Quantum mechanics

Theoretical physics

Algorithm

Quantum thermodynamics

Laws of thermodynamics

Monotonic function

Remainder

Constraint (computer-aided design)

Limit (mathematics)

Second law of thermodynamics

Statistical physics

Thermodynamics

Physics

Mathematics

Political science

Work (physics)

Mathematical analysis

Geometry

Quantum

Zeroth law of thermodynamics

Non-equilibrium thermodynamics

Thermodynamic limit

State (computer science)

Arithmetic

Proceedings of the National Academy of Sciences

Significance In ordinary thermodynamics, transitions are governed by a single quantity–the free energy. Its monotonicity is a formulation of the second law. Here, we find that the second law for microscopic or highly correlated systems takes on a very different form than it does at the macroscopic scale, imposing not just one constraint on state transformations, but many. We find a family of quantum free energies which generalize the standard free energy, and can never increase. The ordinary second law corresponds to the nonincreasing of one of these free energies, with the remainder imposing additional constraints on thermodynamic transitions. In the thermodynamic limit, these additional second laws become equivalent to the standard one. We also prove a strengthened version of the zeroth law of thermodynamics, allowing a definition of temperature.

The second laws of quantum thermodynamics