Thermodynamics is operational in the sense that the very concept of thermal equilibrium depends crucially on the choice of observables, while the amount of extractable work is defined relative to the allowed operations. Here we show that isolated quantum many-body states admit a thermodynamic hierarchical structure of observables and allowed operations, where the same state can be thermal at one level of the hierarchy and athermal at another. Enlarging the set of allowed operations therefore renders such hidden athermality a potential resource for work extraction; the resulting work gain is bounded in terms of the difference between the entropy densities of the two levels. This entropy difference takes the form of the mutual-information density. We establish the bounds for three extensions of operational access: increased spatial resolution, increased duration of control, and nonlocal connectivity, which provide access to position-state Holevo information, correlations between neighboring regions and spatially nonlocal correlations, respectively. Thus the difference between entropies at different levels of the thermodynamic hierarchy governs the bound on the work gain associated with moving to a less restricted level.
Thermodynamics is operational in the sense that the very concept of thermal equilibrium depends crucially on the choice of observables, while the amount of extractable work is defined relative to the allowed operations. Here we show that isolated quantum many-body states admit a thermodynamic hierarchical structure of observables and allowed operations, where the same state can be thermal at one level of the hierarchy and athermal at another. Enlarging the set of allowed operations therefore renders such hidden athermality a potential resource for work extraction; the resulting work gain is bounded in terms of the difference between the entropy densities of the two levels. This entropy difference takes the form of the mutual-information density. We establish the bounds for three extensions of operational access: increased spatial resolution, increased duration of control, and nonlocal connectivity, which provide access to position-state Holevo information, correlations between neighboring regions and spatially nonlocal correlations, respectively. Thus the difference between entropies at different levels of the thermodynamic hierarchy governs the bound on the work gain associated with moving to a less restricted level.
We show that the maximum extractable work (ergotropy) from a quantum many-body system is constrained by "local athermality" of an initial state and "local entropy decrease" brought about by quantum operations. The obtained universal upper bound on ergotropy implies that the eigenstate thermalization hypothesis prohibits work extraction from energy eigenstates by means of finite-time unitary operations. This no-go property implies that Planck's principle, a form of the second law of thermodynamics, holds even for pure quantum states. Our result bridges two independently studied concepts of quantum thermodynamics, the second law and thermalization, via "intrasystem" correlations in many-body systems as a resource for work extraction.
We introduce the resource-theoretic free energy of a quantum channel as the maximal work extractable from the channel as its output equilibrates to a thermal state and its reference system remains locally intact. It is proportional to the relative entropy between the given channel and the absolutely thermal channel. It attains a clear operational meaning as twice the asymptotic rates of athermality distillation and formation under Gibbs-preserving superchannels, which map one absolutely thermal channel to another for a given bath, thereby revealing the asymptotic reversibility of the resource theory of athermality for quantum channels. Consequently, we establish that the optimal extractable work in converting one channel to another through the asymptotic athermality distillation and formation tasks equals the difference in their free energies. We call this optimal work the thermodynamic work capacity of channel conversion. Quantum information processing and computing fundamentally concern the manipulation and transformation of quantum channels, which encompass quantum states, their transformations, and measurements. A quantitative characterization of the optimal thermodynamic work gain or expenditure in quantum information processing constitutes a key step toward formulating thermodynamics of quantum processes.
Understanding the thermal behavior of quantum many-body pure states is one of the most fundamental issues in quantum thermodynamics. It is widely known that typical pure states yield vanishing work, just as thermal states do, when one restricts to local operations that cannot access correlations among subsystems. However, it remains unclear whether this equivalence to thermal states persists under LOCC (local operations and classical communication), where classically accessible correlations can be exploited for work extraction. In this work, we establish criteria for determining whether many-body pure states remain equivalent to thermal states even under LOCC, and show that this thermal equivalence is governed by their multipartite quantum correlation structure. We show that states with asymptotically maximal multipartite entanglement, such as Haar-random states, cannot yield extensive work under LOCC, whereas some states with limited multipartite entanglement, such as constant-degree graph states, allow extensive work extraction despite being locally indistinguishable from thermal states. Thus, our work provides a refined operational notion of thermal equivalence beyond the traditional local regime, which is becoming increasingly important due to the recent expansion of experimentally accessible operations.
We investigate the limitations that emerge in thermodynamic tasks as a result of having local control only over the components of a thermal machine. These limitations are particularly relevant for devices composed of interacting many-body systems. Specifically, we study protocols of work extraction that employ a many-body system as a working medium whose evolution can be driven by tuning the on-site Hamiltonian terms. This provides a restricted set of thermodynamic operations, giving rise to alternative bounds for the performance of engines. Our findings show that those limitations in control render it, in general, impossible to reach Carnot efficiency; in its extreme ramification it can even forbid to reach a finite efficiency or finite work per particle. We focus on the one-dimensional Ising model in the thermodynamic limit as a case study. We show that in the limit of strong interactions the ferromagnetic case becomes useless for work extraction, while the antiferromagnetic case improves its performance with the strength of the couplings, reaching Carnot in the limit of arbitrary strong interactions. Our results provide a promising connection between the study of quantum control and thermodynamics and introduce a more realistic set of physical operations well suited to capture current experimental scenarios.
The second law of thermodynamics for adiabatic operations -- constraints on state transitions in closed systems under external control -- is one of the fundamental principles of thermodynamics. On the other hand, it is recently established that even pure quantum states can represent thermal equilibrium. However, pure quantum states do not satisfy the second law in that they are not passive, i.e., work can be extracted from them if arbitrary unitary operations are allowed. It therefore remains unresolved how quantum mechanics can be reconciled with thermodynamics. Here, based on our key quantum-mechanical notions of thermal equilibrium and adiabatic operations, we address the emergence of the second law for adiabatic operations in the thermodynamics limit. We first introduce infinite-observable macroscopic thermal equilibrium (iMATE); a quantum state, including pure states, is in iMATE if the expectation values of all additive observables agree with their equilibrium values. We also introduce a macroscopic operation as unitary evolution generated by a time-dependent additive Hamiltonian, which is regarded as corresponding to adiabatic operations. Employing these concepts, we show that no extensive work can be extracted from any quantum state in iMATE through any macroscopic operations. Furthermore, we introduce a quantum-mechanical form of entropy density such that it agrees with thermodynamic entropy density for any quantum state in iMATE. We then prove that for any initial state in iMATE, this entropy density cannot be decreased by any macroscopic operations, followed by a time-independent relaxation process. Our theory thus proves two different forms of the second law, by adopting macroscopically reasonable classes of observables, equilibrium states, and operations. We also discuss the time scales of macroscopic operations in these results.
Thermodynamics teaches that if a system initially off-equilibrium is coupled to work sources, the maximum work that it may yield is governed by its energy and entropy. For finite systems this bound is usually not reachable. The maximum extractable work compatible with quantum mechanics ("ergotropy") is derived and expressed in terms of the density matrix and the Hamiltonian. It is related to the property of majorization: more major states can provide more work. Scenarios of work extraction that contrast the thermodynamic intuition are discussed, e.g. a state with larger entropy than another may produce more work, while correlations may increase or reduce the ergotropy.