Conditional entropy8/31/2023 Our approach employs the concept of conditional entropy, which derives from the measure of entropy in images and complex networks. It can be easily implemented for use on physical simulation and experimental datasets. Here we present a widely applicable method to quantify disorder in systems at or away from equilibrium, based on Shannon and conditional entropy. In previous work, the Shannon entropy has been used successfully to quantify the order in fluid mixtures. Hence, it can be a useful tool to describe any macro-state of the system. The information-theoretical derivation of entropy is not restricted to thermodynamic equilibrium and it can be computed directly from the observed frequencies of configurations. (1)where the sum is performed over all possible configurations of the system, and represents the frequency of occurrence of the N-particle state. We here use the Shannon entropy from information theory, which is defined as. In order to develop a useful, more general measure of system disorder, it is therefore necessary to consider alternative approaches. However, since experiments or simulations are often monitoring systems away from equilibrium, and the system Hamiltonian is often unknown in experiments, a simple formulation using the thermodynamic entropy is not readily available. Because of the widespread occurrence of these phenomena, it is desirable to obtain methods to quantify the local and global level of disorder in a system, which can be generally applied to a broad range of systems.Īt equilibrium, disorder can be quantified by the thermodynamic entropy, which typically necessitates the explicit knowledge of the partition function of the system. They play a major role in the description of the behaviour of liquids and solids, the level of spin alignment in ferromagnetic systems, and domain formation in biological fluids such as membranes. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.įunding: MS and UZ acknowledge support from the Scottish Universities' Physics Alliance ( MS, CM and UZ acknowledge external funding from the UK National Physical Laboratory ( The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.Ĭompeting interests: The authors have declared that no competing interests exist.ĭisorder-order Transitions and the Shannon Entropyĭisorder-order transitions are important physical phenomena that are commonly addressed both by simulations and experiments. Received: FebruAccepted: ApPublished: June 10, 2013Ĭopyright: © 2013 Brandani et al. PLoS ONE 8(6):Įditor: Christof Markus Aegerter, University of Zurich, Switzerland Citation: Brandani GB, Schor M, MacPhee CE, Grubmüller H, Zachariae U, Marenduzzo D (2013) Quantifying Disorder through Conditional Entropy: An Application to Fluid Mixing.
0 Comments
Leave a Reply.AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |