Learning the Non-Equilibrium Dynamics of Brownian Movies

Gnesotto, F. S.; Gradziuk, G.; Ronceray, P.; Broedersz, C. P.

doi:10.48550/arxiv.2001.08642

Cited by 4 publications

(8 citation statements)

References 53 publications

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“…(3a) and obtain σ by determining the current and steady-state probability density directly from the timeseries data [6,10]. Another approach is to first infer the terms in the Langvein equation, F µ and D [11,14] and use Eq. (3a) to obtain σ.…”

Section: Modelmentioning

confidence: 99%

“…(3a) to obtain σ. These methods can be applied directly on data obtained from tracking the system or by even using tracking-free methods in image space [11]. Note however that all these methods require the measurement or empirical estimation of the steady-state probability distribution P , its spatial derivatives and current J µ .…”

Section: Modelmentioning

confidence: 99%

“…Not surprisingly, this question has aroused a lot of recent interest. Broadly speaking, measurements from experiments can be used to obtain general information about the system, such as identifying that detailed balance is broken and hence the system is out-of-equilibrium [2][3][4] (not always obvious for microscopic systems such as at the cellular level), or to obtain more specific properties of the system such as the rate of dissipation of energy (equivalently the rate of entropy production) [5][6][7][8][9][10][11][12], the average phase-space velocity field [2,13,14] related to the so-called thermodynamic force field [15,16] or the microscopic forces driving the system [14,17]. The motivation for such studies is that if quantitative information about the system can be directly obtained from experimentally observed quantities, then this understanding can be used for building more realistic and experimentally validated models of the system of interest [2,18,19].…”

mentioning

confidence: 99%

“…These include utilizing the Harada-Sasa equality [5] which involves a spectral analysis of trajectory data [30,31], determining the average steady state current and steady-state probability distribution from the data [6], determining the time-irreversibility of the dynamics [22,[32][33][34][35][36] and relatedly determining estimators for the ratio of forward and backward processes directly from the data [9,37,38]. Very recent approaches [11,14] also advocate inferring first the microscopic force field from which the entropy production rate can be inferred.…”

mentioning

confidence: 99%

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Quantitative analysis of non-equilibrium systems from short-time experimental data

Manikandan,

Ghosh,

Kundu

et al. 2021

Preprint

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We provide a minimal strategy for the quantitative analysis of a large class of non-equilibrium systems in a steady state using the short-time Thermodynamic Uncertainty Relation (TUR). From short-time trajectory data obtained from experiments, we demonstrate how we can simultaneously infer quantitatively, both the thermodynamic force field acting on the system, as well as the exact rate of entropy production. We benchmark this scheme first for an experimental study of a colloidal particle system where exact analytical results are known, before applying it to the case of a colloidal particle in a hydrodynamical flow field, where neither analytical nor numerical results are available. Our scheme hence provides a means, potentially exact for a large class of systems, to get a quantitative estimate of the entropy produced in maintaining a non-equilibrium system in a steady state, directly from experimental data.

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Section: Modelmentioning

confidence: 99%

Section: Modelmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Quantitative analysis of non-equilibrium systems from short-time experimental data

Manikandan,

Ghosh,

Kundu

et al. 2021

Preprint

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“…The entropy production rate can be directly obtained from the system's phase-space trajectory if the underlying dynamical equations of the system are known [14][15][16][17]. This is not the case however for the vast majority of systems, such as biological systems [18][19][20], and consequently, there has been a lot of interest in developing new methods for estimating the entropy production rate directly from trajectory data [1,[21][22][23][24][25][26][27][28][29][30]. Some of these techniques involve the estimation of the probability distribution and currents over the phase-space [21,25], which requires huge amounts of data.…”

Section: Introductionmentioning

confidence: 99%

Estimating time-dependent entropy production from non-equilibrium trajectories

Otsubo,

Manikandan,

Sagawa

et al. 2020

Preprint

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The rate of entropy production provides a useful quantitative measure of a non-equilibrium system and estimating it directly from time-series data from experiments is highly desirable. Several approaches have been considered for stationary dynamics, some of which are based on a variational characterization of the entropy production rate. However the issue of obtaining it in the case of non-stationary dynamics remains largely unexplored. Here, we solve this open problem by demonstrating that the variational approaches can be generalized to give the exact value of the entropy production rate even for arbitrary non-equilibrium non-stationary dynamics. On the basis of this result, we develop an efficient algorithm that estimates the entropy production rate continuously in time by using machine learning techniques, and validate our numerical estimates using analytically tractable Langevin models. Our method is of great practical significance since all it requires is time-series data for the system of interest, under arbitrary non-equilibrium conditions.

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Learning entropy production via neural networks

Kim,

Bae,

Lee

et al. 2020

Preprint

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This Letter presents a neural estimator for entropy production, or NEEP, that estimates entropy production (EP) from trajectories without any prior knowledge of the system. For steady state, we rigorously prove that the estimator, which can be built up from different choices of deep neural networks, provides stochastic EP by optimizing the objective function proposed here. We verify the NEEP with the stochastic processes of the bead-spring and discrete flashing ratchet models, and also demonstrate that our method is applicable to high-dimensional data and non-Markovian systems.Nonequilibrium states are ubiquitously observed from colloidal particles to biological systems [1][2][3][4][5][6]. Injection of energy, lack of relaxation time, or broken detailed balance are ordinary sources of nonequilibrium, and in general, such systems are in contact with a heat bath such as a fluid. Thus, to describe the behavior of a nonequilibrium system, it is necessary to investigate the energetics of the system; however, experimentally, heat flow is difficult to measure directly [7][8][9][10]. In this case, measuring the entropy production (EP) can be one remedy to estimate heat flow in a nonequilibrium system [10][11][12].

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Learning the Non-Equilibrium Dynamics of Brownian Movies

Cited by 4 publications

References 53 publications

Quantitative analysis of non-equilibrium systems from short-time experimental data

Quantitative analysis of non-equilibrium systems from short-time experimental data

Estimating time-dependent entropy production from non-equilibrium trajectories

Learning entropy production via neural networks

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