Optically confined colloidal particles, when placed in close proximity, form a dissipatively coupled system through hydrodynamic interactions. The role of such interactions influencing irreversibility and energy dissipation in out-of-equilibrium systems is often not well deciphered. Here, we demonstrate—through the estimation of the entropy production rate—that the nonequilibrium features of the system with such interactions vary depending on the nature of external driving, and importantly, on the level of coarse graining. Crucially, we show that coarse graining reverses the dependence of the measured entropy production rate on the strength of the hydrodynamic interactions. Furthermore, we clarify that such interactions do not violate energy balance at the level of individual trajectories, as was believed earlier. Our results highlight a previously unnoticed effect of coarse graining in nonequilibrium systems, and have implications for the inference of entropy production in experimental contexts.

Recent experiments have implemented resetting by means of a time-varying external harmonic trap, whereby the trap stiffness is changed in finite-time and the system is reset when it relaxes to an equilibrium distribution in the final trap. Such setups are very similar to those studied in the context of the finite-time Landauer erasure principle. In this work, we analyze the thermodynamic costs of such a setup by deriving a moment generating function for the work cost of recurrently changing the trap stiffness, thereby maintaining a non-equilibrium steady state. For this heretofore unstudied case, we obtain explicit expressions for the mean and variance of the work both for a specific experimentally viable protocol as well as an optimal protocol which minimizes the mean cost. For both these procedures, our analysis captures both the large-time and short-time corrections. For the optimal protocol, we obtain a closed form expression for the mean cost for all protocol durations, thereby making contact with earlier work on geometric measures of dissipation-minimizing optimal protocols that implement information erasure.

Recent experiments have implemented resetting by means of an external trap, whereby a system relaxes to the minimum of the trap and is reset in a finite time. In this work, we set up and analyze the thermodynamics of such a protocol. We present a general framework, valid even for non-Poissonian resetting, that captures the thermodynamic work required to maintain a resetting process up to a given observation time, and exactly calculate the moment generating function of this work. Our framework is valid for a wide range of systems, the only assumption being relaxation to equilibrium in the resetting trap. Examples and extensions are considered. In the case of Brownian motion, we investigate optimal resetting schemes that minimize work and its fluctuations, the mean work for arbitrary switching protocols, and comparisons to previously studied resetting schemes. Numerical simulations are performed to validate our findings.

Stochastic systems that undergo random restarts to their initial state have been widely investigated in recent years, both theoretically and in experiments. Oftentimes, however, resetting to a fixed state is impossible due to thermal noise or other limitations. As a result, the system configuration after a resetting event is random. Here, we consider such a resetting protocol for an overdamped Brownian particle in a confining potential V (x). We assume that the position of the particle is reset at a constant rate to a random location x, drawn from a distribution pR(x). To investigate the thermodynamic cost of resetting, we study the stochastic entropy production STotal. We derive a general expression for the average entropy production for any V(x), and the full distribution P(STotal|t) of the entropy production for V(x) = 0. At late times, we show that this distribution assumes the large-deviation form P(STotal|t) <^> exp{-t2 alpha-1 phi [(STotal - (STotal )/t alpha]}, with 1/2 < alpha 1. We compute the rate function phi(z) and the exponent alpha for exponential and Gaussian resetting distributions pR(x). In the latter case, we find the anomalous exponent alpha = 2/3 and show that phi(z) has a first-order singularity at a critical value of z, corresponding to a real-space condensation transition.

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.

Measurements of any property of a microscopic system are bound to show significant deviations from the average, due to thermal fluctuations. For time-integrated currents such as heat, work, or entropy production in a steady state, it is in fact known that there will be long stretches of fluctuations both above as well as below the average, occurring equally likely at large times. In this paper we demonstrate that for any finite-time measurement in a nonequilibrium steady state—rather counterintuitively—fluctuations below the average are more probable. This discrepancy is found to be higher when the system is further away from equilibrium. For overdamped diffusive processes, there is even an optimal time when time-integrated current fluctuations mostly lie below the average. We demonstrate that these effects are consistent with a nonmonotonic skewness of current fluctuations and provide evidence that they are easily observable in experiments. We also discuss their extensions to discrete space Markov jump processes and implications to biological and synthetic microscopic engines.

Trajectory-based methods are well-developed to approximate steady-state probability distributions for stochastic processes in large-system limits. The trajectories are solutions to equations of motion of Hamiltonian dynamical systems, and are known as eikonals. They also express the leading flow lines along which probability currents balance. The existing eikonal methods for discrete-state processes including chemical reaction networks are based on the Liouville operator that evolves generating functions of the underlying probability distribution. We have previously derived [1, 2] a representation for the generators of such processes that acts directly on the hierarchy of moments of the distribution, rather than on the distribution itself or on its generating function. We show here how in the large-system limit the steady-state condition for that generator reduces to a mapping from eikonals to the ratios of neighboring factorial moments, as a function of the order k of these moments. The construction shows that the boundary values for the moment hierarchy, and thus its whole solution, are anchored in the interior fixed points of the Hamiltonian system, a result familiar from Freidlin-Wenztell theory. The direct derivation of eikonals from the moment representation further illustrates the relation between coherent-state and number fields in Doi-Peliti theory, clarifying the role of canonical transformations in that theory.

Estimating entropy production directly from experimental trajectories is of great current interest but often requires a large amount of data or knowledge of the underlying dynamics. In this paper, we propose a minimal strategy using the short-time Thermodynamic Uncertainty Relation (TUR) by means of which we can simultaneously and quantitatively infer the thermodynamic force field acting on the system and the (potentially exact) rate of entropy production from experimental short-time trajectory data. We benchmark this scheme first for an experimental study of a colloidal particle system where exact analytical results are known, prior to studying the case of a colloidal particle in a hydrodynamical flow field, where neither analytical nor numerical results are available. In the latter case, we build an effective model of the system based on our results. In both cases, we also demonstrate that our results match with those obtained from another recently introduced scheme.

We provide a strategy for the exact inference of the average as well as the fluctuations of the entropy production in nonequilibrium systems in the steady state, from the measurements of arbitrary current fluctuations. Our results are built upon the finite-time generalization of the thermodynamic uncertainty relation, and require only very short time series data from experiments. We illustrate our results with exact and numerical solutions for two colloidal heat engines.

Nanoscale machines are strongly influenced by thermal fluctuations, contrary to their macroscopic counterparts. As a consequence, even the efficiency of such microscopic machines becomes a fluctuating random variable. Using geometric properties and the fluctuation theorem for the total entropy production, a universal theory of efficiency fluctuations at long times, for machines with a finite state space, was developed by Verley et al. [Nat. Commun. 5, 4721 (2014); Phys. Rev. E 90, 052145 (2014)]. We extend this theory to machines with an arbitrary state space. Thereby, we work out more detailed prerequisites for the universal features and explain under which circumstances deviations can occur. We also illustrate our findings with exact results for two nontrivial models of colloidal engines.