Kay Schwieger

How nanomechanical systems can minimize dissipation.

Information processing machines at the nanoscales are unavoidably affected by thermal fluctuations. Efficient design requires understanding how nanomachines can operate at minimal energy dissipation. Here we focus on mechanical systems controlled by smoothly varying potential forces. We show that optimal control equations come about in a natural way if the energy cost to manipulate the potential is taken into account. When such a cost becomes negligible, an optimal control strategy can be constructed by transparent geometrical methods which recover the solution of optimal mass transport equations in the overdamped limit. Our equations are equivalent to hierarchies of kinetic equations of a form well known in the theory of dilute gases. From our results, optimal strategies for energy efficient nanosystems may be devised by established techniques from kinetic theory.

Part III, Free Actions of Compact Quantum Groups on C*-Algebras

We study and classify free actions of compact quantum groups on unital C*-algebras in terms of generalized factor systems. Moreover, we use these factor systems to show that all finite coverings of ...

Diagonal couplings of quantum Markov chains

In this article we extend the coupling method from classical probability theory to quantum Markov chains on atomic von Neumann algebras. In particular, we establish a coupling inequality, which allow us to estimate convergence rates by analyzing couplings. For a given tensor dilation we construct a self-coupling of a Markov operator. It turns out that on a dense subset the coupling is a dual version of the extended dual transition operator previously studied by Gohm etal. We deduce that this coupling is successful if and only if the dilation is asymptotically complete.

An Application of Pontryagin’s Principle to Brownian Particle Engineered Equilibration

We present a stylized model of controlled equilibration of a small system in a fluctuating environment. We derive the optimal control equations steering in finite-time the system between two equilibrium states. The corresponding thermodynamic transition is optimal in the sense that it occurs at minimum entropy if the set of admissible controls is restricted by certain bounds on the time derivatives of the protocols. We apply our equations to the engineered equilibration of an optical trap considered in a recent proof of principle experiment. We also analyze an elementary model of nucleation previously considered by Landauer to discuss the thermodynamic cost of one bit of information erasure. We expect our model to be a useful benchmark for experiment design as it exhibits the same integrability properties of well-known models of optimal mass transport by a compressible velocity field.

Fluctuation relation for qubit calorimetry

Motivated by proposed thermometry measurement on an open quantum system, we present a simple model of an externally driven qubit interacting with a finite-sized fermion environment acting as a calorimeter. The derived dynamics is governed by a stochastic Schrödinger equation coupled to the temperature change of the calorimeter. We prove a fluctuation relation and deduce from it a notion of entropy production. Finally, we discuss the first and second law associated with the dynamics.

Efficient protocols for Stirling heat engines at the micro-scale

We investigate the thermodynamic efficiency of sub-micro-scale heat engines operating under the conditions described by overdamped stochastic thermodynamics. We prove that at maximum power the efficiency obeys the universal law η = 2 ηC/(4 − ηC) for ηC the efficiency of an ideal Carnot cycle. The corresponding power optimizing protocol is specified by the solution of an optimal mass transport problem. It can be determined explicitly using well known Monge–Ampère–Kantorovich reconstruction algorithms. Furthermore, we show that the same law describes the efficiency of heat engines operating at maximum work over short time periods.We investigate the thermodynamic efficiency of sub-micro-scale Stirling heat engines operating under the conditions described by overdamped stochastic thermodynamics. We show how to construct optimal protocols such that at maximum power the efficiency attains for constant isotropic mobility the universal law , where is the efficiency of an ideal Carnot cycle. We show that these protocols are specified by the solution of an optimal mass transport problem. Such solution can be determined explicitly using well-known Monge-Ampere-Kantorovich reconstruction algorithms. Furthermore, we show that the same law describes the efficiency of heat engines operating at maximum work over short time periods. Finally, we illustrate the straightforward extension of these results to cases when the mobility is anisotropic and temperature dependent.