The Synergic Entropy : an efficient frontier output derived from merged input units boosted by synergy and constrained by critical input

The novel approach equates the maximum output deviations caused by combined inputs with affinity-synergy in the same system. The inputs can be assets of a company, companies in a sector or other physical variable that is merged over time. The outputs can be any flow variable that depends on the merged inputs, which symmetric values are the efficient and the inefficient frontiers outputs. Rather than being purely stochastic, the frontiers in the output function are estimated by the parameters named synergy and critical input. Synergy is conceived as a novel parameter for risk and efficiency under the constraint given by scarce resources (critical input). The output acceleration derived from the mergers among inputs, boosted by synergy, is the main foundation of the theory, which special case gives Shannon and Boltzmann-Gibbs equations. Tests are done in the 11 USA Sectors over their quarterly financial statements, proving that synergy is significant for financial statements, whereas typical betas only present significance in stock market data. A practical application is a novel discount rate for valuation using synergy, whose results for each sector are stable and coherent with perceived risk. Systems that rely on causal relations between output and multiple inputs can be regressed under novel parameters, rather than reckoning exclusively in optimization procedures.