Quantum collapse and the second law of thermodynamics

A heat engine undergoes a cyclic operation while in equilibrium with the net result of conversion of heat into work. Quantum effects such as superposition of states can improve an engine's efficiency by breaking detailed balance, but this improvement comes at a cost due to excess entropy generated from collapse of superpositions on measurement. We quantify these competing facets for a quantum ratchet composed of an ensemble of pairs of interacting two-level atoms. We suggest that the measurement postulate of quantum mechanics is intricately connected to the second law of thermodynamics. More precisely, if quantum collapse is not inherently random, then the second law of thermodynamics can be violated. Our results challenge the conventional approach of simply quantifying quantum correlations as a thermodynamic work deficit.

Figure 1

Quantum ratchet. (a) An ensemble of two-level systems in equilibrium at temperature $T$. Application of the pulse excites the atoms that were initially in the ground state, resulting in (b). Atoms in the excited state (highlighted) are not altered. Work is extracted by the demon rotating all the atoms to the ground state (c). Such a pulse violates the principle of detailed balance. However, a physical realization is possible using a collective quantum nondemolition measurement of the entangled pairs of atoms.

Figure 2

Net work extracted. (Left) Probability of finding the pair of atoms in the uncoupled state as a function of coupling parameter $\lambda$, for, from right to left, $\beta =1$, 2, and 10, respectively; $\omega =1$. The inset shows the ratio of the effective temperature of each atom to the actual temperature as a function of inverse temperature, for, from bottom to top, $\lambda =0.2$, $0.3$, and $0.4$, respectively. (Right) Net work extracted from the cycle for the same color-coded values of $\lambda$ as the inset. The three curves on the top correspond to $\delta =0$ and imply a violation of Kelvin's statement.