The learning rate is an information-theoretical quantity for bipartite Markov chains describing two coupled subsystems. It is defined as the rate at which transitions in the downstream subsystem tend to increase the mutual information between the two subsystems, and is bounded by the dissipation arising from these transitions. Its physical interpretation, however, is unclear, although it has been used as a metric for the sensing performance of the downstream subsystem. In this paper, we explore the behaviour of the learning rate for a number of simple model systems, establishing when and how its behaviour is distinct from the instantaneous mutual information between subsystems. In the simplest case, the two are almost equivalent. In more complex steady-state systems, the mutual information and the learning rate behave qualitatively distinctly, with the learning rate clearly now reflecting the rate at which the downstream system must update its information in response to changes in the upstream system. It is not clear whether this quantity is the most natural measure for sensor performance, and, indeed, we provide an example in which optimising the learning rate over a region of parameter space of the downstream system yields an apparently sub-optimal sensor. arXiv:1702.06041v2 [cond-mat.stat-mech]

By designing and leveraging an explicit molecular realisation of a measurement-and-feedbackpowered 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 moleculesand 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 free energy than simpler alternatives, and argue that optimal design of such machines should also consider the free energy reserves required to ensure robustness against fluctuations due to mistakes. perform work [3,4]. A more subtle and equally fundamental possibility is exploiting structure across multiple bits in the array-its entropy can be low due to correlations within the data, rather than an overall bias at the level of individual bits [5][6][7][8][9]. However, the principles of designing devices to optimally exploit correlations in general settings remain unclear [9].Although inspired by the physics of computation, the question of how to exploit correlations is also of fundamental biological relevance. If organisms existed in a homogeneous non-equilibrium environment, there would be no need to develop sophisticated information-processing machinery to survive. However, from the chemotaxis system of E. coli to the brains of humans, complex molecular and cellular networks have been evolved to exploit the fact that the environment exhibits correlated fluctuations. These systems rely on the fact that what is sensed at a certain point in space and time contains information about nearby points [8]: they have evolved even though they are costly to maintain, and despite the fact that the information obtained is limited by features such as the memory and processing power available [11]. However, the fundamental trade-offs that determine the sophistication of these systems are not fully explored.In this paper we take steps towards unifying these two perspectives on the exploitation of correlations. We first present a molecular design for a measurement-and-feedback device (a Szilard engine [12]) in which the mechanics of the feedback is explicit within the molecular system. We then leverage this construct to propose biomolecular machines that make repeated binary choices about how to act based on measurements of their environment (an array of 'molecular bits'). These machines use their single bit of memory to extract chemical work from correlated arrays, demonstrating that it is possible to design minimal biophysical sy...

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