We investigate a motion of a colloid in a harmonic trap driven out of equilibrium by an external ... more We investigate a motion of a colloid in a harmonic trap driven out of equilibrium by an external non-conservative force producing a torque in the presence of a uniform magnetic field. We find that steady state exists only for a proper range of parameters such as mass, viscosity coefficient, and stiffness of the harmonic potential, and the magnetic field, which is not observed in the overdamped limit. We derive the existence condition for the steady state. We examine the combined influence of the non-conservative force and the magnetic field on non-equilibrium characteristics such as non-
Journal of the Korean Physical Society, Mar 1, 2016
We investigate an unconventional nature of the entropy production (EP) in nonequilibrium systems ... more We investigate an unconventional nature of the entropy production (EP) in nonequilibrium systems with odd-parity variables that change signs under time reversal. We consider the Brownian motion of a particle in contact with a heat reservoir, where particle momentum is an odd-parity variable. In the presence of an external momentum-dependent force, the EP transferred to environment is found not equivalent to usual reservoir entropy change due to heat transfer. There appears an additional unconventional contribution to the EP, which is crucial for maintaining the non-negativity of the (average) total EP enforced by the thermodynamic second law. A few examples are considered to elucidate the novel nature of the EP. We also discuss detailed balance conditions with a momentum-dependent force.
We investigate three kinds of heat produced in a system and a bath strongly coupled via an intera... more We investigate three kinds of heat produced in a system and a bath strongly coupled via an interaction Hamiltonian. By studying the energy flows between the system, the bath, and their interaction, we provide rigorous definitions of two types of heat, QS and QB from the energy loss of the system and the energy gain of the bath, respectively. This is in contrast to the equivalence of QS and QB, which is commonly assumed to hold in the weak coupling regime. The bath we consider is equipped with a thermostat which enables it to reach an equilibrium. We identify another kind of heat QSB from the energy dissipation of the bath into the super bath that provides the thermostat. We derive the fluctuation theorems (FT's) with the system variables and various heats, which are discussed in comparison with the FT for the total entropy production. We take an example of a sliding harmonic potential of a single Brownian particle in a fluid and calculate the three heats in a simplified model. These heats are found to equal on average in the steady state of energy, but show different fluctuations at all times.
Conventional wisdom indicates that initial memory should decay away exponentially in time for gen... more Conventional wisdom indicates that initial memory should decay away exponentially in time for general (noncritial) equilibration processes. In particular, time-integrated quantities such as heat are presumed to lose initial memory in a sufficiently long-time limit. However, we show that the large deviation function of time-integrated quantities may exhibit initial memory effect even in the infinite-time limit, if the system is initially prepared sufficiently far away from equilibrium. For a Brownian particle dynamics, as an example, we found a sharp finite threshold rigorously, beyond which the corresponding large deviation function contains everlasting initial memory. The physical origin for this phenomenon is explored with an intuitive argument and also from a toy model analysis.
We investigate the motion of a colloidal particle driven out of equilibrium by an external torque... more We investigate the motion of a colloidal particle driven out of equilibrium by an external torque. We use molecular dynamics simulation as an alternative to the Langevin dynamics. We prepare a heat bath composed of thousands of particles interacting with each other through the Lennard-Jones potential and impose the Langevin thermostat to maintain heat bath in equilibrium. We consider a single colloidal particle to interact with the particles of the heat bath also by the Lennard-Jones potential, without applying any types of dissipative and fluctuating forces used in the Langevin dynamics. We set up simulation protocol fit for the overdamped limit as in real experiments by increasing the size and mass of the colloidal particle. We study nonequilibrium fluctuations for work and heat produced incessantly in time and compare results with those obtained from the previous studies via the overdamped Langevin dynamics. We confirm the Gallavotti-Cohen symmetry and the fluctuation theorem for the work production.
Bulletin of the American Physical Society, Mar 4, 2015
Molecular dynamics study on a nonequilibrium motion of a colloidal particle driven by an external... more Molecular dynamics study on a nonequilibrium motion of a colloidal particle driven by an external torque DONGHWAN YOO, Myongji University, YOUNGKYUN JUNG, KISTI, CHULAN KWON, Myongji University -We investigate the motion of a colloidal particle driven out of equilibrium by an external torque. We use the molecular dynamics simulation that is alternative to the simulation based on the Langevin equation and is expected to mimic an experiment more realistically. We choose a heat bath composed of about a thousand particles interacting to each other through the Lenard-Jones potential and impose the Langevin thermostat to maintain it in equilibrium. We prepare a colloidal particle to interact with the particles of the heat bath also by the Lenard-Jones potential while any dissipative force and noise are not employed explicitly. We study the stochastic properties of the nonequilibrium fluctuation for work and heat produced incessantly in the steady state. We accurately confirm the fluctuation theorem for the work production. We also investigate the motion beyond the overdamped limit by varying the mass of the particle. We compare our result with a previous theoretical result in the overdamped limit based on the Langevin equation 1 .
Statistical inference from data is a foundational task in science. Recently, it has received grow... more Statistical inference from data is a foundational task in science. Recently, it has received growing attention for its central role in inference systems of primary interest in data sciences and machine learning. However, the understanding of statistical inference is not that solid while remains as a matter of subjective belief or as the routine procedures once claimed objective. We here show that there is an objective description of statistical inference for long sequence of exchangeable binary random variables, the prototypal stochasticity in theories and applications. A linear differential equation is derived from the identity known as de Finetti's representation theorem, and it turns out that statistical inference is given by the Green's functions. Our finding is an answer to the normative issue of science that pursues the objectivity based on data, and its significance will be far-reaching in most pure and applied fields.
Bulletin of the American Physical Society, Feb 28, 2012
Initial condition dependence of the probability density function of the injected power in the Lan... more Initial condition dependence of the probability density function of the injected power in the Langevin equation JAE SUNG LEE, Korea Institute for Advanced Study, CHULAN KWON, Department of Physics, Myongji University, HYUNGGYU PARK, School of Physcis, Korea Institute for Advanced Study -We study the diffusive dynamics of a Brownian particle described by the Langevin's equation with time varying heat bath temperature. Initially (when time t < 0) the heat bath temperature is T init and the particle equilibrates with the heat bath. At time t = 0, the temperature abruptly changes from T init to T , where their ratio is denoted by α = T /T init . Then the particle follows the Langevin dynamics with the temperature T for t > 0. Using the path integral method, we compute the probability density function (PDF) of the injection power (injected energy per unit time into the Brownian particle by the random noise, see J. Stat. Phys. 107, 314 (2002)). We find that the PDF or the corresponding large deviation function depends on the initial temperature T init even in the t → ∞ limit. In addition, we show that "phase transition" of the large deviation function occurs at α = 1/4.
Neural Information Processing Systems, Dec 1, 1997
We study the storage capacity of a fully-connected committee machine with a large number K of hid... more We study the storage capacity of a fully-connected committee machine with a large number K of hidden nodes. The storage capacity is obtained by analyzing the geometrical structure of the weight space related to the internal representation . By examining the asymptotic behavior of order parameters in the limit of large K, the storage capacity Q c is found to be proportional to ]{ Jln ]{ up to the leading order. This result satisfies the mathematical bound given by Mitchison and Durbin , whereas the replica-symmetric solution in a conventional Gardner 's approach violates this bound.
Journal of the Korean Physical Society, Sep 1, 2015
A rigorous derivation of nonequilibrium entropy production via the path-integral formalism is pre... more A rigorous derivation of nonequilibrium entropy production via the path-integral formalism is presented. Entropy production is defined as the entropy change piled in a heat reservoir as a result of a nonequilibrium thermodynamic process. It is a central quantity by which various forms of the fluctuation theorem are obtained. The two kinds of the stochastic dynamics are investigated: the Langevin dynamics for an even-parity state and the Brownian motion of a single particle. Mathematical ambiguities in deriving the functional form of the entropy production, which depends on path in state space, are clarified by using a rigorous quantum mechanical approach.
We investigate thermodynamics of feedback processes driven by measurement. Regarding system and m... more We investigate thermodynamics of feedback processes driven by measurement. Regarding system and memory device as a composite system, mutual information as a measure of correlation between the two constituents contributes to the entropy of the composite system, which makes the generalized total entropy of the joint system and reservoir satisfy the second law of thermodynamics. We investigate the thermodynamics of the Szilard engine for an intermediate period before the completion of cycle. We show the second law to hold resolving the paradox of Maxwell's demon independent of the period taken into account. We also investigate a feedback process to confine a particle excessively within a trap, which is operated by repetitions of feedback in a finite time interval. We derive the stability condition for multi-step feedback and find the condition for confinement below thermal fluctuation in the absence of feedback. The results are found to depend on interval between feedback steps and intensity of feedback protocol, which are expected to be important parameters in real experiments.
Journal of Statistical Mechanics: Theory and Experiment, Aug 29, 2006
We investigate the equivalence of different operator-splitting schemes for the integration of the... more We investigate the equivalence of different operator-splitting schemes for the integration of the Langevin equation. We consider a specific problem, so called the directed percolation process, which can be extended to a wider class of problems. We first give a compact mathematical description of the operator-splitting method and introduce two typical splitting schemes that will be useful in numerical studies. We show that the two schemes are essentially equivalent through the map that turns out to be an automorphism. An associated equivalent class of operator-splitting integrations is also defined by generalizing the specified equivalence.
Journal of Statistical Mechanics: Theory and Experiment, Nov 8, 2013
Long-time-integrated quantities in stochastic processes, in or out of equilibrium, usually exhibi... more Long-time-integrated quantities in stochastic processes, in or out of equilibrium, usually exhibit rare but huge fluctuations. Work or heat production is such a quantity, of which the probability distribution function displays an exponential decay characterized by the large deviation function (LDF). The LDF is often deduced from the cumulant generating function through the inverse Fourier transformation. The saddle-point integration method is a powerful technique to obtain the asymptotic results in the Fourier integral, but a special care should be taken when the saddle point is located near a singularity of the integrand. In this paper, we present a modified saddle-point method to handle such a difficulty efficiently. We investigate the dissipated and injected heat production in equilibration processes with various initial conditions, as an example, where the generating functions contain branch-cut singularities as well as power-law ones. Exploiting the new modified saddle-point integrations, we obtain the leading finite-time corrections for the LDF's, which are confirmed by numerical results.
Particles kicked by external forces to produce mobility distinct from thermal diffusion are an ic... more Particles kicked by external forces to produce mobility distinct from thermal diffusion are an iconic feature of the active matter problem. Here, we map this onto a minimal model for experiment and theory covering the wide time and length scales of usual active matter systems. A particle diffusing in a harmonic potential generated by an optical trap is kicked by programmed forces with time correlation at random intervals following the Poisson process. The model's generic simplicity allows us to find conditions for which displacements are Gaussian (or not), how diffusion is perturbed (or not) by kicks, and quantifying heat dissipation to maintain the non-equilibrium steady state in an active bath. The model reproduces experimental results of tracer mobility in an active bath of swimming algal cells. It can be used as a stochastic dynamic simulator for Brownian objects in various active baths without mechanistic understanding, owing to the generic framework of the protocol â… .
The time-dependent work probability distribution function P (W ) is investigated analytically for... more The time-dependent work probability distribution function P (W ) is investigated analytically for a diffusing particle trapped by an anisotropic harmonic potential and driven by a nonconservative drift force in two dimensions. We find that the exponential tail shape of P (W ) characterizing rareevent probabilities undergoes a sequence of dynamic transitions in time. These remarkable lockingunlocking type transitions result from an intricate interplay between a rotational mode induced by the nonconservative force and an anisotropic decaying mode due to the conservative attractive force. We expect that most of high-dimensional dynamical systems should exhibit similar multiple dynamic transitions.
Time-integrated quantities such as work and heat increase incessantly in time during nonequilibri... more Time-integrated quantities such as work and heat increase incessantly in time during nonequilibrium processes near steady states. In the long-time limit, the average values of work and heat become asymptotically equivalent to each other, since they only differ by a finite energy change in average. However, the fluctuation theorem (FT) for the heat is found not to hold with the equilibrium initial ensemble, while the FT for the work holds. This reveals an intriguing effect of everlasting initial memory stored in rare events. We revisit the problem of a Brownian particle in a harmonic potential dragged with a constant velocity, which is in contact with a thermal reservoir. The heat and work fluctuations are investigated with initial Boltzmann ensembles at temperatures generally different from the reservoir temperature. We find that, in the infinite-time limit, the FT for the work is fully recovered for arbitrary initial temperatures, while the heat fluctuations significantly deviate from the FT characteristics except for the infinite initial-temperature limit (a uniform initial ensemble). Furthermore, we succeed in calculating finite-time corrections to the heat and work distributions analytically, using the modified saddle point integral method recently developed by us. Interestingly, we find non-commutativity between the infinite-time limit and the infinite-initial-temperature limit for the probability distribution function (PDF) of the heat.
We investigate the properties of the nonequilibrium steady state for the stochastic system driven... more We investigate the properties of the nonequilibrium steady state for the stochastic system driven by a nonlinear drift force and influenced by noises which are not identically and independently distributed. The nonequilibrium steady state (NESS) current results from a residual part of the drift force which is not cancelled by the diffusive action of noises. From our previous study for the linear drift force the NESS current was found to circulate on the equiprobability surface with the maximum at a stable fixed point of the drift force. For the nonlinear drift force, we use the perturbation theory with respect to the cubic and quartic coefficients of the drift force. We find an interesting potential landscape picture where the probability maximum shifts from the fixed point of the drift force and, furthermore, the NESS current has a nontrivial circulation which flows off the equiprobability surface and has various centers not located at the probability maximum. The theoretical result is well confirmed by the computer simulation.
We investigate a motion of a colloid in a harmonic trap driven out of equilibrium by an external ... more We investigate a motion of a colloid in a harmonic trap driven out of equilibrium by an external non-conservative force producing a torque in the presence of a uniform magnetic field. We find that steady state exists only for a proper range of parameters such as mass, viscosity coefficient, and stiffness of the harmonic potential, and the magnetic field, which is not observed in the overdamped limit. We derive the existence condition for the steady state. We examine the combined influence of the non-conservative force and the magnetic field on non-equilibrium characteristics such as non-
Journal of the Korean Physical Society, Mar 1, 2016
We investigate an unconventional nature of the entropy production (EP) in nonequilibrium systems ... more We investigate an unconventional nature of the entropy production (EP) in nonequilibrium systems with odd-parity variables that change signs under time reversal. We consider the Brownian motion of a particle in contact with a heat reservoir, where particle momentum is an odd-parity variable. In the presence of an external momentum-dependent force, the EP transferred to environment is found not equivalent to usual reservoir entropy change due to heat transfer. There appears an additional unconventional contribution to the EP, which is crucial for maintaining the non-negativity of the (average) total EP enforced by the thermodynamic second law. A few examples are considered to elucidate the novel nature of the EP. We also discuss detailed balance conditions with a momentum-dependent force.
We investigate three kinds of heat produced in a system and a bath strongly coupled via an intera... more We investigate three kinds of heat produced in a system and a bath strongly coupled via an interaction Hamiltonian. By studying the energy flows between the system, the bath, and their interaction, we provide rigorous definitions of two types of heat, QS and QB from the energy loss of the system and the energy gain of the bath, respectively. This is in contrast to the equivalence of QS and QB, which is commonly assumed to hold in the weak coupling regime. The bath we consider is equipped with a thermostat which enables it to reach an equilibrium. We identify another kind of heat QSB from the energy dissipation of the bath into the super bath that provides the thermostat. We derive the fluctuation theorems (FT's) with the system variables and various heats, which are discussed in comparison with the FT for the total entropy production. We take an example of a sliding harmonic potential of a single Brownian particle in a fluid and calculate the three heats in a simplified model. These heats are found to equal on average in the steady state of energy, but show different fluctuations at all times.
Conventional wisdom indicates that initial memory should decay away exponentially in time for gen... more Conventional wisdom indicates that initial memory should decay away exponentially in time for general (noncritial) equilibration processes. In particular, time-integrated quantities such as heat are presumed to lose initial memory in a sufficiently long-time limit. However, we show that the large deviation function of time-integrated quantities may exhibit initial memory effect even in the infinite-time limit, if the system is initially prepared sufficiently far away from equilibrium. For a Brownian particle dynamics, as an example, we found a sharp finite threshold rigorously, beyond which the corresponding large deviation function contains everlasting initial memory. The physical origin for this phenomenon is explored with an intuitive argument and also from a toy model analysis.
We investigate the motion of a colloidal particle driven out of equilibrium by an external torque... more We investigate the motion of a colloidal particle driven out of equilibrium by an external torque. We use molecular dynamics simulation as an alternative to the Langevin dynamics. We prepare a heat bath composed of thousands of particles interacting with each other through the Lennard-Jones potential and impose the Langevin thermostat to maintain heat bath in equilibrium. We consider a single colloidal particle to interact with the particles of the heat bath also by the Lennard-Jones potential, without applying any types of dissipative and fluctuating forces used in the Langevin dynamics. We set up simulation protocol fit for the overdamped limit as in real experiments by increasing the size and mass of the colloidal particle. We study nonequilibrium fluctuations for work and heat produced incessantly in time and compare results with those obtained from the previous studies via the overdamped Langevin dynamics. We confirm the Gallavotti-Cohen symmetry and the fluctuation theorem for the work production.
Bulletin of the American Physical Society, Mar 4, 2015
Molecular dynamics study on a nonequilibrium motion of a colloidal particle driven by an external... more Molecular dynamics study on a nonequilibrium motion of a colloidal particle driven by an external torque DONGHWAN YOO, Myongji University, YOUNGKYUN JUNG, KISTI, CHULAN KWON, Myongji University -We investigate the motion of a colloidal particle driven out of equilibrium by an external torque. We use the molecular dynamics simulation that is alternative to the simulation based on the Langevin equation and is expected to mimic an experiment more realistically. We choose a heat bath composed of about a thousand particles interacting to each other through the Lenard-Jones potential and impose the Langevin thermostat to maintain it in equilibrium. We prepare a colloidal particle to interact with the particles of the heat bath also by the Lenard-Jones potential while any dissipative force and noise are not employed explicitly. We study the stochastic properties of the nonequilibrium fluctuation for work and heat produced incessantly in the steady state. We accurately confirm the fluctuation theorem for the work production. We also investigate the motion beyond the overdamped limit by varying the mass of the particle. We compare our result with a previous theoretical result in the overdamped limit based on the Langevin equation 1 .
Statistical inference from data is a foundational task in science. Recently, it has received grow... more Statistical inference from data is a foundational task in science. Recently, it has received growing attention for its central role in inference systems of primary interest in data sciences and machine learning. However, the understanding of statistical inference is not that solid while remains as a matter of subjective belief or as the routine procedures once claimed objective. We here show that there is an objective description of statistical inference for long sequence of exchangeable binary random variables, the prototypal stochasticity in theories and applications. A linear differential equation is derived from the identity known as de Finetti's representation theorem, and it turns out that statistical inference is given by the Green's functions. Our finding is an answer to the normative issue of science that pursues the objectivity based on data, and its significance will be far-reaching in most pure and applied fields.
Bulletin of the American Physical Society, Feb 28, 2012
Initial condition dependence of the probability density function of the injected power in the Lan... more Initial condition dependence of the probability density function of the injected power in the Langevin equation JAE SUNG LEE, Korea Institute for Advanced Study, CHULAN KWON, Department of Physics, Myongji University, HYUNGGYU PARK, School of Physcis, Korea Institute for Advanced Study -We study the diffusive dynamics of a Brownian particle described by the Langevin's equation with time varying heat bath temperature. Initially (when time t < 0) the heat bath temperature is T init and the particle equilibrates with the heat bath. At time t = 0, the temperature abruptly changes from T init to T , where their ratio is denoted by α = T /T init . Then the particle follows the Langevin dynamics with the temperature T for t > 0. Using the path integral method, we compute the probability density function (PDF) of the injection power (injected energy per unit time into the Brownian particle by the random noise, see J. Stat. Phys. 107, 314 (2002)). We find that the PDF or the corresponding large deviation function depends on the initial temperature T init even in the t → ∞ limit. In addition, we show that "phase transition" of the large deviation function occurs at α = 1/4.
Neural Information Processing Systems, Dec 1, 1997
We study the storage capacity of a fully-connected committee machine with a large number K of hid... more We study the storage capacity of a fully-connected committee machine with a large number K of hidden nodes. The storage capacity is obtained by analyzing the geometrical structure of the weight space related to the internal representation . By examining the asymptotic behavior of order parameters in the limit of large K, the storage capacity Q c is found to be proportional to ]{ Jln ]{ up to the leading order. This result satisfies the mathematical bound given by Mitchison and Durbin , whereas the replica-symmetric solution in a conventional Gardner 's approach violates this bound.
Journal of the Korean Physical Society, Sep 1, 2015
A rigorous derivation of nonequilibrium entropy production via the path-integral formalism is pre... more A rigorous derivation of nonequilibrium entropy production via the path-integral formalism is presented. Entropy production is defined as the entropy change piled in a heat reservoir as a result of a nonequilibrium thermodynamic process. It is a central quantity by which various forms of the fluctuation theorem are obtained. The two kinds of the stochastic dynamics are investigated: the Langevin dynamics for an even-parity state and the Brownian motion of a single particle. Mathematical ambiguities in deriving the functional form of the entropy production, which depends on path in state space, are clarified by using a rigorous quantum mechanical approach.
We investigate thermodynamics of feedback processes driven by measurement. Regarding system and m... more We investigate thermodynamics of feedback processes driven by measurement. Regarding system and memory device as a composite system, mutual information as a measure of correlation between the two constituents contributes to the entropy of the composite system, which makes the generalized total entropy of the joint system and reservoir satisfy the second law of thermodynamics. We investigate the thermodynamics of the Szilard engine for an intermediate period before the completion of cycle. We show the second law to hold resolving the paradox of Maxwell's demon independent of the period taken into account. We also investigate a feedback process to confine a particle excessively within a trap, which is operated by repetitions of feedback in a finite time interval. We derive the stability condition for multi-step feedback and find the condition for confinement below thermal fluctuation in the absence of feedback. The results are found to depend on interval between feedback steps and intensity of feedback protocol, which are expected to be important parameters in real experiments.
Journal of Statistical Mechanics: Theory and Experiment, Aug 29, 2006
We investigate the equivalence of different operator-splitting schemes for the integration of the... more We investigate the equivalence of different operator-splitting schemes for the integration of the Langevin equation. We consider a specific problem, so called the directed percolation process, which can be extended to a wider class of problems. We first give a compact mathematical description of the operator-splitting method and introduce two typical splitting schemes that will be useful in numerical studies. We show that the two schemes are essentially equivalent through the map that turns out to be an automorphism. An associated equivalent class of operator-splitting integrations is also defined by generalizing the specified equivalence.
Journal of Statistical Mechanics: Theory and Experiment, Nov 8, 2013
Long-time-integrated quantities in stochastic processes, in or out of equilibrium, usually exhibi... more Long-time-integrated quantities in stochastic processes, in or out of equilibrium, usually exhibit rare but huge fluctuations. Work or heat production is such a quantity, of which the probability distribution function displays an exponential decay characterized by the large deviation function (LDF). The LDF is often deduced from the cumulant generating function through the inverse Fourier transformation. The saddle-point integration method is a powerful technique to obtain the asymptotic results in the Fourier integral, but a special care should be taken when the saddle point is located near a singularity of the integrand. In this paper, we present a modified saddle-point method to handle such a difficulty efficiently. We investigate the dissipated and injected heat production in equilibration processes with various initial conditions, as an example, where the generating functions contain branch-cut singularities as well as power-law ones. Exploiting the new modified saddle-point integrations, we obtain the leading finite-time corrections for the LDF's, which are confirmed by numerical results.
Particles kicked by external forces to produce mobility distinct from thermal diffusion are an ic... more Particles kicked by external forces to produce mobility distinct from thermal diffusion are an iconic feature of the active matter problem. Here, we map this onto a minimal model for experiment and theory covering the wide time and length scales of usual active matter systems. A particle diffusing in a harmonic potential generated by an optical trap is kicked by programmed forces with time correlation at random intervals following the Poisson process. The model's generic simplicity allows us to find conditions for which displacements are Gaussian (or not), how diffusion is perturbed (or not) by kicks, and quantifying heat dissipation to maintain the non-equilibrium steady state in an active bath. The model reproduces experimental results of tracer mobility in an active bath of swimming algal cells. It can be used as a stochastic dynamic simulator for Brownian objects in various active baths without mechanistic understanding, owing to the generic framework of the protocol â… .
The time-dependent work probability distribution function P (W ) is investigated analytically for... more The time-dependent work probability distribution function P (W ) is investigated analytically for a diffusing particle trapped by an anisotropic harmonic potential and driven by a nonconservative drift force in two dimensions. We find that the exponential tail shape of P (W ) characterizing rareevent probabilities undergoes a sequence of dynamic transitions in time. These remarkable lockingunlocking type transitions result from an intricate interplay between a rotational mode induced by the nonconservative force and an anisotropic decaying mode due to the conservative attractive force. We expect that most of high-dimensional dynamical systems should exhibit similar multiple dynamic transitions.
Time-integrated quantities such as work and heat increase incessantly in time during nonequilibri... more Time-integrated quantities such as work and heat increase incessantly in time during nonequilibrium processes near steady states. In the long-time limit, the average values of work and heat become asymptotically equivalent to each other, since they only differ by a finite energy change in average. However, the fluctuation theorem (FT) for the heat is found not to hold with the equilibrium initial ensemble, while the FT for the work holds. This reveals an intriguing effect of everlasting initial memory stored in rare events. We revisit the problem of a Brownian particle in a harmonic potential dragged with a constant velocity, which is in contact with a thermal reservoir. The heat and work fluctuations are investigated with initial Boltzmann ensembles at temperatures generally different from the reservoir temperature. We find that, in the infinite-time limit, the FT for the work is fully recovered for arbitrary initial temperatures, while the heat fluctuations significantly deviate from the FT characteristics except for the infinite initial-temperature limit (a uniform initial ensemble). Furthermore, we succeed in calculating finite-time corrections to the heat and work distributions analytically, using the modified saddle point integral method recently developed by us. Interestingly, we find non-commutativity between the infinite-time limit and the infinite-initial-temperature limit for the probability distribution function (PDF) of the heat.
We investigate the properties of the nonequilibrium steady state for the stochastic system driven... more We investigate the properties of the nonequilibrium steady state for the stochastic system driven by a nonlinear drift force and influenced by noises which are not identically and independently distributed. The nonequilibrium steady state (NESS) current results from a residual part of the drift force which is not cancelled by the diffusive action of noises. From our previous study for the linear drift force the NESS current was found to circulate on the equiprobability surface with the maximum at a stable fixed point of the drift force. For the nonlinear drift force, we use the perturbation theory with respect to the cubic and quartic coefficients of the drift force. We find an interesting potential landscape picture where the probability maximum shifts from the fixed point of the drift force and, furthermore, the NESS current has a nontrivial circulation which flows off the equiprobability surface and has various centers not located at the probability maximum. The theoretical result is well confirmed by the computer simulation.
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Papers by Chulan Kwon