Emergent quantum mechanics as a thermal ensemble

Abstract

It has been argued that gravity acts dissipatively on quantum-mechanical systems, inducing thermal fluctuations that become indistinguishable from quantum fluctuations. This has led some authors to demand that some form of time irreversibility be incorporated into the formalism of quantum mechanics. As a tool towards this goal we propose a thermodynamical approach to quantum mechanics, based on Onsager's classical theory of irreversible processes and on Prigogine's nonunitary transformation theory. An entropy operator replaces the Hamiltonian as the generator of evolution. The canonically conjugate variable corresponding to the entropy is a dimensionless evolution parameter. Contrary to the Hamiltonian, the entropy operator is not a conserved Noether charge. Our construction succeeds in implementing gravitationally-induced irreversibility in the quantum theory.

Quantum field theory in the Rindler-Rindler spacetime

“…It is well-known that for an uniformly accelerated observer, the fluctuations of a quantum field in the inertial vacuum state appear to be identical to the thermal fluctuations of an real thermal bath indicating some kind of equivalence between thermal and vacuum fluctuations [1,2]. There have also been suggestions that quantum and statistical fluctuations, including thermal ones, are essentially identical [3] (see also [4]). In a recent paper [5], we explored this relationship between thermal and quantum fluctuations beyond the context of the vacuum state.…”

On Non-Equilibrium Thermodynamics of Space–Time and Quantum Gravity

“…This defines both quantum dynamics in (17) and the entropy-action proportionality for the Einstein-Hilbert action S EH (4):…”

“…However, as regards entropy, a complete covariant theory of thermodynamics and statistical mechanics in a full general relativistic context is yet to be established [15]. Initial investigations have shown that for a constant "thermal time" there seems to be a direct relation between temperature and inverse proper time [15,16,17]. With the assumption that entropy is negative information I there is also a direct connection between entropy, energy E and time t in upper limits of the bound on the information I transfer in black hole thermodynamics [18]:…”