62 95 v 2 [ m at hph ] 1 M ay 2 01 3 EMERGENT QUANTUM MECHANICS AS A THERMAL ENSEMBLE

It has been argued that gravity acts dissipatively on quantu m–mechanical systems, inducing thermal fluctuations that become indistingu ishable from quantum fluctuations. This has led some authors to demand that some form o ti e irreversibility be incorporated into the formalism of quantum mechanics. As a t ool towards this goal we propose a thermodynamical approach to quantum mechanics, b ased on Onsager’s classical theory of irreversible processes and on Prigogine’s n onu itary transformation theory. An entropy operator replaces the Hamiltonian as the gen erator of evolution. The canonically conjugate variable corresponding to the entro py is a dimensionless evolution parameter. Contrary to the Hamiltonian, the entropy op erator is not a conserved Noether charge. Our construction succeeds in implementing gravitationally–induced irreversibility in the quantum theory.

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