David Jou is a Professor of Physics of Condensed Matter at the Universitat Autonoma de Barcelona. His research focuses on non-equilibrium thermodynamics and statistical mechanics in classical and quantum systems.Maria Stella Mongiovì was a Professor of Mathematical-Physics at the Università degli Studi di Palermo. Her research focuses on superfluids hydrodynamics and quantum and classical turbulence.

• 1 Fundamental assumptions.- 2 The state of a quantum system as a subsystem of a composite system.- 3 Relation between the state of a system as isolated and as open.- 4 Universality of the probability function.- 5 Appendix A.- 6 Appendix B.- 7 Appendix C.- 8 Appendix D.

David Jou is a Professor of Physics of Condensed Matter at the Universitat Autonoma de Barcelona. His research focuses on non-equilibrium thermodynamics and statistical mechanics in classical and quantum systems.Maria Stella Mongiovì was a Professor of Mathematical-Physics at the Università degli Studi di Palermo. Her research focuses on superfluids hydrodynamics and quantum and classical turbulence.

• 1 Fundamental assumptions.- 2 The state of a quantum system as a subsystem of a composite system.- 3 Relation between the state of a system as isolated and as open.- 4 Universality of the probability function.- 5 Appendix A.- 6 Appendix B.- 7 Appendix C.- 8 Appendix D.

David Jou is a Professor of Physics of Condensed Matter at the Universitat Autonoma de Barcelona. His research focuses on non-equilibrium thermodynamics and statistical mechanics in classical and quantum systems.Maria Stella Mongiovì was a Professor of Mathematical-Physics at the Università degli Studi di Palermo. Her research focuses on superfluids hydrodynamics and quantum and classical turbulence.

• 1 Fundamental assumptions.- 2 The state of a quantum system as a subsystem of a composite system.- 3 Relation between the state of a system as isolated and as open.- 4 Universality of the probability function.- 5 Appendix A.- 6 Appendix B.- 7 Appendix C.- 8 Appendix D.