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abelian group additive function adiabatic process adjoint representation angular momentum anti-equilibrium antinatural arbitrarily arbitrary assume axioms Chapter chemical potential classical mechanics components of content components of potential constant content Q content space corresponding defined Definition denote determined element energy entropy function equation equilibrium surface exists experience finite follows given hysteresis infinitesimal initial and final instance introduced invariant irreversibility function linear Lorentz group Lorentz transformation lower bound mathematical mechanical system natural irreversible process natural process nents of content obtain ordered vector spaces perfect equilibrium physical theory piston positive component positive integer possible process primitive observer Proof properties quantities quasi-entropy function quasi-static process real number reference frame relation relativistic relativistic thermodynamics representation reversible rotation rules of interpretation space-time subadditive subadditive function sublinear function suppose symmetry group temperature test particle Theorem thermodynamic space v(oc values vector space velocity zero