Thermodynamics of Quantum Causal Models: An Inclusive, Hamiltonian Approach

Abstract

Operational quantum stochastic thermodynamics is a recently proposed theory to study the thermodynamics of open systems based on the rigorous notion of a quantum stochastic process or quantum causal model. In there, a stochastic trajectory is defined solely in terms of experimentally accessible measurement results, which serve as the basis to define the corresponding thermodynamic quantities. In contrast to this observer-dependent point of view, a `black box', which evolves unitarily and can simulate a quantum causal model, is constructed here. The quantum thermodynamics of this big isolated system can then be studied using widely accepted arguments from statistical mechanics. It is shown that the resulting definitions of internal energy, heat, work, and entropy have a natural extension to the trajectory level. The canonical choice of them coincides with the proclaimed definitions of operational quantum stochastic thermodynamics, thereby providing strong support in favour of that novel framework. However, a few remaining ambiguities in the definition of stochastic work and heat are also discovered and in light of these findings some other proposals are reconsidered. Finally, it is demonstrated that the first and second law hold for an even wider range of scenarios than previously thought, covering a large class of quantum causal models based solely on a single assumption about the initial system-bath state.

arXiv commentAs accepted in Quantum

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• Quantum stochastic processes and quantum non-Markovian phenomena
• Measurability of nonequilibrium thermodynamics in terms of the Hamiltonian of mean force
• Fisher information of correlated stochastic processes
• Probabilistically Violating the First Law of Thermodynamics in a Quantum Heat Engine
• Informational steady-states and conditional entropy production in continuously monitored systems
• Nonequilibrium thermodynamics of quantum coherence beyond linear response
• Reassessing thermodynamic advantage from indefinite causal order
• Quantum thermodynamics of nonequilibrium processes in lattice gauge theories
• Universal validity of the second law of information thermodynamics
• Informational steady-states and conditional entropy production in continuously monitored systems: the case of Gaussian systems
• Experimentally probing entropy reduction via iterative quantum information transfer