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We present an English translation of Erwin Schr\"odinger's paper on "On the Reversal of the Laws of Nature". In this paper Schr\"odinger analyses the idea of time reversal of a diffusion process. Schr\"odinger's paper acted as a prominent source of inspiration for the works of Bernstein on reciprocal processes and of Kolmogorov on time reversal properties of Markov processes and detailed balance. The ideas outlined by Schr\"odinger also inspired the development of probabilistic interpretations of quantum mechanics by F\'enyes, Nelson and others as well as the notion of "Euclidean Quantum Mechanics" as probabilistic analogue of quantization. In the second part of the paper Schr\"odinger discusses the relation between time reversal and statistical laws of physics. We emphasize in our commentary the relevance of Schr\"odinger's intuitions for contemporary developments in statistical nano-physics., Comment: Revised version. 24 pages, 2 figures. Introduction 2 pages, Translation of the german original pag. 3-10, Commentary pag 10-22

We investigate a framework for coverings of noncommutative spaces. Furthermore, we study noncommutative coverings of irrational quantum tori and characterize all such coverings that are connected in a reasonable sense. Open access

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 ...

We study free actions of compact groups on unital C*-algebras. In particular, we provide a complete classification theory of these actions for compact Abelian groups and explain its relation to the classification of classical principal bundles.

Information processing machines at the nanoscales are unavoidably affected by thermal fluctuations. Efficient design requires understanding how nanomachines can operate at minimal energy dissipation. In this letter 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 cost becomes negligible, the optimal control strategy can be constructed by transparent geometrical methods and recovers 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, Minor revision, 5 pages, 2 figures. Supplemental material downloadable from the web-pages of the authors

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., 21 pages, 2 figures

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.