Peter Werner, Alexander K. Hartmann, Satya N. Majumdar
{"title":"解压进程的工作分配","authors":"Peter Werner, Alexander K. Hartmann, Satya N. Majumdar","doi":"10.1103/physreve.110.024115","DOIUrl":null,"url":null,"abstract":"A simple zipper model is introduced, representing in a simplified way, e.g., the folded DNA double helix or hairpin structures in RNA. The double stranded hairpin is connected to a heat bath at temperature <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>T</mi></math> and subject to an external force <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>f</mi></math>, which couples to the free length <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>L</mi></math> of the unzipped sequence. The leftmost zipped position can be seen as the position of a random walker in a special external field. Increasing the force leads to a zipping-unzipping first-order phase transition at a critical force <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><msub><mi>f</mi><mi>c</mi></msub><mrow><mo>(</mo><mi>T</mi><mo>)</mo></mrow></mrow></math> in the thermodynamic limit of a very large chain. We compute analytically, as a function of temperature <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>T</mi></math> and force <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>f</mi></math>, the full distribution <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>P</mi><mo>(</mo><mi>L</mi><mo>)</mo></mrow></math> of free lengths in the thermodynamic limit and show that it is qualitatively very different for <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>f</mi><mo><</mo><msub><mi>f</mi><mi>c</mi></msub></mrow><mo>,</mo><mo> </mo><mrow><mi>f</mi><mo>=</mo><msub><mi>f</mi><mi>c</mi></msub></mrow></math>, and <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>f</mi><mo>></mo><msub><mi>f</mi><mi>c</mi></msub></mrow></math>. Next we consider quasistatic work processes where the force is incremented according to a linear protocol. Having obtained <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>P</mi><mo>(</mo><mi>L</mi><mo>)</mo></mrow></math> already allows us to derive an analytical expression for the work distribution <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>P</mi><mo>(</mo><mi>W</mi><mo>)</mo></mrow></math> in the zipped phase <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>f</mi><mo><</mo><msub><mi>f</mi><mi>c</mi></msub></mrow></math> for a long chain. We compute the large-deviation tails of the work distribution explicitly. This distribution can be interpreted as work distribution for an oscillatorylike model. Our analytical result for the work distribution is compared over a large range of the support down to probabilities as small as <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msup><mn>10</mn><mrow><mo>−</mo><mn>200</mn></mrow></msup></math> with numerical simulations performed by applying sophisticated large-deviation algorithms.","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":null,"pages":null},"PeriodicalIF":2.4000,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Work distribution for unzipping processes\",\"authors\":\"Peter Werner, Alexander K. Hartmann, Satya N. Majumdar\",\"doi\":\"10.1103/physreve.110.024115\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A simple zipper model is introduced, representing in a simplified way, e.g., the folded DNA double helix or hairpin structures in RNA. The double stranded hairpin is connected to a heat bath at temperature <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><mi>T</mi></math> and subject to an external force <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><mi>f</mi></math>, which couples to the free length <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><mi>L</mi></math> of the unzipped sequence. The leftmost zipped position can be seen as the position of a random walker in a special external field. Increasing the force leads to a zipping-unzipping first-order phase transition at a critical force <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><mrow><msub><mi>f</mi><mi>c</mi></msub><mrow><mo>(</mo><mi>T</mi><mo>)</mo></mrow></mrow></math> in the thermodynamic limit of a very large chain. We compute analytically, as a function of temperature <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><mi>T</mi></math> and force <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><mi>f</mi></math>, the full distribution <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><mrow><mi>P</mi><mo>(</mo><mi>L</mi><mo>)</mo></mrow></math> of free lengths in the thermodynamic limit and show that it is qualitatively very different for <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><mrow><mi>f</mi><mo><</mo><msub><mi>f</mi><mi>c</mi></msub></mrow><mo>,</mo><mo> </mo><mrow><mi>f</mi><mo>=</mo><msub><mi>f</mi><mi>c</mi></msub></mrow></math>, and <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><mrow><mi>f</mi><mo>></mo><msub><mi>f</mi><mi>c</mi></msub></mrow></math>. Next we consider quasistatic work processes where the force is incremented according to a linear protocol. Having obtained <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><mrow><mi>P</mi><mo>(</mo><mi>L</mi><mo>)</mo></mrow></math> already allows us to derive an analytical expression for the work distribution <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><mrow><mi>P</mi><mo>(</mo><mi>W</mi><mo>)</mo></mrow></math> in the zipped phase <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><mrow><mi>f</mi><mo><</mo><msub><mi>f</mi><mi>c</mi></msub></mrow></math> for a long chain. We compute the large-deviation tails of the work distribution explicitly. This distribution can be interpreted as work distribution for an oscillatorylike model. Our analytical result for the work distribution is compared over a large range of the support down to probabilities as small as <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><msup><mn>10</mn><mrow><mo>−</mo><mn>200</mn></mrow></msup></math> with numerical simulations performed by applying sophisticated large-deviation algorithms.\",\"PeriodicalId\":20085,\"journal\":{\"name\":\"Physical review. E\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.4000,\"publicationDate\":\"2024-08-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Physical review. 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引用次数: 0
摘要
我们引入了一个简单的拉链模型,以简化的方式表示折叠的 DNA 双螺旋或 RNA 中的发夹结构。双链发夹连接到温度为 T 的热浴中,并受到外力 f 的作用,该外力与未拉链序列的自由长度 L 相耦合。最左边的拉链位置可以看作是一个随机漫步者在一个特殊外场中的位置。在一个非常大的链的热力学极限中,增加力会导致在临界力 fc(T) 处出现拉链-解拉链的一阶相变。作为温度 T 和力 f 的函数,我们分析计算了热力学极限下自由长度的全分布 P(L),并表明在 f<fc、f=fc 和 f>fc 时,自由长度的全分布有很大不同。接下来,我们将考虑力按照线性协议递增的准静态功过程。得到 P(L) 后,我们就可以推导出长链在拉链阶段 f<fc 的功分布 P(W) 的分析表达式。我们明确计算了工作量分布的大偏差尾部。该分布可解释为类似振荡模型的功分布。我们对功分布的分析结果与应用复杂的大偏差算法进行的数值模拟结果进行了比较。
A simple zipper model is introduced, representing in a simplified way, e.g., the folded DNA double helix or hairpin structures in RNA. The double stranded hairpin is connected to a heat bath at temperature and subject to an external force , which couples to the free length of the unzipped sequence. The leftmost zipped position can be seen as the position of a random walker in a special external field. Increasing the force leads to a zipping-unzipping first-order phase transition at a critical force in the thermodynamic limit of a very large chain. We compute analytically, as a function of temperature and force , the full distribution of free lengths in the thermodynamic limit and show that it is qualitatively very different for , and . Next we consider quasistatic work processes where the force is incremented according to a linear protocol. Having obtained already allows us to derive an analytical expression for the work distribution in the zipped phase for a long chain. We compute the large-deviation tails of the work distribution explicitly. This distribution can be interpreted as work distribution for an oscillatorylike model. Our analytical result for the work distribution is compared over a large range of the support down to probabilities as small as with numerical simulations performed by applying sophisticated large-deviation algorithms.
期刊介绍:
Physical Review E (PRE), broad and interdisciplinary in scope, focuses on collective phenomena of many-body systems, with statistical physics and nonlinear dynamics as the central themes of the journal. Physical Review E publishes recent developments in biological and soft matter physics including granular materials, colloids, complex fluids, liquid crystals, and polymers. The journal covers fluid dynamics and plasma physics and includes sections on computational and interdisciplinary physics, for example, complex networks.