Inferring Entropy Production from Short Experiments

Manikandan, Sreekanth K; Gupta, Deepak; Krishnamurthy, Supriya

doi:10.1103/physrevlett.124.120603

Cited by 137 publications

(99 citation statements)

References 56 publications

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“…(38), (42) as well as (45) to determine the leading orders of the scaled mean values, eqs. ( 30)- (33), their response terms, their corresponding diffusion coefficients, eqs. (A.1)-(A.4), as well as the scaled total entropy production rate (35).…”

Section: Fast Drivingmentioning

confidence: 99%

“…( 50) for fast driving reduces to the result for steady-states in refs. [32,33] in the limit of short observation times. As a consequence, we have generalized this result to arbitrary time-dependent driving and shown that the total entropy production rate can always saturate the TUR in the short-time limit beyond steady-states for arbitrary driving.…”

Section: Observablementioning

confidence: 99%

See 1 more Smart Citation

Thermodynamic Uncertainty Relation for Time-Dependent Driving

2020

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The thermodynamic uncertainty relation originally proven for systems driven into a non-equilibrium steady state (NESS) allows one to infer the total entropy production rate by observing any current in the system. This kind of inference scheme is especially useful when the system contains hidden degrees of freedom or hidden discrete states, which are not accessible to the experimentalist. A recent generalization of the thermodynamic uncertainty relation to arbitrary time-dependent driving allows one to infer entropy production not only by measuring current-observables but also by observing state variables. A crucial question then is to understand which observable yields the best estimate for the total entropy production. In this paper we address this question by analyzing the quality of the thermodynamic uncertainty relation for various types of observables for the generic limiting cases of fast driving and slow driving. We show that in both cases observables can be found that yield an estimate of order one for the total entropy production. We further show that the uncertainty relation can even be saturated in the limit of fast driving.

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Section: Fast Drivingmentioning

confidence: 99%

Section: Observablementioning

confidence: 99%

Thermodynamic Uncertainty Relation for Time-Dependent Driving

2020

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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 [15][16][17][18] . This is not the case however for the vast majority of systems, such as biological systems [19][20][21] , and consequently, there has been a lot of interest in developing new methods for estimating the entropy production rate directly from trajectory data [22][23][24][25][26][27][28][29][30][31][32][33] . Some of these techniques involve the estimation of the probability distribution and currents over the phase-space 22,26 , which requires huge amounts of data.…”

mentioning

confidence: 99%

“…An alternative strategy is to set lower bounds on the entropy production rate [34][35][36][37][38] by measuring experimentally accessible quantities. One class of these bounds, for example, those based on the thermodynamic uncertainty relation (TUR) [38][39][40][41][42] , have been further developed into variational inference schemes which translate the task of identifying entropy production to an optimization problem over the space of a single projected fluctuating current in the system [26][27][28][29] . Recently a similar variational scheme using neural networks was also proposed 30 .…”

mentioning

confidence: 99%

Estimating time-dependent entropy production from non-equilibrium trajectories

et al. 2022

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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 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 in experimentally relevant parameter regimes. Our method only requires time-series data for the system of interest without any prior knowledge of the system’s parameters.

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“…In the absence of currents, potential asymmetries in the forward and reverse trajectories can still be exploited to bound the entropy production rate (29,30,50), but to our knowledge no existing method is capable of producing nonzero bounds when forward and reverse trajectories are statistically identical. Moreover, even though previous bounds can become tight in some cases (51), optimal entropy production estimators for nonequilibrium systems are in general unknown.…”

mentioning

confidence: 99%

Improved bounds on entropy production in living systems

Skinner

Dunkel

2021

Proc. Natl. Acad. Sci. U.S.A.

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Living systems maintain or increase local order by working against the second law of thermodynamics. Thermodynamic consistency is restored as they consume free energy, thereby increasing the net entropy of their environment. Recently introduced estimators for the entropy production rate have provided major insights into the efficiency of important cellular processes. In experiments, however, many degrees of freedom typically remain hidden to the observer, and, in these cases, existing methods are not optimal. Here, by reformulating the problem within an optimization framework, we are able to infer improved bounds on the rate of entropy production from partial measurements of biological systems. Our approach yields provably optimal estimates given certain measurable transition statistics. In contrast to prevailing methods, the improved estimator reveals nonzero entropy production rates even when nonequilibrium processes appear time symmetric and therefore may pretend to obey detailed balance. We demonstrate the broad applicability of this framework by providing improved bounds on the energy consumption rates in a diverse range of biological systems including bacterial flagella motors, growing microtubules, and calcium oscillations within human embryonic kidney cells.

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Inferring Entropy Production from Short Experiments

Cited by 137 publications

References 56 publications

Thermodynamic Uncertainty Relation for Time-Dependent Driving

Thermodynamic Uncertainty Relation for Time-Dependent Driving

Estimating time-dependent entropy production from non-equilibrium trajectories

Improved bounds on entropy production in living systems

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