Maximal power output of a stochastic thermodynamic engine

Classical thermodynamics aimed to quantify the efficiency of thermodynamic engines, by bounding the maximal amount of mechanical energy produced, compared to the amount of heat required. While this was accomplished early on, by Carnot and Clausius, the more practical problem to quantify limits of power that can be delivered, remained elusive due to the fact that quasistatic processes require infinitely slow cycling, resulting in a vanishing power output. Recent insights, drawn from stochastic models, appear to bridge the gap between theory and practice in that they lead to physically meaningful expressions for the dissipation cost in operating a thermodynamic engine over a finite time window. Indeed, the problem to optimize power can be expressed as a stochastic control problem. Building on this framework of stochastic thermodynamics we derive bounds on the maximal power that can be drawn by cycling an overdamped ensemble of particles via a time-varying potential while alternating contact with heat baths of different temperature (Tc cold, and Th hot). Specifically, assuming a suitable bound M on the spatial gradient of the controlling potential, we show that the maximal achievable power is bounded by [Formula presented]. Moreover, we show that this bound can be reached to within a factor of [Formula presented] by operating the cyclic thermodynamic process with a quadratic potential

Ioannis Y. Georgiou

Hydrodynamics and sediment transport in estuaries, lakes, and rivers (deltas), often along the connection of these systems to the coastal ocean. How natural and anthropogenic change affects estuarine gradients and resulting exchange with the coastal ocean, and the transport of sediment across the coastal environment. Beach and barrier island sediment transport using field observations and numerical modeling

An Extended CMOS ISFET Model Incorporating the Physical Design Geometry and the Effects on Performance and Offset Variation

This paper presents an extended model for the CMOS-based ion-sensitive field-effect transistor, incorporating design parameters associated with the physical geometry of the device. This can, for the first time, provide a good match between calculated and measured characteristics by taking into account the effects of nonidealities such as threshold voltage variation and sensor noise. The model is evaluated through a number of devices with varying design parameters (chemical sensing area and MOSFET dimensions) fabricated in a commercially available 0.35-µm CMOS technology. Threshold voltage, subthreshold slope, chemical sensitivity, drift, and noise were measured and compared with the simulated results. The first- and second-order effects are analyzed in detail, and it is shown that the sensors' performance was in agreement with the proposed model

Stochastic control liaisons: Richard Sinkhorn meets gaspard monge on a schr\uf6dinger bridge

In 1931-1932, Erwin Schr\uf6dinger studied a hot gas Gedankenexperiment (an instance of large deviations of the empirical distribution). Schr\uf6dinger's problem represents an early example of a fundamental inference method, the so-called maximum entropy method, having roots in Boltzmann's work and being developed in subsequent years by Jaynes, Burg, Dempster, and Csisz\ue1r. The problem, known as the Schr\uf6dinger bridge problem (SBP) with "uniform"prior, was more recently recognized as a regularization of the Monge-Kantorovich optimal mass transport (OMT) problem, leading to effective computational schemes for the latter. Specifically, OMT with quadratic cost may be viewed as a zerotemperature limit of the problem posed by Schr\uf6dinger in the early 1930s. The latter amounts to minimization of Helmholtz's free energy over probability distributions that are constrained to possess two given marginals. The problem features a delicate compromise, mediated by a temperature parameter, between minimizing the internal energy and maximizing the entropy. These concepts are central to a rapidly expanding area of modern science dealing with the so-called Sinkhorn algorithm, which appears as a special case of an algorithm first studied in the more challenging continuous space setting by the French analyst Robert Fortet in 1938-1940 specifically for Schr\uf6dinger bridges. Due to the constraint on end-point distributions, dynamic programming is not a suitable tool to attack these problems. Instead, Fortet's iterative algorithm and its discrete counterpart, the Sinkhorn iteration, permit computation of the optimal solution by iteratively solving the so-called Schr\uf6dinger system. Convergence of the iteration is guaranteed by contraction along the steps in suitable metrics, such as Hilbert's projective metric. In both the continuous as well as the discrete time and space settings, stochastic control provides a reformulation of and a context for the dynamic versions of general Schr\uf6dinger bridge problems and of their zero-temperature limit, the OMT problem. These problems, in turn, naturally lead to steering problems for flows of one-time marginals which represent a new paradigm for controlling uncertainty. The zero-temperature problem in the continuous-time and space setting turns out to be the celebrated Benamou-Brenier characterization of the McCann displacement interpolation flow in OMT. The formalism and techniques behind these control problems on flows of probability distributions have attracted significant attention in recent years as they lead to a variety of new applications in spacecraft guidance, control of robot or biological swarms, sensing, active cooling, and network routing as well as in computer and data science. This multifaceted and versatile framework, intertwining SBP and OMT, provides the substrate for the historical and technical overview of the field given in this paper. A key motivation has been to highlight links between the classical early work in both topics and the more recent stochastic control viewpoint, which naturally lends itself to efficient computational schemes and interesting generalizations

SpaceMan: Wireless SoC for concurrent potentiometry and amperometry

This work describes the implementation of SPACEMan, a wireless electrochemical system with concurrent potentiometric and amperometric sensing that can be utilised for saliva, sweat or point of care diagnostics. This system is designed with the vision of simpler interfaces for biofluid analysis. With a complete system-on-chip including electrochemical sensing, power management and data transmission, conventional interfaces like wirebonds will no longer be required in post-processing steps. The proposed architecture consists of a sensor front-end with four electrodes for concurrent amperometric and potentiometric sensing. This front-end outputs square wave signals mixed together with varying frequencies dependent on the sensed input, with the output type switchable with a state machine. A power management system consisting of a low dropout regulator (LDO) band gap reference (BGR), and a rectifier bridge is utilised for supplying power from an inductive link at 433MHz. Sensor data is transmitted wirelessly to a base station using LSK (Load-Shift Keying). The sensor front-end consumes 18µW, which the power management system more than adequately provides. The core area of the electronics without the coil is a conservative size of 0.41mm 2

Regularized transport between singular covariance matrices

We consider the problem of steering a linear stochastic system between two end-point degenerate Gaussian distributions in finite time. This accounts for those situations in which some but not all of the state entries are uncertain at the initial, t = 0, and final time, t = T. This problem entails non-trivial technical challenges as the singularity of terminal state-covariance causes the control to grow unbounded at the final time T. Consequently, the entropic interpolation (Schroedinger Bridge) is provided by a diffusion process which is not finite-energy, thereby placing this case outside of most of the current theory. In this paper, we show that a feasible interpolation can be derived as a limiting case of earlier results for non-degenerate cases, and that it can be expressed in closed form. Moreover, we show that such interpolation belongs to the same reciprocal class of the uncontrolled evolution. By doing so we also highlight a time-symmetry of the problem, contrasting dual formulations in the forward and reverse time-directions, where in each the control grows unbounded as time approaches the end-point (in the forward and reverse time-direction, respectively)

Single-layer-coated surfaces with linearized reflectance versus angle of incidence: application to passive and active silicon rotation sensors

A transparent or absorbing substrate can be coated with a transparent thin film to produce a linear reflectanceversus- angle-of-incidence response over a certain range of angles. Linearization at and near normal incidence is a special case that leads to a maximally flat response for p-polarized, s-polarized, or unpolarized light. For midrange and high-range linearization with moderate and high slopes, respectively, the best results are obtained when the incident light is s polarized. Application to a Si substrate that is coated with a SiO2 film leads to novel passive and active reflection rotation sensors. Experimental results and an error analysis of this rotation sensor are presented

Single-layer-coated surfaces with linearized reflectance versus angle of incidence: application to passive and active silicon rotation sensors

A transparent or absorbing substrate can be coated with a transparent thin film to produce a linear reflectanceversus- angle-of-incidence response over a certain range of angles. Linearization at and near normal incidence is a special case that leads to a maximally flat response for p-polarized, s-polarized, or unpolarized light. For midrange and high-range linearization with moderate and high slopes, respectively, the best results are obtained when the incident light is s polarized. Application to a Si substrate that is coated with a SiO2 film leads to novel passive and active reflection rotation sensors. Experimental results and an error analysis of this rotation sensor are presented