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A theory to predict the steady-state position of a dissipative flow-controlled system, as defined by a control volume, is developed based on the maximum entropy principle of Jaynes, involving minimization of a generalized free-energy-like potential. The analysis provides a theoretical justification of a local, conditional form of the maximum entropy(More)
A reduced-order modelling (ROM) strategy is crucial to achieve model-based control in a wide class of flow configurations. In turbulence, ROMs are mostly derived by Galerkin projection of first-principles equations onto the proper orthogonal decomposition (POD) modes. These POD ROMs are known to be relatively fragile when used for control design. To(More)
1 Abstract This study critically analyses the information-theoretic, axiomatic and combinatorial philosophical bases of the entropy and cross-entropy concepts. The combinatorial basis is shown to be the most fundamental (most primitive) of these three bases, since it gives (i) a derivation for the Kullback-Leibler cross-entropy and Shannon entropy(More)
We examine the combinatorial or probabilistic definition (" Boltzmann's principle ") of the en-tropy or cross-entropy function H ∝ ln W or D ∝ − ln P, where W is the statistical weight and P the probability of a given realization of a system. Extremisation of H or D, subject to any constraints, thus selects the " most probable " (MaxProb) realization. If(More)
The combinatorial basis of entropy, given by Boltzmann, can be written H = N −1 ln W, where H is the dimensionless entropy, N is the number of entities and W is number of ways in which a given realization of a system can occur (its statistical weight). This can be broadened to give generalized combinatorial (or probabilistic) definitions of entropy and(More)
This study examines a new formulation of non-equilibrium thermodynamics, which gives a conditional derivation of the 'maximum entropy production' (MEP) principle for flow and/or chemical reaction systems at steady state. The analysis uses a dimensionless potential function (st) for non-equilibrium systems, analogous to the free energy concept of equilibrium(More)