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incorporation of thermodynamics in einsteins equation

Respected sir/madam,

Can we incorporate thermodynamic concepts of enthalpy (and entropy)in Einsteins equation “E=mC2?

it will become something like:
dE/dt=C²/h (dU/dt+dW/dt)

Where ,
h= enthalpy of the system
U= total internal energy
W=total work done

is is possible?

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