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I assume your "either" was meant to be "neither" : )
The FLT axiomizes that there exists a system energy state function
E(S,N,X). S is the entropy, N is the particle number, and X may be one or
several other state variables. The increment in energy may then be
expressed in terms of these state variables and the respective partial
derivatives:
dE = TdS + MdN + YdX. T, M and Y being the appropriate partial
derivatives.