Instantaneous equilibrium transition for Brownian systems under time-dependent temperature and potential variations: Reversibility, heat and work relations, and fast isentropic process (original) (raw)
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2021
The theory of constructing instantaneous equilibrium (ieq) transition under arbitrary time-dependent temperature and potential variation for a Brownian particle is developed. It is shown that it is essential to consider the underdamped dynamics for temperature-changing transitions. The ieq is maintained by a time-dependent auxiliary position and momentum potential, which can be calculated for given time-dependent transition protocols. Explicit analytic results are derived for the work and heat statistics, energy, and entropy changes for harmonic and non-harmonic trapping potential with arbitrary time-dependent potential parameters and temperature protocols. Numerical solutions of the corresponding Langevin dynamics are computed to confirm the theoretical results. Although ieq transition of the reverse process is not the time-reversal of the ieq transition of the forward process due to the odd-parity of controlling parameters, their phase-space distribution functions restore the time...
Physical Review Research
We consider the instantaneous equilibrium (ieq) transition of an underdamped Brownian particle under arbitrary time-dependent temperature and potential variations and derive analytic results for the temperature and potential protocols for minimal dissipative work. Explicit results for the time-dependent minimal dissipation protocols and the associated energetics are obtained for the cases of pure temperature variation, pure potential parameter (stiffness) variation, and isentropic ieq processes. The minimal dissipation condition enforces the forward and backward protocols to be time-reversal related, with the same minimal dissipative work. Remarkably, it is shown that the minimal dissipation path is also the isentropic ieq transition. The energetics in the mdieq transitions are analyzed in detail with emphasis on the conditions for maximizing the mean work and power that can be extracted. Furthermore, exact results for the overdamped limit are derived, indicating that there is great freedom to choose the minimal dissipation protocols, thus allowing the realization of mdieq transitions in Brownian colloidal systems with relative ease.
The long‐time behavior of reversible binary reactions: Theory, Brownian simulations and experiment
Many-body effects' on reversible pseudo-unimolecular reactions are investigated using a" combination of theory, simulation, and experiment. Theoretically, we rederive the superposition approximation starting from the fundamental N-particle equations. All the relations obtained are actually rigorous, except for a requirement that the concentration profile outside a vacant trap obeys a diffusion equation. Our derivation also yields a new numerical procedure for evaluating the superposition solution. Brownian dynamics simulations of one-dimensional competitive binding are presented over an unprecedented time regime. Comparison with the superposition approximation shows that this mean-field theory is exact at infinite dilution, but breaks down at high particle concentration. The main discrepancy is not at asymptotically long times as previously suspected, but rather at intermediate times, where a neW power law-phase emerges. This is reflected in a maximum in the logarithmic derivative of the survival probability, which is more pronounced in our simulation as compared with the approximate theory. Finally, we show that the transient fluorescence data from an excited dye molecule which transfers a proton reversibly to water, develops a similar maximum in its logarithmic derivative at low pH values.
Non-equilibrium thermodynamics and fluctuations
Physica A: Statistical Mechanics and its Applications, 2004
In the last ten years, a number of "Conventional Fluctuation Theorems" have been derived for systems with deterministic or stochastic dynamics, in a transient or in a non-equilibrium stationary state. These theorems gave explicit expressions for the ratio of the probability to find the system with a certain value of entropy (or heat) production to that of finding the opposite value. A similar theorem for the fluctuations of the work done on a system has recently been demonstrated experimentally for a simple system in a transient state, consisting of a Brownian particle in water, confined by a moving harmonic potential. In this paper we show that because of the interaction between the stochastic motion of the particle in water and its deterministic motion in the potential, very different new heat theorems are found than in the conventional case. One of the consequences of these new heat Fluctuation Theorems is that the ratio of the probability for the Brownian particle to absorb heat from rather than supply heat to the water is much larger than in the Conventional Fluctuation Theorems. This could be of relevance for micro/nanotechnology.
Adiabatic processes realized with a trapped brownian particle
Physical review letters, 2015
The ability to implement adiabatic processes in the mesoscale is of key importance in the study of artificial or biological micro- and nanoengines. Microadiabatic processes have been elusive to experimental implementation due to the difficulty in isolating Brownian particles from their fluctuating environment. Here we report on the experimental realization of a microscopic quasistatic adiabatic process employing a trapped Brownian particle. We circumvent the complete isolation of the Brownian particle by designing a protocol where both characteristic volume and temperature of the system are changed in such a way that the entropy of the system is conserved along the process. We compare the protocols that follow from either the overdamped or underdamped descriptions, demonstrating that the latter is mandatory in order to obtain a vanishing average heat flux to the particle. We provide analytical expressions for the distributions of the fluctuating heat and entropy and verify them expe...
Physical Review E, 2007
We analyze the equations governing the evolution of distributions of the work and the heat exchanged with the environment by a manipulated stochastic system, by means of a compact and general derivation. We obtain explicit solutions for these equations for the case of a dragged Brownian particle in a harmonic potential. We successfully compare the resulting predictions with the outcomes of experiments, consisting in dragging a micron-sized colloidal particle through water with a laser trap. PACS numbers: 05.40.-a, 05.70.Ln
We explore the noise-induced barrier crossing dynamics of a Brownian particle in the high temperature quantum regime under large damping. We assume the associated heat bath not to be in thermal equilibrium; it is rather driven by an externally applied random force which exposes the system particles to a nonequilibrium environment. We propose a system + reservoir model to study the stochastic Langevin dynamics. We also construct the corresponding Fokker-Planck equation in the said regime and solve it to explore the bistable kinetics. We investigate the role of different parameters in shaping the nature of such a bistable kinetics in detail and hence allowing one to get some insight into the very complicated dynamics of quantum dissipative system(s). Finally, we analyze the semiclassical rate vis-à-vis the classical analog.
Physical Review E, 2009
A recent theoretical model developed by Imparato et al. ͓Phys. Rev. E 76, 050101͑R͒ ͑2007͔͒ of the experimentally measured heat and work effects produced by the thermal fluctuations of single micron-sized polystyrene beads in stationary and moving optical traps has proved to be quite successful in rationalizing the observed experimental data. The model, based on the overdamped Brownian dynamics of a particle in a harmonic potential that moves at a constant speed under a time-dependent force, is used to obtain an approximate expression for the distribution of the heat dissipated by the particle at long times. In this paper, we generalize the above model to consider particle dynamics in the presence of colored noise, without passing to the overdamped limit, as a way of modeling experimental situations in which the fluctuations of the medium exhibit long-lived temporal correlations, of the kind characteristic of polymeric solutions, for instance, or of similar viscoelastic fluids. Although we have not been able to find an expression for the heat distribution itself, we do obtain exact expressions for its mean and variance, both for the static and for the moving trap cases. These moments are valid for arbitrary times and they also hold in the inertial regime, but they reduce exactly to the results of Imparato et al. in appropriate limits.
2006
The translational Brownian motion in a (2-4) double-well potential is considered. The escape rate, the position correlation function and correlation time, and the generalized susceptibility are evaluated from the solution of the underlying Langevin equation by using the matrix continued fraction method. The escape rate and the correlation time are compared with the Kramers theory of the escape rate of a Brownian particle from a potential well as extended by Mel'nikov and Meshkov [J. Chem. Phys. 85, 1018 (1986)]. It is shown that in the low temperature limit, the universal Mel'nikov and Meshkov expression for the escape rate provides a good estimate of both escape rate and inverse position correlation time for all values of the dissipation including the very low damping (VLD), very high damping (VHD), and turnover regimes. Moreover, for low barriers, where the Mel'nikov and Meshkov method is not applicable, analytic equations for the correlation time in the VLD and VHD limits are derived.