ABSTRACT
Entropy production characterizes the thermodynamic irreversibility and reflects the amount of heat dissipated into the environment and free energy lost in nonequilibrium systems. According to the thermodynamic uncertainty relation, we propose a deterministic method to estimate the entropy production from a single trajectory of system states. We explicitly and approximately compute an optimal current that yields the tightest lower bound using predetermined basis currents. Notably, the obtained tightest lower bound is intimately related to the multidimensional thermodynamic uncertainty relation. By proving the saturation of the thermodynamic uncertainty relation in the short-time limit, the exact estimate of the entropy production can be obtained for overdamped Langevin systems, irrespective of the underlying dynamics. For Markov jump processes, because the attainability of the thermodynamic uncertainty relation is not theoretically ensured, the proposed method provides the tightest lower bound for the entropy production. When entropy production is the optimal current, a more accurate estimate can be further obtained using the integral fluctuation theorem. We illustrate the proposed method using three systems: a four-state Markov chain, a periodically driven particle, and a multiple bead-spring model. The estimated results in all examples empirically verify the effectiveness and efficiency of the proposed method.
ABSTRACT
The total entropy production quantifies the extent of irreversibility in thermodynamic systems, which is nonnegative for any feasible dynamics. When additional information such as the initial and final states or moments of an observable is available, it is known that tighter lower bounds on the entropy production exist according to the classical speed limits and the thermodynamic uncertainty relations. Here we obtain a universal lower bound on the total entropy production in terms of probability distributions of an observable in the time forward and backward processes. For a particular case, we show that our universal relation reduces to a classical speed limit, imposing a constraint on the speed of the system's evolution in terms of the Hatano-Sasa entropy production. Notably, the obtained classical speed limit is tighter than the previously reported bound by a constant factor. Moreover, we demonstrate that a generalized thermodynamic uncertainty relation can be derived from another particular case of the universal relation. Our uncertainty relation holds for systems with time-reversal symmetry breaking and recovers several existing bounds. Our approach provides a unified perspective on two closely related classes of inequality: classical speed limits and thermodynamic uncertainty relations.
ABSTRACT
The structure of real-world networks is usually difficult to characterize owing to the variation of topological scales, the nondyadic complex interactions, and the fluctuations in the network. We aim to address these problems by introducing a general framework using a method based on topological data analysis. By considering the diffusion process at a single specified timescale in a network, we map the network nodes to a finite set of points that contains the topological information of the network at a single scale. Subsequently, we study the shape of these point sets over variable timescales that provide scale-variant topological information, to understand the varying topological scales and the complex interactions in the network. We conduct experiments on synthetic and real-world data to demonstrate the effectiveness of the proposed framework in identifying network models, classifying real-world networks, and detecting transition points in time-evolving networks. Overall, our study presents a unified analysis that can be applied to more complex network structures, as in the case of multilayer and multiplex networks.
