A proposition based on the fluctuation theorem in thermodynamics is formulated to quantitatively describe molecular evolution processes in biology. Although we cannot give full proof of its generality, we demonstrate ...A proposition based on the fluctuation theorem in thermodynamics is formulated to quantitatively describe molecular evolution processes in biology. Although we cannot give full proof of its generality, we demonstrate via computer simulation its applicability in an example of DNA in vitro evolution. According to this theorem, the evolution process is a series of exponentially rare fluctuations fixed by the force of natural selection展开更多
We present a fluctuation theorem for Floquet quantum master equations. This is a detailed version of the famous Gallavotti–Cohen theorem. In contrast to the latter theorem, which involves the probability distribution...We present a fluctuation theorem for Floquet quantum master equations. This is a detailed version of the famous Gallavotti–Cohen theorem. In contrast to the latter theorem, which involves the probability distribution of the total heat current, the former involves the joint probability distribution of positive and negative heat currents and can be used to derive the latter. A quantum two-level system driven by a periodic external field is used to verify this result.展开更多
Fluctuation theorems have been applied successfully to any system away from thermal equilibrium,which are helpful for understanding the thermodynamic state evolution.We investigate fluctuation theorems for strong coup...Fluctuation theorems have been applied successfully to any system away from thermal equilibrium,which are helpful for understanding the thermodynamic state evolution.We investigate fluctuation theorems for strong coupling between a system and its reservoir,by path-dependent definition of work and heat satisfying the first law of thermodynamics.We present the fluctuation theorems for two kinds of entropy productions.One is the informational entropy production,which is always non-negative and can be employed in either strong or weak coupling systems.The other is the thermodynamic entropy production,which differs from the informational entropy production at strong coupling by the effects regarding the reservoir.We find that,it is the negative work on the reservoir,rather than the nonequilibrium of the thermal reservoir,which invalidates the thermodynamic entropy production at strong coupling.Our results indicate that the effects from the reservoir are essential to understanding thermodynamic processes at strong coupling.展开更多
Fluctuation theorem for entropy production in a mesoscopic chemical reaction network is discussed. When the system size is sufficiently large, it is found that, by defining a kind of coarse-grained dissipation functio...Fluctuation theorem for entropy production in a mesoscopic chemical reaction network is discussed. When the system size is sufficiently large, it is found that, by defining a kind of coarse-grained dissipation function, the entropy production in a reversible reaction channel can be approximately described by a type of detailed fluctuation theorem. Such a fluctuation relation has been successfully tested by direct simulations in a linear reaction model consisting of two reversible channels and in an oscillatory model wherein only one channel is reversible.展开更多
In this review, we give a retrospect of the recent progress in nonequilibrium statistical mechanics and thermodynamics in small dynamical systems. For systems with only a few number of particles, fluctuations and nonl...In this review, we give a retrospect of the recent progress in nonequilibrium statistical mechanics and thermodynamics in small dynamical systems. For systems with only a few number of particles, fluctuations and nonlinearity become sig- nificant and contribute to the nonequilibrium behaviors of the systems, hence the statistical properties and thermodynamics should be carefully studied. We review recent developments of this topic by starting from the Gallavotti-Cohen fluctuation theorem, and then to the Evans-Searles transient fluctuation theorem, Jarzynski free-energy equality, and the Crooks fluc- tuation relation. We also investigate the nonequilibrium free energy theorem for trajectories involving changes of the heat bath temperature and propose a generalized free-energy relation. It should be noticed that the non-Markovian property of the heat bath may lead to the violation of the free-energy relation.展开更多
The bacterial flagellar motor is a nanometer-sized rotary motor that generates the torque to drive the rotation of the flagellar filament.The output torque is an important property of the motor.The motor rotation was ...The bacterial flagellar motor is a nanometer-sized rotary motor that generates the torque to drive the rotation of the flagellar filament.The output torque is an important property of the motor.The motor rotation was usually monitored by attaching aμm-sized bead to a shortened flagellar filament,and the torque was extracted by calculating the torque due to the viscous drag of the medium on the bead rotation.We sought for an independent extraction of the torque from thermal fluctuation in the motor rotation using the fluctuation theorem(FT).However,we identified an overwhelming fluctuation beyond the thermal noise that precluded the use of FT.We further characterized the timescale and the amplitude of this fluctuation,finding that it was probably due to the stepping of the motor.The amplitude of torque fluctuation we characterized here provided new information on the torque-generating interaction potential curve.展开更多
In this work, we discussed the stochastic thermodynamics of mesoscopic electron transfer reactions between ions and electrodes. With a relationship between the reaction rate con- stant and the electrode potential, we ...In this work, we discussed the stochastic thermodynamics of mesoscopic electron transfer reactions between ions and electrodes. With a relationship between the reaction rate con- stant and the electrode potential, we find that the heat dissipation βq equals to the dynamic irreversibility of the reaction system minus an internal entropy change term. The total en- tropy change Ast is defined as the summation of the system entropy change As and the heat dissipation/βq such that △st=△s＋βq. Even though the heat dissipation depends linearly on the electrode potential, the total entropy change is found to satisfy the fluctuation theo- rem 〈e-△st 〉=1, and hence a second law-like inequality reads （△st）≥0. Our study provides a practical methodology for the stochastic thermodynamics of electrochemical reactions, which may find applications in biochemical and electrochemical reaction systems.展开更多
The crucial condition in the derivation of the Jarzynski equality （JE） from the fluctuation theorem is that the time integral of the phase space contraction factor can be exactly expressed as the entropy production ...The crucial condition in the derivation of the Jarzynski equality （JE） from the fluctuation theorem is that the time integral of the phase space contraction factor can be exactly expressed as the entropy production resulting from the heat absorbed by the system from the thermal bath. For the system violating this condition, a more general form of JE may exist. This existence is verified by three Gedanken experiments and numerical simulations, and may be confirmed by the real experiment in the nanoscale.展开更多
In this paper, we define the harmonic oscillator with random damping in non-Markovian thermal bath. This model represents new version of the random oscillators. In this side, we derive the overdamped harmonic oscillat...In this paper, we define the harmonic oscillator with random damping in non-Markovian thermal bath. This model represents new version of the random oscillators. In this side, we derive the overdamped harmonic oscillator with multiplicative colored noise and translate it into the additive colored noise by changing the variables. The overdamped harmonic oscillator is stochastic differential equation driving by colored noise. We derive the change in the total entropy production (CTEP) of the model and calculate the mean and variance. We show the fluctuation theorem (FT) which is invalid at any order in the time correlation. The problem of the deriving of the CTEP is studied in two different examples of the harmonic potential. Finally, we give the conclusion and plan for future works.展开更多
Classical thermodynamics has been a great achievement in dealing with systems that are in equilibrium or near equilibrium.As an emerging field,nonequilibrium thermodynamics provides a general framework for understandi...Classical thermodynamics has been a great achievement in dealing with systems that are in equilibrium or near equilibrium.As an emerging field,nonequilibrium thermodynamics provides a general framework for understanding the nonequilibrium processes,particularly in small systems that are typically far-from-equilibrium and are dominated by thermal or quantum fluctuations.Cavity optomechanical systems hold great promise among the various experimental platforms for studying nonequilibrium thermodynamics owing to their high controllability,excellent mechanical performance,and ability to operate deep in the quantum regime.Here,we present an overview of the recent advances in nonequilibrium thermodynamics with cavity optomechanical systems.The experimental results in entropy production assessment,fluctuation theorems,heat transfer,and heat engines are highlighted.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant No. 10721403)the National Basic Research Program of China (Grant No. 2007CB814802)the Jun-Zheng Foundation at Peking University
文摘A proposition based on the fluctuation theorem in thermodynamics is formulated to quantitatively describe molecular evolution processes in biology. Although we cannot give full proof of its generality, we demonstrate via computer simulation its applicability in an example of DNA in vitro evolution. According to this theorem, the evolution process is a series of exponentially rare fluctuations fixed by the force of natural selection
基金supported by the National Science Foundation of China under Grants No. 11 174 025 and No. 11 575 016the support of the CAS Interdisciplinary Innovation Team, No. 2060 299。
文摘We present a fluctuation theorem for Floquet quantum master equations. This is a detailed version of the famous Gallavotti–Cohen theorem. In contrast to the latter theorem, which involves the probability distribution of the total heat current, the former involves the joint probability distribution of positive and negative heat currents and can be used to derive the latter. A quantum two-level system driven by a periodic external field is used to verify this result.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11674360,11734018,11835011,and 11965012)the Applied Basic Research Project of Yunnan Province,China(Grant No.2017FB004)
文摘Fluctuation theorems have been applied successfully to any system away from thermal equilibrium,which are helpful for understanding the thermodynamic state evolution.We investigate fluctuation theorems for strong coupling between a system and its reservoir,by path-dependent definition of work and heat satisfying the first law of thermodynamics.We present the fluctuation theorems for two kinds of entropy productions.One is the informational entropy production,which is always non-negative and can be employed in either strong or weak coupling systems.The other is the thermodynamic entropy production,which differs from the informational entropy production at strong coupling by the effects regarding the reservoir.We find that,it is the negative work on the reservoir,rather than the nonequilibrium of the thermal reservoir,which invalidates the thermodynamic entropy production at strong coupling.Our results indicate that the effects from the reservoir are essential to understanding thermodynamic processes at strong coupling.
基金supported by the National Natural Science Foundation of China (Grant Nos. 20873130 and 20933006)
文摘Fluctuation theorem for entropy production in a mesoscopic chemical reaction network is discussed. When the system size is sufficiently large, it is found that, by defining a kind of coarse-grained dissipation function, the entropy production in a reversible reaction channel can be approximately described by a type of detailed fluctuation theorem. Such a fluctuation relation has been successfully tested by direct simulations in a linear reaction model consisting of two reversible channels and in an oscillatory model wherein only one channel is reversible.
基金supported by the National Natural Science Foundation of China (Grant No. 11075016)the Foundation for Doctoral Training from the Ministry of Education of China (Grant No. 20100003110007)
文摘In this review, we give a retrospect of the recent progress in nonequilibrium statistical mechanics and thermodynamics in small dynamical systems. For systems with only a few number of particles, fluctuations and nonlinearity become sig- nificant and contribute to the nonequilibrium behaviors of the systems, hence the statistical properties and thermodynamics should be carefully studied. We review recent developments of this topic by starting from the Gallavotti-Cohen fluctuation theorem, and then to the Evans-Searles transient fluctuation theorem, Jarzynski free-energy equality, and the Crooks fluc- tuation relation. We also investigate the nonequilibrium free energy theorem for trajectories involving changes of the heat bath temperature and propose a generalized free-energy relation. It should be noticed that the non-Markovian property of the heat bath may lead to the violation of the free-energy relation.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11925406 and 12090053)the National Key R&D Program of China(Grant No.2019YFA0709303)。
文摘The bacterial flagellar motor is a nanometer-sized rotary motor that generates the torque to drive the rotation of the flagellar filament.The output torque is an important property of the motor.The motor rotation was usually monitored by attaching aμm-sized bead to a shortened flagellar filament,and the torque was extracted by calculating the torque due to the viscous drag of the medium on the bead rotation.We sought for an independent extraction of the torque from thermal fluctuation in the motor rotation using the fluctuation theorem(FT).However,we identified an overwhelming fluctuation beyond the thermal noise that precluded the use of FT.We further characterized the timescale and the amplitude of this fluctuation,finding that it was probably due to the stepping of the motor.The amplitude of torque fluctuation we characterized here provided new information on the torque-generating interaction potential curve.
基金supported by the National Natural Science Foundation of China(No.21403041 and No.21503048)the Startup Packages from Guizhou Education University
文摘In this work, we discussed the stochastic thermodynamics of mesoscopic electron transfer reactions between ions and electrodes. With a relationship between the reaction rate con- stant and the electrode potential, we find that the heat dissipation βq equals to the dynamic irreversibility of the reaction system minus an internal entropy change term. The total en- tropy change Ast is defined as the summation of the system entropy change As and the heat dissipation/βq such that △st=△s＋βq. Even though the heat dissipation depends linearly on the electrode potential, the total entropy change is found to satisfy the fluctuation theo- rem 〈e-△st 〉=1, and hence a second law-like inequality reads （△st）≥0. Our study provides a practical methodology for the stochastic thermodynamics of electrochemical reactions, which may find applications in biochemical and electrochemical reaction systems.
基金We are grateful to the useful comments from Profs. C. Jarzynski, U. Seifert, M. Bier, and Dr. Gomez-Marin.
文摘The crucial condition in the derivation of the Jarzynski equality （JE） from the fluctuation theorem is that the time integral of the phase space contraction factor can be exactly expressed as the entropy production resulting from the heat absorbed by the system from the thermal bath. For the system violating this condition, a more general form of JE may exist. This existence is verified by three Gedanken experiments and numerical simulations, and may be confirmed by the real experiment in the nanoscale.
文摘In this paper, we define the harmonic oscillator with random damping in non-Markovian thermal bath. This model represents new version of the random oscillators. In this side, we derive the overdamped harmonic oscillator with multiplicative colored noise and translate it into the additive colored noise by changing the variables. The overdamped harmonic oscillator is stochastic differential equation driving by colored noise. We derive the change in the total entropy production (CTEP) of the model and calculate the mean and variance. We show the fluctuation theorem (FT) which is invalid at any order in the time correlation. The problem of the deriving of the CTEP is studied in two different examples of the harmonic potential. Finally, we give the conclusion and plan for future works.
基金supported by the National Key R&D Program of China(2022YFA1404202)the National Natural Science Foundation of China(11925401,12234008,11734008,12222404,11974115)+2 种基金the Shanghai Municipal Science and Technology Major Project(2019SHZDZX01)Natural Science Foundation Project of CQ(cstc2021jcyj-msxmX0914)Equipment Development Department Rapid Support Project(80917020109)。
文摘Classical thermodynamics has been a great achievement in dealing with systems that are in equilibrium or near equilibrium.As an emerging field,nonequilibrium thermodynamics provides a general framework for understanding the nonequilibrium processes,particularly in small systems that are typically far-from-equilibrium and are dominated by thermal or quantum fluctuations.Cavity optomechanical systems hold great promise among the various experimental platforms for studying nonequilibrium thermodynamics owing to their high controllability,excellent mechanical performance,and ability to operate deep in the quantum regime.Here,we present an overview of the recent advances in nonequilibrium thermodynamics with cavity optomechanical systems.The experimental results in entropy production assessment,fluctuation theorems,heat transfer,and heat engines are highlighted.
