Thermodynamics of Quantum Causal Models: An Inclusive, Hamiltonian Approach

TL;DR

This paper develops a Hamiltonian-based approach to quantum thermodynamics of causal models, validating and extending the operational framework by connecting it to traditional statistical mechanics and clarifying foundational ambiguities.

Contribution

It introduces a Hamiltonian formalism for quantum causal models, linking operational definitions to standard thermodynamics, and broadens the applicability of thermodynamic laws in quantum causal scenarios.

Findings

Definitions of energy, heat, work, and entropy align with operational thermodynamics.

First and second laws hold for a wider class of quantum causal models.

Clarifies ambiguities in stochastic work and heat definitions.

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.