The second law of thermodynamics for pure quantum states

TL;DR

This paper proves a version of the second law of thermodynamics for pure quantum states, showing that energy cannot be lowered through cyclic operations without relying on statistical ensembles.

Contribution

It establishes the second law for isolated quantum systems using pure states and unitary evolution, avoiding statistical ensemble assumptions.

Findings

Energy cannot be significantly lowered after typical unitary evolution

Probability of observing energy below initial level is negligibly small

Validates thermodynamic principles within pure quantum state framework

Abstract

A version of the second law of thermodynamics states that one cannot lower the energy of an isolated system by a cyclic operation. We prove this law without introducing statistical ensembles and by resorting only to quantum mechanics. We choose the initial state as a pure quantum state whose energy is almost E_0 but not too sharply concentrated at energy eigenvalues. Then after an arbitrary unitary time evolution which follows a typical "waiting time", the probability of observing the energy lower than E_0 is proved to be negligibly small.