Statistical mechanical expression of entropy production for an open quantum system

A quantum statistical expression for the entropy of a nonequilibrium system is defined so as to be consistent with Gibbs' relation, and is shown to corresponds to dynamical variable by introducing analogous to the Heisenberg picture in quantum mechanics. The general relation between system-reservoir interactions and an entropy change operator in an open quantum system, relying just on the framework of statistical mechanics and the definition of von Neumann entropy. By using this formula, we can obtain the correct entropy production in the linear response framework. The present derivation of entropy production is directly based on the first principle of microscopic time-evolution, while the previous standard argument is due to the thermodynamic energy balance.Comment: 4 pages, no figure. Published in AIP Conf. Pro

Motion Switching with Sensory and Instruction Signals by designing Dynamical Systems using Deep Neural Network

To ensure that a robot is able to accomplish an extensive range of tasks, it is necessary to achieve a flexible combination of multiple behaviors. This is because the design of task motions suited to each situation would become increasingly difficult as the number of situations and the types of tasks performed by them increase. To handle the switching and combination of multiple behaviors, we propose a method to design dynamical systems based on point attractors that accept (i) "instruction signals" for instruction-driven switching. We incorporate the (ii) "instruction phase" to form a point attractor and divide the target task into multiple subtasks. By forming an instruction phase that consists of point attractors, the model embeds a subtask in the form of trajectory dynamics that can be manipulated using sensory and instruction signals. Our model comprises two deep neural networks: a convolutional autoencoder and a multiple time-scale recurrent neural network. In this study, we apply the proposed method to manipulate soft materials. To evaluate our model, we design a cloth-folding task that consists of four subtasks and three patterns of instruction signals, which indicate the direction of motion. The results depict that the robot can perform the required task by combining subtasks based on sensory and instruction signals. And, our model determined the relations among these signals using its internal dynamics.Comment: 8 pages, 6 figures, accepted for publication in RA-L. An accompanied video is available at this https://youtu.be/a73KFtOOB5

Proof of the renormalizability of the gradient flow

We give an alternative perturbative proof of the renormalizability of the system defined by the gradient flow and the fermion flow in vector-like gauge theories.Comment: 29 pages, the final version to appear in Nuclear Physics

Group approximation in Cayley topology and coarse geometry, Part III: Geometric property (T)

In this series of papers, we study correspondence between the following: (1) large scale structure of the metric space bigsqcup_m {Cay(G(m))} consisting of Cayley graphs of finite groups with k generators; (2) structure of groups which appear in the boundary of the set {G(m)}_m in the space of k-marked groups. In this third part of the series, we show the correspondence among the metric properties `geometric property (T),' `cohomological property (T),' and the group property `Kazhdan's property (T).' Geometric property (T) of Willett--Yu is stronger than being expander graphs. Cohomological property (T) is stronger than geometric property (T) for general coarse spaces.Comment: 20 pages, Appendix withdrawn due to the error in the proof of Theorem A.2 (v3); 24 pages, Appendix added (v2); 20 pages, no figur