The role of the entropy in a quantum system

A deep understanding of the irreversibility of the arrow of time cannot ignore the quantum nature of the world that surrounds us. The is the key result of the work carried out by Vincenzo Alba and Pasquale Calabrese of the International School for Advanced Studies (SISSA) of Trieste, recently published in the journal Proceedings of the National Academy of Sciences (PNAS).

According to one of the main laws of thermodynamics, the entropy of a system, isolated and far from thermal equilibrium, tends to increase in time until equilibrium is reached.

This accounts for the irreversibility of the flow of time for macroscopic phenomena. Since the beginning of the last century physicists have been dealing with the dilemma on how to reconcile this law of thermodynamics with the microscopic laws of nature, which have no privileged temporal direction.

The problem becomes conceptually more difficult within the context of quantum mechanics where if an isolated system is pure (with zero entropy) it will remain thus for ever, even if not in thermodynamic equilibrium.

The work by Alba and Calabrese allows us to understand how this vision, despite being substantially correct, actually does not get to the root of the problem. In particular, the authors have shown that if in an extended quantum system far from equilibrium we look at just one part thereof, this has an entropy that increases in time, exactly like in thermodynamics.

The origin of this entropy is in the entanglement between the part we are looking at and the rest of the system. The entanglement is a peculiar correlation that exists only in quantum mechanics and is at the very foundation of the possible functioning of quantum computers.

Research paper