Geometric Optimisation of Quantum Thermodynamic Processes

Differential geometry offers a powerful framework for optimising and characterising finite-time thermodynamic processes, both classical and quantum. Here, we start by a pedagogical introduction to the notion of thermodynamic length. We review and connect different frameworks where it emerges in the quantum regime: adiabatically driven closed systems, time-dependent Lindblad master equations, and discrete processes. A geometric lower bound on entropy production in finite-time is then presented, which represents a quantum generalisation of the original classical bound. Following this, we review and develop some general principles for the optimisation of thermodynamic processes in the linear-response regime. These include constant speed of control variation according to the thermodynamic metric, absence of quantum coherence, and optimality of small cycles around the point of maximal ratio between heat capacity and relaxation time for Carnot engines.

A MULTI-DIMENSIONAL CONFIGURATION ALGORITHM FOR MODULAR PRODUCT ARCHITECTURES

With an increasing demand for product individualisation leading to increased product architecture complexity and -costs, modular kits are one common measure to cope with this issue. The management of such a modular kit as well as the methodical determination of a specific product variant is key to the manufacturer's success. As multiple influence factors need to be taken into account when configuring product variants, we propose a multi-dimensional geometric optimisation algorithm, allowing for prioritising varying customer demands and thereby determining the ideally balanced product variant.

Modelling Training Adaptation in Swimming Using Artificial Neural Network Geometric Optimisation

This study aims to model training adaptation using Artificial Neural Network (ANN) geometric optimisation. Over 26 weeks, 38 swimmers recorded their training and recovery data on a web platform. Based on these data, ANN geometric optimisation was used to model and graphically separate adaptation from maladaptation (to training). Geometric Activity Performance Index (GAPI), defined as the ratio of the adaptation to the maladaptation area, was introduced. The techniques of jittering and ensemble modelling were used to reduce overfitting of the model. Correlation (Spearman rank) and independence (Blomqvist β) tests were run between GAPI and performance measures to check the relevance of the collected parameters. Thirteen out of 38 swimmers met the prerequisites for the analysis and were included in the modelling. The GAPI based on external load (distance) and internal load (session-Rating of Perceived Exertion) showed the strongest correlation with performance measures. ANN geometric optimisation seems to be a promising technique to model training adaptation and GAPI could be an interesting numerical surrogate to track during a season.