\/p>\n


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\u590d\u6742\u7cfb\u7edf\u81ea\u52a8\u5efa\u6a21\u8bfb\u4e66\u4f1a<\/strong>
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\u201c\u590d\u6742\u4e16\u754c\uff0c\u7b80\u5355\u89c4\u5219\u201d\u3002<\/span><\/p>\n


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\u8bfb\u4e66\u4f1a\u5c06\u4e8e9\u67087\u65e5\u6bcf\u5468\u516d\u665a\u4e0a20:00-22:00\u8fdb\u884c\uff0c\u63a2\u8ba8\u56db\u4e2a\u6838\u5fc3\u6a21\u5757\uff1a\u6570\u636e\u9a71\u52a8\u7684\u590d\u6742\u7cfb\u7edf\u5efa\u6a21\u3001\u590d\u6742\u7f51\u7edc\u7ed3\u6784\u63a8\u65ad\u3001\u5177\u6709\u53ef\u89e3\u91ca\u6027\u7684\u590d\u6742\u7cfb\u7edf\u63a8\u65ad\uff08\u52a8\u529b\u5b66+\u7f51\u7edc\u7ed3\u6784\uff09\u3001\u5e94\u7528-\u8d85\u6750\u6599\u8bbe\u8ba1\u548c\u57ce\u5e02\u7cfb\u7edf\uff0c\u901a\u8fc7\u91cd\u70b9\u8ba8\u8bba75\u7bc7\u7ecf\u5178\u3001\u524d\u6cbf\u7684\u91cd\u8981\u6587\u732e\uff0c\u4ece\u9ed1\u76d2\uff08\u6570\u636e\u9a71\u52a8\uff09\u5230\u767d\u76d2\uff08\u53ef\u89e3\u91ca<\/span>\u6027\uff09\uff0c\u9010\u6b65\u6355\u6349\u7cfb\u7edf\u7684\u201c\u672c\u8d28\u201d\u89c4\u5f8b\uff0c\u5e2e\u52a9\u5927\u5bb6\u66f4\u597d\u7684\u8ba4\u8bc6\u3001\u7406\u89e3\u3001\u9884\u6d4b\u3001\u63a7\u5236\u3001\u8bbe\u8ba1\u590d\u6742\u7cfb\u7edf\uff0c\u4e3a\u76f8\u5173\u9886\u57df\u7684\u7814\u7a76\u548c\u5e94\u7528\u63d0\u4f9b\u6d1e\u89c1\u3002\u6b22\u8fce\u611f\u5174\u8da3\u7684\u670b\u53cb\u62a5\u540d\u53c2\u4e0e\uff01<\/span><\/p>\n

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\u8be6\u60c5\u8bf7\u89c1\uff1a<\/span><\/section>\n

\u590d\u6742\u7cfb\u7edf\u81ea\u52a8\u5efa\u6a21\u8bfb\u4e66\u4f1a\uff1a\u4ece\u6570\u636e\u9a71\u52a8\u5230\u53ef\u89e3\u91ca\u6027\uff0c\u63a2\u7d22\u7cfb\u7edf\u5185\u5728\u89c4\u5f8b\uff5c\u5185\u964475\u7bc7\u9886\u57df\u5fc5\u8bfb\u6587\u732e<\/strong><\/a><\/p>\n


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<\/p>\n

\u63a8\u8350\u9605\u8bfb<\/span><\/strong><\/strong><\/strong>
<\/section>\n
1. <\/strong>\u524d\u6cbf\u7efc\u8ff0\uff1a\u63cf\u8ff0\u751f\u7269\u7cfb\u7edf\u6d8c\u73b0\u884c\u4e3a\u7684\u666f\u89c2\u548c\u6d41\u7406\u8bba\u89c6\u89d2<\/a><\/strong><\/span><\/strong><\/strong><\/section>\n
2. <\/strong>\u8017\u6563\u7ed3\u6784\u4e0e\u81ea\u7136\u754c\u7684\u4e0d\u53ef\u9006\u6027\u2014\u2014\u201c\u70ed\u529b\u5b66\u8bd7\u4eba\u201d\u666e\u91cc\u9ad8\u6d25<\/a><\/strong><\/span><\/strong><\/strong><\/section>\n
3. <\/strong>Nat. Rev. Phys.\u7efc\u8ff0\uff1a\u7edf\u8ba1\u7269\u7406\u57fa\u7840\u4e2d\u7684\u71b5\u3001\u53ef\u9006\u6027\u4e0e\u63a8\u65ad<\/a><\/strong><\/span><\/section>\n
4. <\/strong><\/span>\u5f20\u6c5f\uff1a\u7b2c\u4e09\u4ee3\u4eba\u5de5\u667a\u80fd\u6280\u672f\u57fa\u7840\u2014\u2014\u4ece\u53ef\u5fae\u5206\u7f16\u7a0b\u5230\u56e0\u679c\u63a8\u7406 | \u96c6\u667a\u5b66\u56ed\u5168\u65b0\u8bfe\u7a0b<\/a><\/strong><\/strong><\/span><\/section>\n
<\/strong>5.<\/strong> \u9f99\u5e74\u5927\u8fd0\u8d77\uff0c\u5b66\u4e60\u6b63\u5f53\u65f6\uff01\u89e3\u9501\u96c6\u667a\u5168\u7ad9\u5185\u5bb9\uff0c\u5f00\u542f\u65b0\u5e74\u5b66\u4e60\u8ba1\u5212<\/a><\/strong><\/strong><\/strong><\/strong><\/span><\/strong><\/strong><\/section>\n

6. <\/strong>\u52a0\u5165\u96c6\u667a\uff0c\u4e00\u8d77\u590d\u6742\uff01<\/strong><\/span><\/a><\/p>\n


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\u70b9\u51fb\u201c\u9605\u8bfb\u539f\u6587\u201d\uff0c\u62a5\u540d\u8bfb\u4e66\u4f1a<\/strong><\/span><\/strong><\/span><\/strong><\/p>\n


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<\/mp-style-type><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

\u5bfc\u8bed \u8fd1\u65e5\uff0c\u5317\u4eac\u5e08\u8303\u5927\u5b66\u7269\u7406\u4e0e\u5929\u6587\u5b66\u9662\u5305\u666f\u4e1c\u6559\u6388\u4e0e\u5408\u4f5c\u8005\u5728\u671f\u520a Communications Physics \u53d1\u8868\u6700\u65b0\u7814\u7a76\uff0c\u63a8\u5e7f\u7231\u56e0\u65af\u5766\u5173\u7cfb\u5230\u7269\u7406\u8001\u5316\u8fc7\u7a0b\uff0c\u5f97\u5230\u4e86\u4e00\u7cfb\u5217\u91cd\u8981\u53d1\u73b0\u3002\u672c\u6587\u4ece\u5e03\u6717\u8fd0\u52a8\u3001\u7231\u56e0\u65af\u5766\u5173\u7cfb\u3001\u904d\u5386\u6027\u7834\u7f3a\u7b49\u57fa\u7840\u6982\u5ff5\u8bb2\u8d77\uff0c\u4ecb\u7ecd\u4e86\u8fd9\u9879\u6700\u65b0\u6210\u679c\u3002 \u7814\u7a76\u9886\u57df\uff1a\u5e03\u6717\u8fd0\u52a8\uff0c\u904d\u5386\u6027\uff0c\u7231\u56e0\u65af…<\/p>\n","protected":false},"author":0,"featured_media":52626,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[1],"tags":[],"special":[],"_links":{"self":[{"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/posts\/52634"}],"collection":[{"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/types\/post"}],"replies":[{"embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=52634"}],"version-history":[{"count":0,"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/posts\/52634\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/media\/52626"}],"wp:attachment":[{"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=52634"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=52634"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=52634"},{"taxonomy":"special","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fspecial&post=52634"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}