Continuous-variable quantum thermodynamics in the Gaussian regime provides a promising framework for investigating the energetic role of quantum correlations, particularly in optical systems. In this Letter, we introduce an entropy-free criterion for entanglement detection in bipartite Gaussian states, rooted in a distinct thermodynamic quantity: ergotropy-the maximum extractable work via unitary operations. By defining the "relative ergotropic gap," which quantifies the disparity between global and local ergotropy, we derive two independent analytical bounds that distinguish entangled from separable states. These bounds coincide for a broad class of quantum states, making the criterion both necessary and sufficient in such cases. Unlike entropy-based measures, our ergotropic approach captures fundamentally different aspects of quantum correlations and entanglement, particularly in mixed continuous-variable systems. We also extend our analysis beyond the Gaussian regime to certain non-Gaussian states and observe that Gaussian ergotropy continues to reflect thermodynamic signatures in entangled states, albeit with some limitations. These findings establish a direct operational link between entanglement and energy storage, offering an experimentally accessible approach to entanglement detection in continuous-variable optical platforms.
Extracting work from quantum system is one of the important areas in quantum thermodynamics. As a significant thermodynamic quantity, the ergotropy gap characterizes the difference between the global and local maximum extractable works. We derive an analytical upper bound of the ergotropic gap with respect to [Formula: see text] tripartite separable states. This bound also provides a necessary criterion for the separability of tripartite states. Detailed examples are presented to illustrate the efficiency of this separability criterion.
We develop a thermodynamic characterization of multimode entanglement in pure continuous-variable systems by quantifying the gap between globally and locally extractable work (ergotropy). For arbitrary pure multimode Gaussian states, we prove that the
2-local ergotropic gap is a faithful entanglement monotone across any bipartition and constitutes a functionally independent upper bound to the Renyi-2 entanglement entropy. We further introduce the
k-ergotropic score, the minimum
k-local ergotropic gap, and show that it faithfully quantifies multimode entanglement across
k partitions. For pure three-mode Gaussian states, we derive its closed-form relation with the geometric measure for genuine multimode entanglement
(k=2), and total Gaussian multimode entanglement
(k=3). For systems with more than three modes, the
k-ergotropic score becomes a functionally independent measure of multimode entanglement to the standard geometric measures. Our results reveal a direct operational hierarchy linking Gaussian multimode entanglement to work extraction under locality constraints, and provide a computable and experimentally accessible thermodynamic framework for characterizing quantum correlations.
The presence of quantum multipartite entanglement implies the existence of a thermodynamic quantity known as the ergotropic gap, which is defined as the difference between the maximal global and local extractable works from the system. We establish a direct relation between the geometric measure of entanglement and the ergotropic gaps. We show that all the marginal ergotropic gaps form a convex polytope for each class of quantum states that are equivalent under stochastic local operations and classical communication (SLOCC). We finally introduce the concept of multipartite ergotropic gap indicators and use them to present a refined criterion for classifying entanglement under SLOCC.
The presence of quantum multipartite entanglement implies the existence of a thermodynamic quantity known as the ergotropic gap, which is defined as the difference between the maximal global and local extractable works from the system. We establish a direct relation between the geometric measure of entanglement and the ergotropic gaps. We show that all the marginal ergotropic gaps form a convex polytope for each class of quantum states that are equivalent under stochastic local operations and classical communication (SLOCC). We finally introduce the concept of multipartite ergotropic gap indicators and use them to present a refined criterion for classifying entanglement under SLOCC.
For finite-dimensional bipartite systems with additive endpoint Hamiltonians, the ergotropic gap measures the work advantage of global over independent local cyclic unitary control. We express this gap through mutual information and the Gibbs-relative entropies of the local and global passive states. The balance retains local passive-state corrections for arbitrary marginals and reduces to the established locally thermal ergotropy identity when those corrections vanish. Dropping the global correction gives a separability-independent upper bound whose exact slack is the global passive-state free-energy excess. We show that optimizing the reference temperature is equivalent to matching the Gibbs entropy to the joint-state entropy. The optimized result is precisely the equal-entropy Gibbs bound on global ergotropy minus the local ergotropies, rather than a new thermodynamic bound. We characterize saturation and temperature endpoints, including degenerate ground spaces. Werner states yield a unique implicit crossover with a separability-based majorization bound and a small-correlation bound-to-gap ratio approaching 3/2. Structured and random two-qubit comparisons illustrate complementary performance. We also specify pointwise quantum-battery applicability and the obstruction from persistent interactions.