Quantum Thermodynamics: Energetics, Complexity, and Thermalisation

Energetics of Quantum Computation

How much energy is fundamentally required to run a quantum process, and what does this mean for future quantum technologies [Auf22]? In classical physics, Landauer’s principle [Lan61; Ben82] sets a lower bound on the heat released when erasing a single bit, establishing a framework for the thermodynamics of computation. In the quantum world, the situation is richer and more subtle: creating coherence, maintaining entanglement, or performing measurements can themselves carry irreducible energetic costs with no classical analogue. Significant progress has been made in special scenarios such as quantifying the energy needed to generate coherence or extract entanglement [MSB+16; BCF+18] but these results are often protocol-specific or asymptotic. A general, operational understanding of the energetic cost of arbitrary finite-size quantum operations remains an open challenge. Understanding these limits is essential for designing sustainable, large-scale quantum devices.   

Thermalisation in Closed Quantum Systems

Why do isolated quantum systems appear to thermalise, even though their dynamics are perfectly reversible? The eigenstate thermalisation hypothesis (ETH) [Sre94; AKP+16] proposes that in chaotic systems, local observables behave as if the system is in thermal equilibrium. Similarly, canonical typicality [PSW06; GLT+06] shows that a small subsystem of a randomly chosen pure state can appear thermal. However, these frameworks rely on idealised conditions such as very large, non-integrable systems or fully random states whereas modern experiments probe intermediate-scale, structured platforms [KTL+16; NRF+16] that do not meet these assumptions. Furthermore, while entanglement entropy typically grows during evolution, it is neither necessary nor sufficient for thermalisation [SGB+24; BWG+25]. These findings highlight the need for new approaches to thermalisation that can capture equilibrium behavior in finite, constrained, and experimentally relevant quantum systems.

 

Computational Complexity of Thermodynamic Tasks

Even when the physical laws governing a quantum system are known, predicting or exploiting its behavior can be computationally formidable. For example, approximating the partition function or free energy of a local quantum Hamiltonian is QMA-hard in the worst case [BCG+21], and preparing low-temperature Gibbs states is generally intractable [RW24], although certain high-temperature or specially structured systems allow efficient preparation [BLM+24]. Work-extraction tasks highlight complementary challenges: in black-box scenarios, extracting non-trivial work from a single unknown copy is essentially impossible, with meaningful bounds emerging only when multiple copies are available [CDG+24]. A complementary work has shown that black-box work extraction can be framed as a composite hypothesis testing problem, revealing a conceptual link between extractable work and information-theoretic hardness [WT24]. Further, deciding whether a finite many-body system relaxes to a given expectation value can be PSPACE-complete [DMW25]. These results show that thermodynamic behavior is constrained not only by the laws of physics but also by fundamental computational limits, emphasizing the need to consider physical and algorithmic constraints together when exploring quantum thermodynamics. nother striking application of quantum physics to cryptography was initiated by the work of Broadbent and Islam in 2019 that led to a sequence of increasingly capable functionalities. Very basically, it is a sophisticated version of the no-cloning theorem. The key observation is that classical information cannot be deleted because it can always be copied. Could it be that somehow a message, encoded into a quantum system, can be certifiably deleted?