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Register a new userBiochemical Szilard engines for memory-limited inference
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By developing and leveraging an explicit molecular realisation of a measurement-and-feedback-powered Szilard engine, we investigate the extraction of work from complex environments by minimal machines with finite capacity for memory and decision-making. Living systems perform inference to exploit complex structure, or correlations, in their environment, but the physical limits and underlying cost/benefit trade-offs involved in doing so remain unclear. To probe these questions, we consider a minimal model for a structured environment - a correlated sequence of molecules - and explore mechanisms based on extended Szilard engines for extracting the work stored in these non-equilibrium correlations. We consider systems limited to a single bit of memory making binary choices at each step. We demonstrate that increasingly complex environments allow increasingly sophisticated inference strategies to extract more energy than simpler alternatives, and argue that optimal design of such machines should also consider the energy reserves required to ensure robustness against fluctuations due to mistakes.
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We propose a physically-realisable biochemical device that is coupled to a biochemical reservoir of mutual information, fuel molecules and a chemical bath. Mutual information allows work to be done on the bath even when the fuel molecules appear to be in equilibrium; alternatively, mutual information can be created by driving from the fuel or the bath. The system exhibits diverse behaviour, including a regime in which the information, despite increasing during the reaction, enhances the extracted work. We further demonstrate that a modified device can function without the need for external manipulation, eliminating the need for a complex and potentially costly control.
We consider the performance of periodically driven stochastic heat engines in the linear response regime. Reaching the theoretical bounds for efficiency and efficiency at maximum power typically requires full control over the design and the driving of the system. We develop a framework which allows to quantify the role that limited control over the system has on the performance. Specifically, we show that optimizing the driving entering the work extraction for a given temperature protocol leads to a universal, one-parameter dependence for both maximum efficiency and maximum power as a function of efficiency. In particular, we show that reaching Carnot efficiency (and, hence, Curzon-Ahlborn efficiency at maximum power) requires to have control over the amplitude of the full Hamiltonian of the system. Since the kinetic energy cannot be controlled by an external parameter, heat engines based on underdamped dynamics can typically not reach Carnot efficiency. We illustrate our general theory with a paradigmatic case study of a heat engine consisting of an underdamped charged particle in a modulated two-dimensional harmonic trap in the presence of a magnetic field.
Stochastic fluctuations of molecule numbers are ubiquitous in biological systems. Important examples include gene expression and enzymatic processes in living cells. Such systems are typically modelled as chemical reaction networks whose dynamics are governed by the Chemical Master Equation. Despite its simple structure, no analytic solutions to the Chemical Master Equation are known for most systems. Moreover, stochastic simulations are computationally expensive, making systematic analysis and statistical inference a challenging task. Consequently, significant effort has been spent in recent decades on the development of efficient approximation and inference methods. This article gives an introduction to basic modelling concepts as well as an overview of state of the art methods. First, we motivate and introduce deterministic and stochastic methods for modelling chemical networks, and give an overview of simulation and exact solution methods. Next, we discuss several approximation methods, including the chemical Langevin equation, the system size expansion, moment closure approximations, time-scale separation approximations and hybrid methods. We discuss their various properties and review recent advances and remaining challenges for these methods. We present a comparison of several of these methods by means of a numerical case study and highlight some of their respective advantages and disadvantages. Finally, we discuss the problem of inference from experimental data in the Bayesian framework and review recent methods developed the literature. In summary, this review gives a self-contained introduction to modelling, approximations and inference methods for stochastic chemical kinetics.
Brownian heat engines use local temperature gradients in asymmetric potentials to move particles against an external force. The energy efficiency of such machines is generally limited by irreversible heat flow carried by particles that make contact with different heat baths. Here we show that, by using a suitably chosen energy filter, electrons can be transferred reversibly between reservoirs that have different temperatures and electrochemical potentials. We apply this result to propose heat engines based on mesoscopic semiconductor ratchets, which can quasistatically operate arbitrarily close to Carnot efficiency.
We analyse the emergence of Kovacs-like memory effects in athermal systems within the linear response regime. This is done by starting from both the master equation for the probability distribution and the equations for the physically relevant moments. The general results are applied to a general class of models with conserved momentum and non-conserved energy. Our theoretical predictions, obtained within the first Sonine approximation, show an excellent agreement with the numerical results.
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