{"id":624163,"date":"2026-11-15T08:53:10","date_gmt":"2026-11-15T01:53:10","guid":{"rendered":"https:\/\/hoanghamobile.com\/tin-tuc\/?p=624163"},"modified":"2026-11-15T08:53:10","modified_gmt":"2026-11-15T01:53:10","slug":"entropy-la-gi","status":"publish","type":"post","link":"https:\/\/hoanghamobile.com\/tin-tuc\/entropy-la-gi\/","title":{"rendered":"Entropy l\u00e0 g\u00ec? \u0110\u1ecbnh ngh\u0129a, c\u00f4ng th\u1ee9c v\u00e0 v\u00ed d\u1ee5 d\u1ec5 hi\u1ec3u"},"content":{"rendered":"<p><strong>Entropy l\u00e0 \u0111\u1ea1i l\u01b0\u1ee3ng v\u1eadt l\u00fd \u0111o ph\u1ea7n n\u0103ng l\u01b0\u1ee3ng c\u1ee7a m\u1ed9t h\u1ec7 kh\u00f4ng th\u1ec3 d\u00f9ng \u0111\u1ec3 sinh c\u00f4ng, \u0111\u1ed3ng th\u1eddi th\u01b0\u1eddng \u0111\u01b0\u1ee3c hi\u1ec3u l\u00e0 th\u01b0\u1edbc \u0111o m\u1ee9c \u0111\u1ed9 h\u1ed7n lo\u1ea1n (m\u1ea5t tr\u1eadt t\u1ef1) c\u1ee7a h\u1ec7. Kh\u00e1i ni\u1ec7m n\u00e0y do nh\u00e0 v\u1eadt l\u00fd ng\u01b0\u1eddi \u0110\u1ee9c Rudolf Clausius x\u00e2y d\u1ef1ng t\u1eeb n\u0103m 1850 v\u00e0 \u0111\u1eb7t t\u00ean &#8220;entropy&#8221; v\u00e0o n\u0103m 1865.<\/strong> Entropy g\u1eafn li\u1ec1n v\u1edbi \u0111\u1ecbnh lu\u1eadt th\u1ee9 hai c\u1ee7a nhi\u1ec7t \u0111\u1ed9ng l\u1ef1c h\u1ecdc: trong h\u1ec7 c\u00f4 l\u1eadp, c\u00e1c qu\u00e1 tr\u00ecnh t\u1ef1 ph\u00e1t lu\u00f4n l\u00e0m entropy t\u0103ng. \u0110\u00f3 l\u00e0 l\u00fd do n\u01b0\u1edbc n\u00f3ng v\u00e0 n\u01b0\u1edbc l\u1ea1nh t\u1ef1 h\u00f2a tr\u1ed9n m\u00e0 kh\u00f4ng bao gi\u1edd t\u1ef1 t\u00e1ch ra. D\u01b0\u1edbi \u0111\u00e2y l\u00e0 \u0111\u1ecbnh ngh\u0129a, ba c\u00f4ng th\u1ee9c quan tr\u1ecdng nh\u1ea5t (Clausius, Boltzmann, Shannon), v\u00ed d\u1ee5 c\u00f3 l\u1eddi gi\u1ea3i v\u00e0 c\u00e1ch hi\u1ec3u entropy ngo\u00e0i v\u1eadt l\u00fd.<\/p>\n<h2>Entropy l\u00e0 g\u00ec?<\/h2>\n<p>Entropy l\u00e0 \u0111\u1ea1i l\u01b0\u1ee3ng tr\u1ea1ng th\u00e1i (k\u00fd hi\u1ec7u S) cho bi\u1ebft n\u0103ng l\u01b0\u1ee3ng c\u1ee7a h\u1ec7 &#8220;ph\u00e2n t\u00e1n&#8221; \u0111\u1ebfn m\u1ee9c n\u00e0o, v\u00e0 v\u00ec th\u1ebf c\u00f2n bao nhi\u00eau ph\u1ea7n c\u00f3 th\u1ec3 d\u00f9ng \u0111\u1ec3 sinh c\u00f4ng. Theo Britannica, entropy l\u00e0 &#8220;th\u01b0\u1edbc \u0111o ph\u1ea7n n\u0103ng l\u01b0\u1ee3ng nhi\u1ec7t c\u1ee7a h\u1ec7 tr\u00ean m\u1ed9t \u0111\u01a1n v\u1ecb nhi\u1ec7t \u0111\u1ed9 kh\u00f4ng th\u1ec3 d\u00f9ng \u0111\u1ec3 sinh c\u00f4ng&#8221;, hay m\u1ee9c \u0111\u1ed9 h\u1ed7n lo\u1ea1n c\u1ee7a h\u1ec7. Trong ng\u00f4n ng\u1eef \u0111\u1eddi th\u01b0\u1eddng, entropy th\u01b0\u1eddng \u0111\u01b0\u1ee3c m\u00f4 t\u1ea3 \u0111\u01a1n gi\u1ea3n l\u00e0 m\u1ee9c \u0111\u1ed9 h\u1ed7n lo\u1ea1n hay ng\u1eabu nhi\u00ean c\u1ee7a m\u1ed9t h\u1ec7.<\/p>\n<p>M\u1ed9t c\u00e1ch hi\u1ec3u tr\u1ef1c quan h\u01a1n: entropy c\u00e0ng l\u1edbn th\u00ec c\u00e0ng c\u00f3 nhi\u1ec1u c\u00e1ch s\u1eafp x\u1ebfp vi m\u00f4 (v\u1ecb tr\u00ed, v\u1eadn t\u1ed1c c\u1ee7a c\u00e1c ph\u00e2n t\u1eed) cho c\u00f9ng m\u1ed9t tr\u1ea1ng th\u00e1i v\u0129 m\u00f4 m\u00e0 ta quan s\u00e1t \u0111\u01b0\u1ee3c. Kh\u1ed1i n\u01b0\u1edbc \u0111\u00e1 c\u00f3 c\u00e1c ph\u00e2n t\u1eed x\u1ebfp ngay ng\u1eafn trong m\u1ea1ng tinh th\u1ec3 n\u00ean entropy th\u1ea5p; h\u01a1i n\u01b0\u1edbc c\u00f3 ph\u00e2n t\u1eed chuy\u1ec3n \u0111\u1ed9ng t\u1ef1 do n\u00ean entropy cao.<\/p>\n<table>\n<thead>\n<tr>\n<th>Th\u00f4ng tin<\/th>\n<th>Chi ti\u1ebft<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>K\u00fd hi\u1ec7u<\/td>\n<td>S<\/td>\n<\/tr>\n<tr>\n<td>\u0110\u01a1n v\u1ecb (h\u1ec7 SI)<\/td>\n<td>J\/K (jun tr\u00ean kelvin)<\/td>\n<\/tr>\n<tr>\n<td>Ng\u01b0\u1eddi \u0111\u1ec1 xu\u1ea5t<\/td>\n<td>Rudolf Clausius (1822\u20131888), nh\u00e0 v\u1eadt l\u00fd ng\u01b0\u1eddi \u0110\u1ee9c<\/td>\n<\/tr>\n<tr>\n<td>Th\u1eddi \u0111i\u1ec3m<\/td>\n<td>Kh\u00e1i ni\u1ec7m x\u00e2y d\u1ef1ng t\u1eeb n\u0103m 1850, thu\u1eadt ng\u1eef &#8220;entropy&#8221; \u0111\u01b0\u1ee3c Clausius d\u00f9ng t\u1eeb n\u0103m 1865<\/td>\n<\/tr>\n<tr>\n<td>\u0110\u1ecbnh lu\u1eadt li\u00ean quan<\/td>\n<td>\u0110\u1ecbnh lu\u1eadt th\u1ee9 hai c\u1ee7a nhi\u1ec7t \u0111\u1ed9ng l\u1ef1c h\u1ecdc<\/td>\n<\/tr>\n<tr>\n<td>\u00dd ngh\u0129a \u0111\u1eddi th\u01b0\u1eddng<\/td>\n<td>M\u1ee9c \u0111\u1ed9 h\u1ed7n lo\u1ea1n, ng\u1eabu nhi\u00ean<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>C\u00f4ng th\u1ee9c t\u00ednh bi\u1ebfn thi\u00ean entropy (Clausius)<\/h2>\n<p>C\u00f4ng th\u1ee9c Clausius cho bi\u1ebft entropy thay \u0111\u1ed5i bao nhi\u00eau khi h\u1ec7 nh\u1eadn ho\u1eb7c nh\u1ea3 nhi\u1ec7t \u1edf nhi\u1ec7t \u0111\u1ed9 kh\u00f4ng \u0111\u1ed5i. Khi m\u1ed9t l\u01b0\u1ee3ng nhi\u1ec7t Q truy\u1ec1n theo c\u00e1ch thu\u1eadn ngh\u1ecbch v\u00e0o h\u1ec7 \u1edf nhi\u1ec7t \u0111\u1ed9 tuy\u1ec7t \u0111\u1ed1i T, \u0111\u1ed9 bi\u1ebfn thi\u00ean entropy l\u00e0:<\/p>\n<p><strong>\u0394S = Q \/ T<\/strong><\/p>\n<p>Trong \u0111\u00f3:<\/p>\n<ul>\n<li><strong>\u0394S:<\/strong> bi\u1ebfn thi\u00ean entropy (J\/K).<\/li>\n<li><strong>Q:<\/strong> nhi\u1ec7t l\u01b0\u1ee3ng trao \u0111\u1ed5i theo c\u00e1ch thu\u1eadn ngh\u1ecbch (J); Q &gt; 0 khi h\u1ec7 nh\u1eadn nhi\u1ec7t, Q &lt; 0 khi h\u1ec7 t\u1ecfa nhi\u1ec7t.<\/li>\n<li><strong>T:<\/strong> nhi\u1ec7t \u0111\u1ed9 tuy\u1ec7t \u0111\u1ed1i (K), v\u1edbi T(K) = t(\u00b0C) + 273,15.<\/li>\n<\/ul>\n<p>C\u00f4ng th\u1ee9c cho th\u1ea5y c\u00f9ng m\u1ed9t l\u01b0\u1ee3ng nhi\u1ec7t, khi truy\u1ec1n v\u00e0o v\u1eadt \u1edf nhi\u1ec7t \u0111\u1ed9 th\u1ea5p s\u1ebd l\u00e0m entropy t\u0103ng nhi\u1ec1u h\u01a1n so v\u1edbi v\u1eadt \u1edf nhi\u1ec7t \u0111\u1ed9 cao. Nhi\u1ec7t l\u01b0\u1ee3ng Q trong c\u00e1c b\u00e0i to\u00e1n th\u01b0\u1eddng t\u00ednh b\u1eb1ng Q = mc\u0394t ho\u1eb7c Q = m\u03bb (n\u00f3ng ch\u1ea3y); b\u1ea1n c\u00f3 th\u1ec3 \u00f4n l\u1ea1i trong b\u00e0i <a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/nhiet-dung-rieng\/\">nhi\u1ec7t dung ri\u00eang l\u00e0 g\u00ec v\u00e0 c\u00f4ng th\u1ee9c Q = mc\u0394t<\/a>.<\/p>\n<p><img fetchpriority=\"high\" decoding=\"async\" class=\"aligncenter size-full wp-image-624164\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/entropy-la-gi-1.jpg\" alt=\"entropy-la-gi-1\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/entropy-la-gi-1.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/entropy-la-gi-1-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/entropy-la-gi-1-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2>C\u00f4ng th\u1ee9c Boltzmann: entropy v\u00e0 s\u1ed1 tr\u1ea1ng th\u00e1i vi m\u00f4<\/h2>\n<p>C\u00f4ng th\u1ee9c Boltzmann gi\u1ea3i th\u00edch entropy \u1edf c\u1ea5p \u0111\u1ed9 ph\u00e2n t\u1eed, n\u1ed1i &#8220;m\u1ee9c \u0111\u1ed9 h\u1ed7n lo\u1ea1n&#8221; v\u1edbi m\u1ed9t con s\u1ed1 c\u1ee5 th\u1ec3. Nh\u00e0 v\u1eadt l\u00fd ng\u01b0\u1eddi \u00c1o Ludwig Boltzmann ch\u1ec9 ra:<\/p>\n<p><strong>S = k \u00b7 ln W<\/strong><\/p>\n<p>Trong \u0111\u00f3:<\/p>\n<ul>\n<li><strong>k:<\/strong> h\u1eb1ng s\u1ed1 Boltzmann, k = 1,380649 \u00d7 10\u207b\u00b2\u00b3 J\/K (gi\u00e1 tr\u1ecb ch\u00ednh x\u00e1c theo \u0111\u1ecbnh ngh\u0129a SI t\u1eeb n\u0103m 2019).<\/li>\n<li><strong>W:<\/strong> s\u1ed1 tr\u1ea1ng th\u00e1i vi m\u00f4 (s\u1ed1 c\u00e1ch s\u1eafp x\u1ebfp c\u00e1c h\u1ea1t) \u1ee9ng v\u1edbi c\u00f9ng m\u1ed9t tr\u1ea1ng th\u00e1i v\u0129 m\u00f4.<\/li>\n<li><strong>ln:<\/strong> logarit t\u1ef1 nhi\u00ean.<\/li>\n<\/ul>\n<p>C\u00f4ng th\u1ee9c n\u00e0y \u0111\u01b0\u1ee3c kh\u1eafc tr\u00ean bia m\u1ed9 c\u1ee7a Boltzmann \u1edf Vienna. \u00dd ngh\u0129a: h\u1ec7 c\u00e0ng c\u00f3 nhi\u1ec1u c\u00e1ch s\u1eafp x\u1ebfp vi m\u00f4 th\u00ec entropy c\u00e0ng l\u1edbn. \u1ede 0 K, m\u1ed9t tinh th\u1ec3 ho\u00e0n h\u1ea3o ch\u1ec9 c\u00f3 m\u1ed9t c\u00e1ch s\u1eafp x\u1ebfp (W = 1) n\u00ean S = k\u00b7ln 1 = 0, \u0111\u00e2y ch\u00ednh l\u00e0 n\u1ed9i dung c\u1ee7a \u0111\u1ecbnh lu\u1eadt th\u1ee9 ba nhi\u1ec7t \u0111\u1ed9ng l\u1ef1c h\u1ecdc.<\/p>\n<h2>Entropy v\u00e0 \u0111\u1ecbnh lu\u1eadt th\u1ee9 hai c\u1ee7a nhi\u1ec7t \u0111\u1ed9ng l\u1ef1c h\u1ecdc<\/h2>\n<p>\u0110\u1ecbnh lu\u1eadt th\u1ee9 hai kh\u1eb3ng \u0111\u1ecbnh entropy c\u1ee7a m\u1ed9t h\u1ec7 c\u00f4 l\u1eadp kh\u00f4ng bao gi\u1edd gi\u1ea3m. Theo c\u00e1ch ph\u00e1t bi\u1ec3u c\u1ee7a Clausius, nhi\u1ec7t kh\u00f4ng bao gi\u1edd t\u1ef1 truy\u1ec1n t\u1eeb v\u1eadt l\u1ea1nh h\u01a1n sang v\u1eadt n\u00f3ng h\u01a1n. V\u1edbi m\u1ed9t h\u1ec7 c\u00f4 l\u1eadp, entropy t\u0103ng trong qu\u00e1 tr\u00ecnh kh\u00f4ng thu\u1eadn ngh\u1ecbch v\u00e0 ch\u1ec9 gi\u1eef nguy\u00ean trong gi\u1edbi h\u1ea1n l\u00fd t\u01b0\u1edfng c\u1ee7a qu\u00e1 tr\u00ecnh thu\u1eadn ngh\u1ecbch:<\/p>\n<p><strong>\u0394S(h\u1ec7 c\u00f4 l\u1eadp) \u2265 0<\/strong><\/p>\n<p>Trong h\u1ec7 c\u00f4 l\u1eadp, entropy ti\u1ebfp t\u1ee5c t\u0103ng khi nhi\u1ec7t ph\u00e2n t\u00e1n, cho \u0111\u1ebfn khi \u0111\u1ea1t c\u1ef1c \u0111\u1ea1i \u1edf tr\u1ea1ng th\u00e1i c\u00e2n b\u1eb1ng; khi \u0111\u00f3 kh\u00f4ng c\u00f2n ch\u00eanh l\u1ec7ch nhi\u1ec7t \u0111\u1ed9 \u0111\u1ec3 sinh c\u00f4ng. \u0110\u1ecbnh lu\u1eadt n\u00e0y c\u0169ng gi\u1ea3i th\u00edch v\u00ec sao kh\u00f4ng c\u00f3 \u0111\u1ed9ng c\u01a1 nhi\u1ec7t n\u00e0o chuy\u1ec3n h\u00f3a \u0111\u01b0\u1ee3c to\u00e0n b\u1ed9 nhi\u1ec7t th\u00e0nh c\u00f4ng. L\u01b0u \u00fd, entropy c\u1ee7a m\u1ed9t ph\u1ea7n h\u1ec7 (nh\u01b0 t\u1ee7 l\u1ea1nh l\u00e0m l\u1ea1nh th\u1ef1c ph\u1ea9m) v\u1eabn c\u00f3 th\u1ec3 gi\u1ea3m, nh\u01b0ng entropy m\u00f4i tr\u01b0\u1eddng xung quanh t\u0103ng nhi\u1ec1u h\u01a1n, n\u00ean t\u1ed5ng v\u1eabn t\u0103ng. \u0110\u1ec3 ph\u00e2n bi\u1ec7t v\u1edbi \u0111\u1ecbnh lu\u1eadt th\u1ee9 nh\u1ea5t (n\u0103ng l\u01b0\u1ee3ng kh\u00f4ng t\u1ef1 sinh ra hay m\u1ea5t \u0111i), b\u1ea1n xem b\u00e0i <a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/dinh-luat-bao-toan-nang-luong\/\">\u0111\u1ecbnh lu\u1eadt b\u1ea3o to\u00e0n n\u0103ng l\u01b0\u1ee3ng: ph\u00e1t bi\u1ec3u v\u00e0 b\u00e0i t\u1eadp<\/a>.<\/p>\n<table>\n<thead>\n<tr>\n<th>\u0110\u1ecbnh lu\u1eadt<\/th>\n<th>N\u1ed9i dung ch\u00ednh<\/th>\n<th>Li\u00ean h\u1ec7 v\u1edbi entropy<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>Th\u1ee9 nh\u1ea5t<\/td>\n<td>N\u0103ng l\u01b0\u1ee3ng \u0111\u01b0\u1ee3c b\u1ea3o to\u00e0n: \u0394U = Q + A<\/td>\n<td>Kh\u00f4ng n\u00f3i g\u00ec v\u1ec1 chi\u1ec1u c\u1ee7a qu\u00e1 tr\u00ecnh<\/td>\n<\/tr>\n<tr>\n<td>Th\u1ee9 hai<\/td>\n<td>Nhi\u1ec7t kh\u00f4ng t\u1ef1 truy\u1ec1n t\u1eeb v\u1eadt l\u1ea1nh sang v\u1eadt n\u00f3ng<\/td>\n<td>Entropy h\u1ec7 c\u00f4 l\u1eadp kh\u00f4ng gi\u1ea3m (\u0394S \u2265 0)<\/td>\n<\/tr>\n<tr>\n<td>Th\u1ee9 ba<\/td>\n<td>Kh\u00f4ng th\u1ec3 \u0111\u1ea1t t\u1edbi 0 K b\u1eb1ng h\u1eefu h\u1ea1n b\u01b0\u1edbc<\/td>\n<td>Entropy tinh th\u1ec3 ho\u00e0n h\u1ea3o \u1edf 0 K b\u1eb1ng 0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><img decoding=\"async\" class=\"aligncenter size-full wp-image-624165\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/entropy-la-gi-2.jpg\" alt=\"entropy-la-gi-2\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/entropy-la-gi-2.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/entropy-la-gi-2-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/entropy-la-gi-2-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2>V\u00ed d\u1ee5 t\u00ednh entropy c\u00f3 l\u1eddi gi\u1ea3i<\/h2>\n<p>B\u1ed1n v\u00ed d\u1ee5 d\u01b0\u1edbi \u0111\u00e2y gi\u00fap b\u1ea1n \u00e1p d\u1ee5ng tr\u1ef1c ti\u1ebfp c\u00e1c c\u00f4ng th\u1ee9c tr\u00ean, t\u1eeb nhi\u1ec7t h\u1ecdc \u0111\u1ebfn l\u00fd thuy\u1ebft th\u00f4ng tin.<\/p>\n<p><strong>V\u00ed d\u1ee5 1: N\u00f3ng ch\u1ea3y n\u01b0\u1edbc \u0111\u00e1 \u1edf 0\u00b0C.<\/strong> T\u00ednh bi\u1ebfn thi\u00ean entropy khi 10 g n\u01b0\u1edbc \u0111\u00e1 \u1edf 0\u00b0C n\u00f3ng ch\u1ea3y ho\u00e0n to\u00e0n th\u00e0nh n\u01b0\u1edbc \u1edf 0\u00b0C. Bi\u1ebft nhi\u1ec7t n\u00f3ng ch\u1ea3y ri\u00eang c\u1ee7a n\u01b0\u1edbc \u0111\u00e1 \u03bb \u2248 334 J\/g.<\/p>\n<p><em>L\u1eddi gi\u1ea3i:<\/em><\/p>\n<ul>\n<li>Nhi\u1ec7t \u0111\u1ed9 tuy\u1ec7t \u0111\u1ed1i: T = 0 + 273,15 = 273,15 K (kh\u00f4ng \u0111\u1ed5i trong su\u1ed1t qu\u00e1 tr\u00ecnh n\u00f3ng ch\u1ea3y).<\/li>\n<li>Nhi\u1ec7t l\u01b0\u1ee3ng nh\u1eadn v\u00e0o: Q = m\u00b7\u03bb = 10 \u00d7 334 = 3.340 J.<\/li>\n<li>Bi\u1ebfn thi\u00ean entropy: \u0394S = Q\/T = 3.340 \u00f7 273,15 \u2248 12,23 J\/K.<\/li>\n<\/ul>\n<p>M\u1ed7i gam n\u01b0\u1edbc \u0111\u00e1 tan l\u00e0m entropy t\u0103ng kho\u1ea3ng 334 \u00f7 273,15 \u2248 1,22 J\/K. Entropy t\u0103ng v\u00ec ph\u00e2n t\u1eed n\u01b0\u1edbc chuy\u1ec3n t\u1eeb m\u1ea1ng tinh th\u1ec3 tr\u1eadt t\u1ef1 sang tr\u1ea1ng th\u00e1i l\u1ecfng linh \u0111\u1ed9ng h\u01a1n.<\/p>\n<p><strong>V\u00ed d\u1ee5 2: Truy\u1ec1n nhi\u1ec7t t\u1eeb v\u1eadt n\u00f3ng sang v\u1eadt l\u1ea1nh.<\/strong> 1.000 J nhi\u1ec7t truy\u1ec1n t\u1eeb m\u1ed9t ngu\u1ed3n n\u00f3ng 400 K sang ngu\u1ed3n l\u1ea1nh 300 K (nhi\u1ec7t \u0111\u1ed9 hai ngu\u1ed3n coi nh\u01b0 kh\u00f4ng \u0111\u1ed5i). T\u1ed5ng entropy thay \u0111\u1ed5i th\u1ebf n\u00e0o?<\/p>\n<p><em>L\u1eddi gi\u1ea3i:<\/em><\/p>\n<ul>\n<li>Ngu\u1ed3n n\u00f3ng m\u1ea5t nhi\u1ec7t: \u0394S\u2081 = \u22121.000 \u00f7 400 = \u22122,5 J\/K.<\/li>\n<li>Ngu\u1ed3n l\u1ea1nh nh\u1eadn nhi\u1ec7t: \u0394S\u2082 = +1.000 \u00f7 300 \u2248 +3,33 J\/K.<\/li>\n<li>T\u1ed5ng: \u0394S = \u22122,5 + 3,33 \u2248 +0,83 J\/K &gt; 0.<\/li>\n<\/ul>\n<p>T\u1ed5ng entropy t\u0103ng, \u0111\u00fang nh\u01b0 \u0111\u1ecbnh lu\u1eadt th\u1ee9 hai. N\u1ebfu nhi\u1ec7t \u0111i theo chi\u1ec1u ng\u01b0\u1ee3c l\u1ea1i (l\u1ea1nh sang n\u00f3ng), t\u1ed5ng s\u1ebd \u00e2m, v\u00ec v\u1eady qu\u00e1 tr\u00ecnh \u0111\u00f3 kh\u00f4ng t\u1ef1 x\u1ea3y ra.<\/p>\n<p><strong>V\u00ed d\u1ee5 3: C\u00f4ng th\u1ee9c Boltzmann.<\/strong> M\u1ed9t h\u1ec7 c\u00f3 s\u1ed1 tr\u1ea1ng th\u00e1i vi m\u00f4 t\u0103ng g\u1ea5p \u0111\u00f4i (W \u2192 2W). Entropy t\u0103ng th\u00eam bao nhi\u00eau?<\/p>\n<p><em>L\u1eddi gi\u1ea3i:<\/em> \u0394S = k\u00b7ln(2W) \u2212 k\u00b7ln W = k\u00b7ln 2 = 1,380649 \u00d7 10\u207b\u00b2\u00b3 \u00d7 0,6931 \u2248 9,57 \u00d7 10\u207b\u00b2\u2074 J\/K. Con s\u1ed1 r\u1ea5t nh\u1ecf v\u00ec \u0111\u00e2y ch\u1ec9 l\u00e0 thay \u0111\u1ed5i \u1edf c\u1ea5p \u0111\u1ed9 v\u00e0i h\u1ea1t; v\u1edbi c\u00e1c h\u1ec7 th\u1ef1c c\u00f3 kho\u1ea3ng 10\u00b2\u00b3 ph\u00e2n t\u1eed, entropy m\u1edbi \u0111\u1ea1t c\u1ee1 v\u00e0i J\/K.<\/p>\n<p><strong>V\u00ed d\u1ee5 4: Tung \u0111\u1ed3ng xu v\u00e0 entropy th\u00f4ng tin.<\/strong> Xem ph\u1ea7n entropy Shannon ngay b\u00ean d\u01b0\u1edbi.<\/p>\n<h2>Entropy trong l\u00fd thuy\u1ebft th\u00f4ng tin (entropy Shannon)<\/h2>\n<p>Entropy Shannon \u0111o m\u1ee9c \u0111\u1ed9 &#8220;b\u1ea5t \u0111\u1ecbnh&#8221; trung b\u00ecnh c\u1ee7a m\u1ed9t ngu\u1ed3n th\u00f4ng tin, t\u00ednh b\u1eb1ng bit. N\u0103m 1948, k\u1ef9 s\u01b0 ng\u01b0\u1eddi M\u1ef9 Claude Shannon \u0111\u01b0a ra c\u00f4ng th\u1ee9c c\u00f3 d\u1ea1ng r\u1ea5t gi\u1ed1ng c\u00f4ng th\u1ee9c Boltzmann:<\/p>\n<p><strong>H = \u2212\u03a3 p\u1d62 \u00b7 log\u2082 p\u1d62<\/strong><\/p>\n<p>Trong \u0111\u00f3 p\u1d62 l\u00e0 x\u00e1c su\u1ea5t x\u1ea3y ra c\u1ee7a k\u1ebft qu\u1ea3 th\u1ee9 i. K\u1ebft qu\u1ea3 c\u00e0ng kh\u00f3 \u0111o\u00e1n th\u00ec H c\u00e0ng l\u1edbn; n\u1ebfu ch\u1eafc ch\u1eafn bi\u1ebft tr\u01b0\u1edbc k\u1ebft qu\u1ea3 (p = 1) th\u00ec H = 0.<\/p>\n<p><em>L\u1eddi gi\u1ea3i v\u00ed d\u1ee5 4:<\/em><\/p>\n<ul>\n<li><strong>\u0110\u1ed3ng xu c\u00e2n \u0111\u1ed1i<\/strong> (p = 0,5 cho m\u1ed7i m\u1eb7t): H = \u2212(0,5 \u00d7 log\u2082 0,5 + 0,5 \u00d7 log\u2082 0,5) = \u2212(0,5 \u00d7 (\u22121) + 0,5 \u00d7 (\u22121)) = 1 bit.<\/li>\n<li><strong>\u0110\u1ed3ng xu l\u1ec7ch<\/strong> (s\u1ea5p 0,9, ng\u1eeda 0,1): H = \u2212(0,9 \u00d7 log\u2082 0,9 + 0,1 \u00d7 log\u2082 0,1) \u2248 0,9 \u00d7 0,152 + 0,1 \u00d7 3,322 \u2248 0,47 bit.<\/li>\n<li><strong>X\u00fac x\u1eafc 6 m\u1eb7t c\u00e2n \u0111\u1ed1i:<\/strong> H = log\u2082 6 \u2248 2,585 bit.<\/li>\n<\/ul>\n<p>\u0110\u1ed3ng xu l\u1ec7ch d\u1ec5 \u0111o\u00e1n h\u01a1n n\u00ean ch\u1ee9a \u00edt th\u00f4ng tin h\u01a1n m\u1ed7i l\u1ea7n tung. Entropy Shannon l\u00e0 n\u1ec1n t\u1ea3ng c\u1ee7a n\u00e9n d\u1eef li\u1ec7u: n\u00f3 cho bi\u1ebft gi\u1edbi h\u1ea1n s\u1ed1 bit trung b\u00ecnh t\u1ed1i thi\u1ec3u c\u1ea7n \u0111\u1ec3 m\u00e3 h\u00f3a m\u1ed9t ngu\u1ed3n tin, \u00e1p d\u1ee5ng trong file ZIP, \u1ea3nh, video v\u00e0 truy\u1ec1n d\u1eef li\u1ec7u.<\/p>\n<table>\n<thead>\n<tr>\n<th>Lo\u1ea1i entropy<\/th>\n<th>C\u00f4ng th\u1ee9c<\/th>\n<th>\u0110\u01a1n v\u1ecb<\/th>\n<th>L\u0129nh v\u1ef1c<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>Clausius (nhi\u1ec7t \u0111\u1ed9ng)<\/td>\n<td>\u0394S = Q\/T<\/td>\n<td>J\/K<\/td>\n<td>Nhi\u1ec7t h\u1ecdc, h\u00f3a h\u1ecdc<\/td>\n<\/tr>\n<tr>\n<td>Boltzmann (th\u1ed1ng k\u00ea)<\/td>\n<td>S = k\u00b7ln W<\/td>\n<td>J\/K<\/td>\n<td>V\u1eadt l\u00fd th\u1ed1ng k\u00ea<\/td>\n<\/tr>\n<tr>\n<td>Shannon (th\u00f4ng tin)<\/td>\n<td>H = \u2212\u03a3 p\u00b7log\u2082 p<\/td>\n<td>bit<\/td>\n<td>C\u00f4ng ngh\u1ec7 th\u00f4ng tin, n\u00e9n d\u1eef li\u1ec7u<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>V\u00ed d\u1ee5 v\u1ec1 entropy trong \u0111\u1eddi s\u1ed1ng<\/h2>\n<p>H\u1ea7u h\u1ebft hi\u1ec7n t\u01b0\u1ee3ng t\u1ef1 ph\u00e1t quanh ta \u0111\u1ec1u l\u00e0 qu\u00e1 tr\u00ecnh l\u00e0m entropy t\u0103ng.<\/p>\n<ul>\n<li><strong>N\u01b0\u1edbc n\u00f3ng tr\u1ed9n n\u01b0\u1edbc l\u1ea1nh:<\/strong> hai c\u1ed1c n\u00f3ng l\u1ea1nh \u0111\u1ed5 chung th\u00e0nh n\u01b0\u1edbc \u1ea5m, kh\u00f4ng bao gi\u1edd t\u1ef1 t\u00e1ch l\u1ea1i.<\/li>\n<li><strong>Kh\u00ed gi\u00e3n n\u1edf v\u00e0o ch\u00e2n kh\u00f4ng:<\/strong> kh\u00ed t\u1ef1 lan ra to\u00e0n b\u1ed9 kh\u00f4ng gian tr\u1ed1ng, kh\u00f4ng t\u1ef1 co v\u1ec1 m\u1ed9t g\u00f3c.<\/li>\n<li><strong>\u0110\u1ed1t nhi\u00ean li\u1ec7u:<\/strong> m\u1ed9t ph\u1ea7n n\u0103ng l\u01b0\u1ee3ng tho\u00e1t ra d\u01b0\u1edbi d\u1ea1ng nhi\u1ec7t &#8220;ch\u1ea5t l\u01b0\u1ee3ng th\u1ea5p&#8221;, l\u00e0m entropy t\u0103ng.<\/li>\n<li><strong>Gi\u1ecdt m\u1ef1c loang trong n\u01b0\u1edbc:<\/strong> m\u1ef1c khu\u1ebfch t\u00e1n \u0111\u1ec1u kh\u1eafp c\u1ed1c, kh\u00f4ng t\u1ef1 gom l\u1ea1i th\u00e0nh gi\u1ecdt.<\/li>\n<li><strong>C\u0103n ph\u00f2ng ngu\u1ed9i d\u1ea7n:<\/strong> n\u1ebfu kh\u00f4ng s\u01b0\u1edfi th\u00eam, ph\u00f2ng d\u1ea7n c\u00e2n b\u1eb1ng nhi\u1ec7t v\u1edbi m\u00f4i tr\u01b0\u1eddng.<\/li>\n<\/ul>\n<p>Hi\u1ec7n t\u01b0\u1ee3ng thi\u1ebft b\u1ecb \u0111i\u1ec7n t\u1eed n\u00f3ng l\u00ean khi ho\u1ea1t \u0111\u1ed9ng c\u0169ng l\u00e0 v\u00ed d\u1ee5 n\u0103ng l\u01b0\u1ee3ng \u0111i\u1ec7n b\u1ecb chuy\u1ec3n th\u00e0nh nhi\u1ec7t r\u1ed3i ph\u00e1t t\u00e1n ra m\u00f4i tr\u01b0\u1eddng. T\u00ecm hi\u1ec3u th\u00eam trong b\u00e0i <a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/tan-nhiet-la-gi\/\">t\u1ea3n nhi\u1ec7t l\u00e0 g\u00ec v\u00e0 c\u00e1c ph\u01b0\u01a1ng ph\u00e1p l\u00e0m m\u00e1t<\/a>.<\/p>\n<h2>Entropy trong ng\u00f4n ng\u1eef \u0111\u1eddi th\u01b0\u1eddng<\/h2>\n<p>Ngo\u00e0i khoa h\u1ecdc, &#8220;entropy&#8221; th\u01b0\u1eddng \u0111\u01b0\u1ee3c d\u00f9ng theo ngh\u0129a b\u00f3ng \u0111\u1ec3 ch\u1ec9 xu h\u01b0\u1edbng m\u1ecdi th\u1ee9 d\u1ea7n tr\u1edf n\u00ean l\u1ed9n x\u1ed9n n\u1ebfu kh\u00f4ng \u0111\u01b0\u1ee3c duy tr\u00ec, v\u00ed d\u1ee5 g\u00f3c l\u00e0m vi\u1ec7c t\u1ef1 b\u1eeba b\u1ed9n theo th\u1eddi gian. C\u00e1ch d\u00f9ng n\u00e0y gi\u00fap d\u1ec5 h\u00ecnh dung, nh\u01b0ng khi h\u1ecdc v\u1eadt l\u00fd, b\u1ea1n n\u00ean b\u00e1m v\u00e0o \u0111\u1ecbnh ngh\u0129a ch\u00ednh x\u00e1c: entropy li\u00ean quan \u0111\u1ebfn n\u0103ng l\u01b0\u1ee3ng kh\u00f4ng th\u1ec3 sinh c\u00f4ng, s\u1ed1 tr\u1ea1ng th\u00e1i vi m\u00f4 v\u00e0 \u0111\u1ecbnh lu\u1eadt th\u1ee9 hai c\u1ee7a nhi\u1ec7t \u0111\u1ed9ng l\u1ef1c h\u1ecdc.<\/p>\n<p><img decoding=\"async\" class=\"aligncenter size-full wp-image-624166\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/entropy-la-gi-3.jpg\" alt=\"entropy-la-gi-3\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/entropy-la-gi-3.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/entropy-la-gi-3-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/entropy-la-gi-3-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2>C\u00e2u h\u1ecfi th\u01b0\u1eddng g\u1eb7p<\/h2>\n<h3>Entropy l\u00e0 g\u00ec n\u00f3i \u0111\u01a1n gi\u1ea3n?<\/h3>\n<p>Entropy l\u00e0 th\u01b0\u1edbc \u0111o ph\u1ea7n n\u0103ng l\u01b0\u1ee3ng kh\u00f4ng th\u1ec3 d\u00f9ng \u0111\u1ec3 sinh c\u00f4ng, th\u01b0\u1eddng \u0111\u01b0\u1ee3c hi\u1ec3u l\u00e0 m\u1ee9c \u0111\u1ed9 h\u1ed7n lo\u1ea1n c\u1ee7a m\u1ed9t h\u1ec7.<\/p>\n<h3>Ai \u0111\u1eb7t ra kh\u00e1i ni\u1ec7m entropy?<\/h3>\n<p>Nh\u00e0 v\u1eadt l\u00fd ng\u01b0\u1eddi \u0110\u1ee9c Rudolf Clausius x\u00e2y d\u1ef1ng kh\u00e1i ni\u1ec7m t\u1eeb n\u0103m 1850 v\u00e0 \u0111\u1eb7t t\u00ean &#8220;entropy&#8221; v\u00e0o n\u0103m 1865.<\/p>\n<h3>\u0110\u01a1n v\u1ecb c\u1ee7a entropy l\u00e0 g\u00ec?<\/h3>\n<p>Entropy nhi\u1ec7t \u0111\u1ed9ng k\u00fd hi\u1ec7u S, \u0111\u01a1n v\u1ecb J\/K; entropy th\u00f4ng tin Shannon t\u00ednh b\u1eb1ng bit.<\/p>\n<h3>C\u00f4ng th\u1ee9c t\u00ednh bi\u1ebfn thi\u00ean entropy l\u00e0 g\u00ec?<\/h3>\n<p>V\u1edbi nhi\u1ec7t l\u01b0\u1ee3ng Q trao \u0111\u1ed5i thu\u1eadn ngh\u1ecbch \u1edf nhi\u1ec7t \u0111\u1ed9 tuy\u1ec7t \u0111\u1ed1i kh\u00f4ng \u0111\u1ed5i T, \u0394S = Q\/T. \u1ede c\u1ea5p \u0111\u1ed9 ph\u00e2n t\u1eed, S = k\u00b7ln W.<\/p>\n<h3>Entropy c\u00f3 gi\u1ea3m \u0111\u01b0\u1ee3c kh\u00f4ng?<\/h3>\n<p>Entropy c\u1ee7a m\u1ed9t ph\u1ea7n h\u1ec7 c\u00f3 th\u1ec3 gi\u1ea3m (nh\u01b0 khi n\u01b0\u1edbc \u0111\u00f4ng \u0111\u00e1 trong t\u1ee7 l\u1ea1nh), nh\u01b0ng entropy c\u1ee7a h\u1ec7 c\u00f4 l\u1eadp th\u00ec kh\u00f4ng bao gi\u1edd gi\u1ea3m theo \u0111\u1ecbnh lu\u1eadt th\u1ee9 hai.<\/p>\n<h3>V\u00ec sao tung \u0111\u1ed3ng xu c\u00f3 entropy 1 bit?<\/h3>\n<p>\u0110\u1ed3ng xu c\u00e2n \u0111\u1ed1i c\u00f3 hai k\u1ebft qu\u1ea3 c\u00f9ng x\u00e1c su\u1ea5t 0,5, n\u00ean H = \u22122 \u00d7 0,5 \u00d7 log\u2082 0,5 = 1 bit.<\/p>\n<h2>K\u1ebft lu\u1eadn<\/h2>\n<p>Entropy (k\u00fd hi\u1ec7u S, \u0111\u01a1n v\u1ecb J\/K) \u0111o ph\u1ea7n n\u0103ng l\u01b0\u1ee3ng kh\u00f4ng th\u1ec3 sinh c\u00f4ng v\u00e0 m\u1ee9c \u0111\u1ed9 h\u1ed7n lo\u1ea1n c\u1ee7a h\u1ec7, do Rudolf Clausius \u0111\u1ec1 xu\u1ea5t. Ba c\u00f4ng th\u1ee9c c\u1ea7n nh\u1edb l\u00e0 \u0394S = Q\/T, S = k\u00b7ln W v\u00e0 entropy Shannon H = \u2212\u03a3 p\u00b7log\u2082 p. Theo \u0111\u1ecbnh lu\u1eadt th\u1ee9 hai, entropy c\u1ee7a h\u1ec7 c\u00f4 l\u1eadp kh\u00f4ng bao gi\u1edd gi\u1ea3m, gi\u1ea3i th\u00edch v\u00ec sao nhi\u1ec1u qu\u00e1 tr\u00ecnh trong t\u1ef1 nhi\u00ean ch\u1ec9 di\u1ec5n ra theo m\u1ed9t chi\u1ec1u. B\u1ea1n h\u00e3y t\u1ef1 gi\u1ea3i l\u1ea1i c\u00e1c v\u00ed d\u1ee5 tr\u00ean \u0111\u1ec3 n\u1eafm ch\u1eafc c\u00e1ch t\u00ednh.<\/p>\n<p>Xem th\u00eam:<\/p>\n<p><a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/dien-truong-la-gi\/\">\u0110i\u1ec7n tr\u01b0\u1eddng l\u00e0 g\u00ec? C\u01b0\u1eddng \u0111\u1ed9 \u0111i\u1ec7n tr\u01b0\u1eddng v\u00e0 c\u00f4ng th\u1ee9c E = F\/q<\/a><\/p>\n<p><a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/the-nao-la-vat-nhiem-dien\/\">Th\u1ebf n\u00e0o l\u00e0 v\u1eadt nhi\u1ec5m \u0111i\u1ec7n? C\u00e1ch l\u00e0m v\u1eadt nhi\u1ec5m \u0111i\u1ec7n<\/a><br \/>\n<script type=\"application\/ld+json\">{\"@context\":\"https:\/\/schema.org\",\"@type\":\"FAQPage\",\"mainEntity\":[\n{\"@type\":\"Question\",\"name\":\"Entropy l\u00e0 g\u00ec n\u00f3i \u0111\u01a1n gi\u1ea3n?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Entropy l\u00e0 th\u01b0\u1edbc \u0111o ph\u1ea7n n\u0103ng l\u01b0\u1ee3ng kh\u00f4ng th\u1ec3 d\u00f9ng \u0111\u1ec3 sinh c\u00f4ng, th\u01b0\u1eddng \u0111\u01b0\u1ee3c hi\u1ec3u l\u00e0 m\u1ee9c \u0111\u1ed9 h\u1ed7n lo\u1ea1n c\u1ee7a m\u1ed9t h\u1ec7.\"}},\n{\"@type\":\"Question\",\"name\":\"Ai \u0111\u1eb7t ra kh\u00e1i ni\u1ec7m entropy?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Nh\u00e0 v\u1eadt l\u00fd ng\u01b0\u1eddi \u0110\u1ee9c Rudolf Clausius x\u00e2y d\u1ef1ng kh\u00e1i ni\u1ec7m t\u1eeb n\u0103m 1850 v\u00e0 \u0111\u1eb7t t\u00ean \\\"entropy\\\" v\u00e0o n\u0103m 1865.\"}},\n{\"@type\":\"Question\",\"name\":\"\u0110\u01a1n v\u1ecb c\u1ee7a entropy l\u00e0 g\u00ec?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Entropy nhi\u1ec7t \u0111\u1ed9ng k\u00fd hi\u1ec7u S, \u0111\u01a1n v\u1ecb J\/K; entropy th\u00f4ng tin Shannon t\u00ednh b\u1eb1ng bit.\"}},\n{\"@type\":\"Question\",\"name\":\"C\u00f4ng th\u1ee9c t\u00ednh bi\u1ebfn thi\u00ean entropy l\u00e0 g\u00ec?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"V\u1edbi nhi\u1ec7t l\u01b0\u1ee3ng Q trao \u0111\u1ed5i thu\u1eadn ngh\u1ecbch \u1edf nhi\u1ec7t \u0111\u1ed9 tuy\u1ec7t \u0111\u1ed1i kh\u00f4ng \u0111\u1ed5i T, \u0394S = Q\/T. \u1ede c\u1ea5p \u0111\u1ed9 ph\u00e2n t\u1eed, S = k\u00b7ln W.\"}},\n{\"@type\":\"Question\",\"name\":\"Entropy c\u00f3 gi\u1ea3m \u0111\u01b0\u1ee3c kh\u00f4ng?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Entropy c\u1ee7a m\u1ed9t ph\u1ea7n h\u1ec7 c\u00f3 th\u1ec3 gi\u1ea3m (nh\u01b0 khi n\u01b0\u1edbc \u0111\u00f4ng \u0111\u00e1 trong t\u1ee7 l\u1ea1nh), nh\u01b0ng entropy c\u1ee7a h\u1ec7 c\u00f4 l\u1eadp th\u00ec kh\u00f4ng bao gi\u1edd gi\u1ea3m theo \u0111\u1ecbnh lu\u1eadt th\u1ee9 hai.\"}},\n{\"@type\":\"Question\",\"name\":\"V\u00ec sao tung \u0111\u1ed3ng xu c\u00f3 entropy 1 bit?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"\u0110\u1ed3ng xu c\u00e2n \u0111\u1ed1i c\u00f3 hai k\u1ebft qu\u1ea3 c\u00f9ng x\u00e1c su\u1ea5t 0,5, n\u00ean H = \u22122 \u00d7 0,5 \u00d7 log\u2082 0,5 = 1 bit.\"}}\n]}<\/script><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Entropy l\u00e0 \u0111\u1ea1i l\u01b0\u1ee3ng v\u1eadt l\u00fd \u0111o ph\u1ea7n n\u0103ng l\u01b0\u1ee3ng c\u1ee7a m\u1ed9t h\u1ec7 kh\u00f4ng th\u1ec3 d\u00f9ng \u0111\u1ec3 sinh c\u00f4ng, \u0111\u1ed3ng th\u1eddi th\u01b0\u1eddng \u0111\u01b0\u1ee3c hi\u1ec3u l\u00e0 th\u01b0\u1edbc \u0111o m\u1ee9c \u0111\u1ed9 h\u1ed7n lo\u1ea1n (m\u1ea5t tr\u1eadt t\u1ef1) c\u1ee7a h\u1ec7. Kh\u00e1i ni\u1ec7m n\u00e0y do nh\u00e0 v\u1eadt l\u00fd ng\u01b0\u1eddi \u0110\u1ee9c Rudolf Clausius x\u00e2y d\u1ef1ng t\u1eeb n\u0103m 1850 v\u00e0 \u0111\u1eb7t t\u00ean [&hellip;]<\/p>\n","protected":false},"author":102,"featured_media":624167,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"entropy l\u00e0 g\u00ec","_yoast_wpseo_title":"Entropy l\u00e0 g\u00ec? \u0110\u1ecbnh ngh\u0129a, c\u00f4ng th\u1ee9c v\u00e0 v\u00ed d\u1ee5 d\u1ec5 hi\u1ec3u","_yoast_wpseo_metadesc":"Entropy l\u00e0 g\u00ec? Hi\u1ec3u \u0111\u1ecbnh ngh\u0129a, c\u00f4ng th\u1ee9c \u0394S = Q\/T, S = k\u00b7ln W, entropy Shannon v\u00e0 v\u00ed d\u1ee5 c\u00f3 l\u1eddi gi\u1ea3i d\u1ec5 hi\u1ec3u. \u0110\u1ecdc ngay \u0111\u1ec3 n\u1eafm ch\u1eafc ki\u1ebfn th\u1ee9c nh\u00e9!","footnotes":""},"categories":[3910,30453],"tags":[],"class_list":["post-624163","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-kham-pha","category-kien-thuc"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v27.3 (Yoast SEO v27.4) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>Entropy l\u00e0 g\u00ec? \u0110\u1ecbnh ngh\u0129a, c\u00f4ng th\u1ee9c v\u00e0 v\u00ed d\u1ee5 d\u1ec5 hi\u1ec3u<\/title>\n<meta name=\"description\" content=\"Entropy l\u00e0 g\u00ec? Hi\u1ec3u \u0111\u1ecbnh ngh\u0129a, c\u00f4ng th\u1ee9c \u0394S = Q\/T, S = k\u00b7ln W, entropy Shannon v\u00e0 v\u00ed d\u1ee5 c\u00f3 l\u1eddi gi\u1ea3i d\u1ec5 hi\u1ec3u. \u0110\u1ecdc ngay \u0111\u1ec3 n\u1eafm ch\u1eafc ki\u1ebfn th\u1ee9c nh\u00e9!\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/hoanghamobile.com\/tin-tuc\/entropy-la-gi\/\" \/>\n<meta property=\"og:locale\" content=\"vi_VN\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Entropy l\u00e0 g\u00ec? \u0110\u1ecbnh ngh\u0129a, c\u00f4ng th\u1ee9c v\u00e0 v\u00ed d\u1ee5 d\u1ec5 hi\u1ec3u\" \/>\n<meta property=\"og:description\" content=\"Entropy l\u00e0 g\u00ec? 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