Projected ensembles---the collections of conditional pure states induced on a system by measuring an entangled environment---have become central objects in quantum science, underlying deep thermalization, quantum state designs, the emergence of classicality, and exhibiting interesting phase transitions. Here we develop a general and exact theory of their dynamics, yielding a systematic approach to their dynamics and equilibrium and non-equilibrium stationary states. We derive an exact continuity equation on quantum state space for the projected ensemble, together with microscopic kinetic equations and analytical expressions for the probability flux and source terms generated by the system-environment interaction. The resulting dynamics admits a classical representation: isolated systems obey Hamiltonian transport and Liouville's theorem, while open systems are described by a kinetic theory of probability transport. The stationary continuity equation provides a general characterization of equilibrium and non-equilibrium stationary projected ensembles, which can be analyzed through the method of characteristics. The theory provides an analytical framework for studying the emergence, structure, and timescales of equilibrium and non-equilibrium stationary projected ensembles, with applications ranging from deep thermalization and the emergence of classicality to random quantum-state generation and quantum device benchmarking.
We build a framework for the thermodynamics of macroscopic quantum systems. In contrast with approaches requiring access to the full density matrix, our framework relies on a coarse-grained description, based on measurement statistics of a few observables. When these observables commute, the outcomes define classical macrostates whose entropy is quantified by observational entropy, accounting for uncertainty about both the macrostate and the microstate within it. We extend this notion to non-commuting observables forming a subalgebra of the operator space, and use Jaynes'principle to define an algebra-dependent entropy interpolating between von Neumann and observational entropies. Given initial and final measurement sets, connected by internal and/or environment-induced dynamics, we derive a second law for the coarse-grained dynamics. Unlike formulations based on von Neumann entropy, our inequality captures irreversibility from both non-unitary environment-induced dynamics and internal equilibration. It takes the usual form of a positive entropy production when the system is initially at internal equilibrium, while correction terms capture nonequilibrium resources ignored by the coarse-graining. We also derive fluctuation theorems for coarse-grained thermodynamic quantities. Along a quasi-static path of measurement schemes, we identify quantum macroscopic notions of work and heat fulfilling the first and second laws, including an additional work contribution from manipulating the algebra to which the system is confined, through external constraints or quantum measurement backaction. Finally, we apply our framework to examples illustrating the impact of varying the coarse-graining scheme. Our approach unifies macroscopic and stochastic thermodynamics in a genuinely quantum framework, laying the basis for a versatile, experimentally friendly toolbox to analyze complex quantum dynamics.
When only local observables of a many-body quantum system are of interest, it is desirable to formulate a reduced description within the Hilbert space of the corresponding subsystem, with the remaining degrees of freedom traced out and acting as an environment. Assuming initially uncorrelated states and Gaussian environments, we develop a framework for reconstructing the local dynamical generator of noninteracting quantum chains, with polynomial computational complexity. As an application, we consider two representative models: a bipartitioned Kitaev chain and a Kitaev chain boundary-coupled to a fully connected free-fermion environment. In both models, strong subsystem-environment coupling leads to non-Markovian dynamics characterized by ballistic spreading of the Lindblad dissipator support within the subsystem. On the other hand, weak coupling to a fully connected environment yields predominantly boundary-localized, Markovian dissipation. Our work highlights the implications of subsystem-environment correlations on the generator of local dynamics, beyond the conventional weak-coupling approximations.
The dynamics of an open quantum system in the high-temperature regime of the Caldeira–Leggett (CL) model using a Bohmian language is investigated. By expressing the density matrix in polar form, generalized continuity and Hamilton–Jacobi equations are obtained. Thermal effects appear explicitly in the former, while they influence the latter only indirectly through an effective potential. Remarkably, the effective potential does not vanish in the classical limit and cannot, in general, be decomposed into simple additive quantum and thermal contributions. Instead, it retains a nontrivial structure leading to a residual temperature dependence in the resulting dynamics. As a consequence, the resulting temperature-dependent-classical trajectories remain deterministic even in the presence of a thermal environment. This behavior contrasts with the stochastic dynamics observed in the Langevin description and reflects the ensemble-based nature of the present approach. To further explore the quantum-to-classical transition, a scaled version of the CL equation is introduced by scaling both the density matrix and Planck constant through a quantumness parameter. This parameter takes the value one in the fully quantum regime and smoothly approaches zero in the classical limit. Applications to Gaussian states demonstrate a gradual suppression of coherence and interference, governed jointly by thermal effects and the transition parameter.
S. Mousavi, Salvador Miret-Artés· Physica Scripta· 0 citations
Reverse Physics is a methodology that breaks physical theories into separate mathematical and physical conditions to establish their logical relationships. To showcase the power of the methodology, we present several results for quantum mechanics and their related insights. The standard Hilbert-space formulation conflicts with basic physical requirements, while a minimal topological modification can solve these problems. The ensemble space, rather than the pure-state space, distinguishes classical from quantum systems. The Born rule is an additional assumption linking orthogonality, mutual exclusivity and information entropy. Under explicit background conditions, unitary evolution is equivalent to deterministic and reversible evolution. Nonselective projective measurements can be characterized as Lindblad equilibration processes, while unitary evolution can be characterized as a limit of infinitesimal projective processes. Classical mechanics is recovered as the high-entropy limit of quantum mechanics, and every quantum state, pure or mixed, is a dynamical, spectral and thermodynamic equilibrium. These results are self-contained, use the standard vector-space representation and can thus be used as common tools and constraints for teaching, interpretations, reconstructions and future theories.
G. Carcassi, Tobias Thrien, C. Aidala· 0 citations
Quantum mechanics describes the unitary time evolution of closed systems. In practice, every quantum system interacts with the environment, leading to an irreversible loss of coherence. The spin-boson model (SBM) is central to the understanding of the fundamental process of decoherence of a two-state quantum system interacting with a bosonic heat bath, but the nature of transient dynamics in the presence of hybrid diagonal and off-diagonal system-bath interactions remains much less explored. Here, we investigate how the hybrid system-bath interactions of an Ohmic environment induce localization in the bias-free SBM. For strong coupling to the environment, localization is strongly affected by a dynamically generated bias via the renormalization of the tunneling amplitude. We find that counteracting effects of Hamiltonian parameters on non-exponential short-time dynamics and long-time population equilibration can lead to a separation of timescales and transient quantum coherent dynamics that can persist even for ultra-strong system-bath interaction. The findings offer novel insight into the equilibration behavior of quantum devices operating in the ultra-strong coupling regime.
Nirmalendu Acharyya, Martin Richter, B. Fingerhut· Journal of Chemical Physics· 0 citations
We present a unifying description of dynamical phase transitions in the unitary evolution of an isolated quantum particle and the dissipative relaxation of a classical Brownian particle, based on a dynamical generat- ing function. In the semiclassical and weak-noise limits, Fisher zeros of this function condense in the complex- time plane and reach the corresponding physical axes, producing dynamical phase transitions through a competition between return trajectories. This establishes a direct connection between quantum and classical (finite-time) dynamical phase transitions, where the semiclassical limit plays the role of the thermodynamic limit. In particular, the established link naturally provides a classical version of the Loschmidt amplitude and shows how dynamical quantum phase transitions, typically associated with isolated many-body systems, can arise in a single-particle quantum system. The dynamical phases are distinguished by a unifying, trajectory- based order parameter, realized as a classical correlation function and a sequential quantum weak value.
N. Asriyan, Jan Meibohm, Vasco Cavina et al.· 2 citations
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