In the first paper of the tensor-centric warfare (TCW) series [1], we proposed a tensor model of combat generalizing earlier Lanchester-type systems with a particular emphasis on contemporary military thinking, including the distributed C4ISR system (Command, Control, Communications, Computing, Intelligence, Surveillance and Reconnaissance). In the present paper, we extend this initial tensor combat model with entropic Lie-derivative machinery in order to capture some aspects of this deep uncertainty, while, in the process, formalizing into our model military notion of symmetry and asymmetry in warfare as a commutator, also known as a Lie bracket. In doing so, we have sought to shift the question from the prediction of outcomes of combat, upon which previous combat models such as the Lanchester-type equations have been typically constructed, towards determining the uncertainty outcomes, using a rigorous analytical basis.
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