Thermodynamics of Entanglement

Shinji Mukohyama A, Masafumi Seriu, Hideo Kodama

Entanglement entropy is often speculated as a strong candidate for the origin of black-hole entropy. To judge whether or not this speculation is true, it is effective to investigate the whole structure of thermodynamics obtained from the entanglement entropy, rather than just to examine the apparent structure of the entropy alone or to compare it with that of black-hole entropy. This is because entropy acquires a physical significance only when it is related to the energy and the temperature of a system. From this point of view, we construct a ``thermodynamics of entanglement'' by introducing an entanglement energy and compare it with black-hole thermodynamics. We consider two possible definitions of entanglement energy. Then we construct two different kinds of thermodynamics by combining each of these different definitions of entanglement energy with the entanglement entropy. We find that both of these two kinds of thermodynamics show significant differences from black-hole thermodynamics if no gravitational effects are taken into account. These differences are, in particular, highlighted in the context of the third law of thermodynamics. Finally we see how the inclusion of gravity alters the thermodynamics of the entanglement. We give a suggestive argument that the thermodynamics of the entanglement behaves like black-hole thermodynamics if the gravitational effects are included properly. Thus the entanglement entropy passes a nontrivial check to be the origin of black-hole entropy.

Joan Alba, Laura Ares, Jan Sperling +1 more

The role of quantum entanglement in thermodynamical systems remains elusive. Does entanglement result in thermodynamic advantages or does it impose fundamental limitations? Here, we unambiguously quantify the amount of heat and work in a quantum system that is due to the presence of entanglement. This is achieved by constraining the system's non-equilibrium dynamics to separable states, thereby isolating the impact entanglement has on thermodynamic effects. Unlike thermodynamic entanglement measures, which signify a loose connection between entanglement and thermodynamic properties, imposing a constraint constitutes an active intervention into a system -- answering how much of a system's thermodynamics is caused by (not correlated with) its quantumness. We benchmark our theory by applying the constrained dynamics to several multipartite systems, including quantum batteries and quantum refrigerators.

Mohsen Alishahiha, Davood Allahbakhshi, Ali Naseh

Fernando G. S. L. Brandão, Martin Bodo Plenio

Shinji Mukohyama A, Masafumi Seriu, Hideo Kodama

Extending the analysis in our previous paper, we construct the entanglement thermodynamics for a massless scalar field on Schwarzschild spacetime. Contrary to the flat case, the entanglement energy ${E}_{\mathrm{ent}}$ turns out to be proportional to the area radius of the boundary if it is near the horizon. This peculiar behavior of ${E}_{\mathrm{ent}}$ can be understood by the redshift effect caused by the curved background. Combined with the behavior of the entanglement entropy, this result yields, quite surprisingly, the entanglement thermodynamics of the same structure as black hole thermodynamics. On the basis of these results, we discuss the relevance of the concept of entanglement as the microscopic origin of black hole thermodynamics.

Sibel Başkal, Young S Kim, Marilyn E. Noz