Jonathan Oppenheim

If the second law of thermodynamics forbids a transition from one state to another, then it is still possible to make the transition happen by using a sufficient amount of work. But if we do not have access to this amount of work, can the transition happen probabilistically? In the thermodynamic limit, this probability tends to zero, but here we find that for finite-sized systems, it can be finite. We compute the maximum probability of a transition or a thermodynamical fluctuation from any initial state to any final state, and show that this maximum can be achieved for any final state which is block-diagonal in the energy eigenbasis. As a bi-product, we introduce a finite set of thermodynamical monotones related to the thermo-majorization criteria which governs state transitions, and compute the work of transition in terms of them. We also find upper and lower bounds on this transition probability, in terms of the work of transition. These results, which allow one to not take the thermodynamic limit, are made possible by using and extending techniques from quantum information theory, developed in the context of understanding entanglement theory. As a consequence, our results find application in entanglement theory, and we find the amount of entanglement required (or gained) when transforming one pure entangled state into any other.

We give a strengthening as well as a generalization of an inequality for the quantum conditional mutual information of a tripartite quantum state recently proved by Fawzi and Renner, connecting it with the ability to reconstruct the state from its bipartite reductions. We provide three alternative and simplified proofs ranging from quantum state redistribution via duality of semidefinite programming to elementary properties of pinching maps and the operator logarithm.