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p. 1-26
Received: 23 May 2006 / Accepted: 5 January 2007 / Published: 20 January 2007
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| Download PDF Full-text (197 KB) Abstract: We review a decision theoretic, i.e., utility-based, motivation for entropy and Kullback-Leibler relative entropy, the natural generalizations that follow, and various properties of thesegeneralized quantities. We then consider these generalized quantities in an easily interpreted spe-cial case. We show that the resulting quantities, share many of the properties of entropy andrelative entropy, such as the data processing inequality and the second law of thermodynamics.We formulate an important statistical learning problem – probability estimation – in terms of ageneralized relative entropy. The solution of this problem reflects general risk preferences via theutility function; moreover, the solution is optimal in a sense of robust absolute performance.
p. 27-29
Received: 7 September 2006 / Accepted: 23 January 2007 / Published: 31 January 2007
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| Download PDF Full-text (17 KB) Abstract: There are two types of decisions: given the estimated state of affairs, one decidesto change oneself in a certain way (that is best suited for the given conditions); given whatone is, one decides to change the state of affairs in a certain way (that is best suited for whatone wants for oneself). Jaynes' approach to decision theory accounts only for the first type ofdecisions, the case when one is just an observer of the external world and the decisiondoesn't change the world. However, many decisions involve the wish to transform theexternal environment. To account for this we need to add an additional step in Jaynes'proposed algorithm.
p. 30-41
Received: 11 January 2007 / Accepted: 20 February 2007 / Published: 30 March 2007
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| Download PDF Full-text (139 KB) Abstract: The second law analysis of heat transfer of a non-Newtonian, laminar fallingliquid film along an inclined heated plate is investigated. The upper surface of the liquidfilm is considered free and adiabatic. Velocity and temperature profiles are obtainedanalytically and used to compute the entropy generation number (Ns ), irreversibility ratio (Φ) and the Bejan number (Be) for several values of the viscous dissipation parameter(Br -1 ), viscosity index (n) and the dimensionless axial distance (X). The Bejan numberincreases in the transverse direction and decreases as the viscous dissipation parameter(BrΩ -1 ) increases. The numerical results show that the Bejan number decreases as theviscous dissipation parameter (BrΩ -1 ), Peclet number (Pe) and the viscosity index (n)increase.
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