The second laws of quantum thermodynamics

TLDR

The second law forbids statistically unlikely state changes, originally Clausius’ statement, and while traditionally applied to many‑particle systems, recent work extends thermodynamic reasoning to few‑particle systems coupled to a heat bath. The authors investigate whether a second law exists for microscopic systems. By formalizing thermal operations, they show the first law defines the allowed operations, the zeroeth law guarantees a nontrivial theory, and the remaining laws arise as monotonicity of generalized free energies. They discover that for (nearly) cyclic processes microscopic systems obey a family of second laws—generalized free energies that never increase—dividing into three regimes of cyclicity, one permitting apparent violations via work embezzlement, and that these laws also govern macroscopic systems with long‑range interactions.

Abstract

The second law of thermodynamics tells us which state transformations are so statistically unlikely that they are effectively forbidden. Its original formulation, due to Clausius, states that "Heat can never pass from a colder to a warmer body without some other change, connected therewith, occurring at the same time". The second law applies to systems composed of many particles interacting; however, we are seeing that one can make sense of thermodynamics in the regime where we only have a small number of particles interacting with a heat bath. Is there a second law of thermodynamics in this regime? Here, we find that for processes which are cyclic or very close to cyclic, the second law for microscopic systems takes on a very different form than it does at the macroscopic scale, imposing not just one constraint on what state transformations are possible, but an entire family of constraints. In particular, we find a family of free energies which generalise the traditional one, and show that they can never increase. We further find that there are three regimes which determine which family of second laws govern state transitions, depending on how cyclic the process is. In one regime one can cause an apparent violation of the usual second law, through a process of embezzling work from a large system which remains arbitrarily close to its original state. These second laws are not only relevant for small systems, but also apply to individual macroscopic systems interacting via long-range interactions, which only satisfy the ordinary second law on average. By making precise the definition of thermal operations, the laws of thermodynamics take on a simple form with the first law defining the class of thermal operations, the zeroeth law emerging as a unique condition ensuring the theory is nontrivial, and the remaining laws being a monotonicity property of our generalised free energies.