Linear irreversible thermodynamics and Onsager reciprocity for information-driven engines

Efficiency at Maximum Power of a Carnot Quantum Information Engine

Optimizing the performance of thermal machines is an essential task of thermodynamics. We here consider the optimization of information engines that convert information about the state of a system into work. We concretely introduce a generalized finite-time Carnot cycle for a quantum information engine and optimize its power output in the regime of low dissipation. We derive a general formula for its efficiency at maximum power valid for arbitrary working media. We further investigate the optimal performance of a qubit information engine subjected to weak energy measurements.

General linear thermodynamics for periodically driven systems with multiple reservoirs

We derive a linear thermodynamics theory for general Markov dynamics with both steady-state and time-periodic drivings. Expressions for thermodynamic quantities, such as chemical work, heat, and entropy production are obtained in terms of equilibrium probability distribution and the drivings. The entropy production is derived as a bilinear function of thermodynamic forces and the associated fluxes. We derive explicit formulae for the Onsager coefficients and use them to verify the Onsager-Casimir reciprocal relations. Our results are illustrated on a periodically driven quantum dot in contact with two electron reservoirs and optimization protocols are discussed.

Stochastic Thermodynamic Interpretation of Information Geometry

In recent years, the unified theory of information and thermodynamics has been intensively discussed in the context of stochastic thermodynamics. The unified theory reveals that information theory would be useful to understand nonstationary dynamics of systems far from equilibrium. In this Letter, we have found a new link between stochastic thermodynamics and information theory well-known as information geometry. By applying this link, an information geometric inequality can be interpreted as a thermodynamic uncertainty relationship between speed and thermodynamic cost. We have numerically applied an information geometric inequality to a thermodynamic model of a biochemical enzyme reaction.

Role of sufficient statistics in stochastic thermodynamics and its implication to sensory adaptation

A sufficient statistic is a significant concept in statistics, which means a probability variable that has sufficient information required for an inference task. We investigate the roles of sufficient statistics and related quantities in stochastic thermodynamics. Specifically, we prove that for general continuous-time bipartite networks, the existence of a sufficient statistic implies that an informational quantity called the sensory capacity takes the maximum. Since the maximal sensory capacity imposes a constraint that the energetic efficiency cannot exceed one-half, our result implies that the existence of a sufficient statistic is inevitably accompanied by energetic dissipation. We also show that, in a particular parameter region of linear Langevin systems there exists the optimal noise intensity at which the sensory capacity, the information-thermodynamic efficiency, and the total entropy production are optimized at the same time. We apply our general result to a model of sensory adaptation of E. coli and find that the sensory capacity is nearly maximal with experimentally realistic parameters.

The underdamped Brownian duet and stochastic linear irreversible thermodynamics

Building on our earlier work [Proesmans et al., Phys. Rev. X 6, 041010 (2016)], we introduce the underdamped Brownian duet as a prototype model of a dissipative system or of a work-to-work engine. Several recent advances from the theory of stochastic thermodynamics are illustrated with explicit analytic calculations and corresponding Langevin simulations. In particular, we discuss the Onsager-Casimir symmetry, the trade-off relations between power, efficiency and dissipation, and stochastic efficiency.

Stationary engines in and beyond the linear response regime at the Carnot efficiency

The condition for stationary engines to attain the Carnot efficiency in and beyond the linear response regime is investigated. We find that this condition for finite-size engines is significantly different from that for macroscopic engines in the thermodynamic limit. For the case of finite-size engines, the tight-coupling condition in the linear response regime directly implies the attainability of the Carnot efficiency beyond the linear response regime. As opposed to this, for the case of macroscopic engines in the thermodynamic limit, there are three types of mechanisms to attain the Carnot efficiency. One mechanism allows engines to attain the Carnot efficiency only in the linear response limit, while the other two mechanisms enable engines to attain the Carnot efficiency beyond the linear response regime. These three mechanisms are classified by introducing a tight-coupling window.

Backward transfer entropy: Informational measure for detecting hidden Markov models and its interpretations in thermodynamics, gambling and causality

The transfer entropy is a well-established measure of information flow, which quantifies directed influence between two stochastic time series and has been shown to be useful in a variety fields of science. Here we introduce the transfer entropy of the backward time series called the backward transfer entropy, and show that the backward transfer entropy quantifies how far it is from dynamics to a hidden Markov model. Furthermore, we discuss physical interpretations of the backward transfer entropy in completely different settings of thermodynamics for information processing and the gambling with side information. In both settings of thermodynamics and the gambling, the backward transfer entropy characterizes a possible loss of some benefit, where the conventional transfer entropy characterizes a possible benefit. Our result implies the deep connection between thermodynamics and the gambling in the presence of information flow, and that the backward transfer entropy would be useful as a novel measure of information flow in nonequilibrium thermodynamics, biochemical sciences, economics and statistics.