Towards an information-theoretic foundation of (quantum) thermodynamics

Abstract

In the classical world of Newton and Laplace, fundamental physics and thermodynamics do not blend well: the former puts forward a picture of nature where states are pure and processes are fundamentally reversible, while the latter deals with scenarios where states are mixed and processes are irreversible. Many attempts have been made at reconciling the two paradigms, but ultimately the source of all troubles remains: if every particle possesses a definite position and a definite velocity, why should experimental data depend on the expectations of agents who have only partial information? Quantum theory offers a way out. Thanks to entanglement, a system and its environment can be jointly in a pure state, while the system alone is in a mixed state. Similarly, the evolution of system and environment can be jointly reversible, but locally irreversible. At the level of axioms, these facts are captured by the Purification Principle [1], from which the whole of quantum theory was derived in Ref. [2]. In this talk I will report on a new research programme, aimed at establishing the Purification Principle as the conceptual foundation for thermodynamics. I will start from the idea that thermodynamical transformations can be mapped into transformations that degrade entanglement. This will lead to a duality between entanglement and thermodynamics, which will be used to define measures of entanglement/entropy and to explore operational tasks like information erasure. At this level, thermodynamical requirements lead directly to requirements on the particular type of Purifications allowed by the theory: for example, forbidding the existence of Entropy Sinks (systems that can absorb entropy from the environment without increasing their internal entropy) is equivalent to imposing the existence of Symmetric Purifications (purifications in which the environment is a mirror image of the system). I will conclude by giving a glimpse on quantitative measures of entanglement/entropy. By adding a requirement about the existence of sharp measurements, I will show that Purification leads directly the an operational version of the spectral theorem, allowing one to define a zoo of well-behaved entropies. [1] G. Chiribella, G. M. D’Ariano, and P. Perinotti, Probabilistic Theories with Purification, Phys. Rev. A 81, 062348 (2010) [2] G. Chiribella, G. M. D’Ariano, and P. Perinotti, Informational Derivation of Quantum Theory, Phys. Rev. A 84, 012311 (2011)