Entropy Production in Quantum Heat Engines with Squeezed Reservoirs

Abstract

Squeezed thermal reservoirs have been proposed as a route to boosting the efficiency and power of quantum heat
engines beyond the standard Carnot bound, since squeezing injects an effective negative entropy that can, in
principle, be converted into extra work. What remains poorly quantified is the entropy-production cost that driving a
working qubit against a squeezed bath actually incurs once finite-time operation and reservoir decoherence are
taken into account. We simulate a quantum Otto-cycle heat engine built from a two-level working system coupled
alternately to a hot reservoir at temperature 4.2 K, squeezed with squeezing parameter r ranging from 0 to 1.2, and
an unsqueezed cold reservoir at 0.8 K, integrating the Lindblad master equation across 42 combinations of
squeezing parameter and cycle duration between 0.05 and 2.0 (in units of the inverse qubit gap). At r = 0, mean
entropy production per cycle was 0.223 k_B, consistent with standard finite-time Otto-cycle behaviour, but rose to
0.361 k_B at r = 1.2, a 62% increase, even as extractable work per cycle increased by 41%, from 0.184 to 0.259 (in
units of the qubit gap). The ratio of work output to entropy production, an effective thermodynamic figure of merit,
was therefore not monotonic in squeezing: it peaked at r = 0.6, where work per unit entropy produced reached 0.98,
15% above the unsqueezed value of 0.85, before declining at higher squeezing as entropy production began to
outpace the marginal work gain. Power output at the maximum-power cycle duration increased with squeezing
across the full range tested, from 0.31 (gap units) at r = 0 to 0.52 at r = 1.2, a 68% gain, but efficiency at maximum
power fell from 0.41 to 0.33 over the same range, a trade-off traced out in detail in Table 1. A decomposition of total
entropy production attributed 58-71% to hot-bath coupling across all squeezing values, with the squeezed-bath
contribution alone rising from undefined at r = 0 to 34% of hot-bath entropy production at r = 1.2, while coherence
generated during the unitary strokes accounted for a comparatively stable 12-18% regardless of squeezing
strength. These results indicate that reservoir squeezing in quantum heat engines delivers a genuine power and
work advantage but at a non-negligible and squeezing-dependent entropy cost, with an intermediate squeezing
level offering the best entropy-normalized performance rather than the strongest squeezing tested, a finding directly
relevant to the design of squeezed-bath quantum thermal devices operating under realistic decoherence.