Complete dynamics and entropy balances of all proper subsystems need not determine global irreversibility. A three-qubit construction keeps one initial product state and every one- and two-qubit reduced semigroup fixed while changing only the organisation of energy-preserving shared phase events. The global entropy production changes, and the thermodynamic ranking of the full system against its proper subsystems reverses. Both trajectories remain separable, every compared score is positive, and interval bounds certify the opposite rankings.The comparison uses the finite-window Thermodynamic Criterion Index, the entropy reduction per unit outward entropy transfer. An exact lift identity determines when relational-information change exceeds the component deficit and the signed nonadditivity of entropy transfer. With common lower-order marginals and equal global export, a larger increment of irreducible higher-order information means an exactly equal reduction of global entropy production. At a common temperature and for an additive Hamiltonian, that information has a precise nonequilibrium free-energy value.Within the parity-contact model, fixed lower-order dynamics leave an explicit physical fibre of higher-order generators. Selective control inside this fibre changes a chosen collective decay rate. Two controllers with equal amounts of parity correlation can produce opposite thermodynamic rankings. Finite adaptive protocols confined to any fixed proper subsystem with private memory cannot identify the change; outcomes jointly retained from all three sites can reveal it. A certified pair of compatible generators gives nonzero lower bounds on the minimax absolute errors for global entropy production and the full-versus-proper yield gap, even with exact lower-order data. Complete lower-order descriptions therefore leave a physically controllable coordinate of global irreversibility undetermined.
Complete dynamics and entropy balances of all proper subsystems need not determine global irreversibility. A three-qubit construction keeps one initial product state and every one- and two-qubit reduced semigroup fixed while changing only the organisation of energy-preserving shared phase events. The global entropy production changes, and the thermodynamic ranking of the full system against its proper subsystems reverses. Both trajectories remain separable, every compared score is positive, and interval bounds certify the opposite rankings.The comparison uses the finite-window Thermodynamic Criterion Index, the entropy reduction per unit outward entropy transfer. An exact lift identity determines when relational-information change exceeds the component deficit and the signed nonadditivity of entropy transfer. With common lower-order marginals and equal global export, a larger increment of irreducible higher-order information means an exactly equal reduction of global entropy production. At a common temperature and for an additive Hamiltonian, that information has a precise nonequilibrium free-energy value.Within the parity-contact model, fixed lower-order dynamics leave an explicit physical fibre of higher-order generators. Selective control inside this fibre changes a chosen collective decay rate. Two controllers with equal amounts of parity correlation can produce opposite thermodynamic rankings. Finite adaptive protocols confined to any fixed proper subsystem with private memory cannot identify the change; outcomes jointly retained from all three sites can reveal it. A certified pair of compatible generators gives nonzero lower bounds on the minimax absolute errors for global entropy production and the full-versus-proper yield gap, even with exact lower-order data. Complete lower-order descriptions therefore leave a physically controllable coordinate of global irreversibility undetermined.
This work introduces a unified dynamical law of irreversibility that links three fundamental quantities in open quantum systems: coherence change, information flux, and irreversible entropy production.For finite-dimensional systems evolving under completely positive trace-preserving (CPTP) Markovian semigroups, we prove the exact identity κ˙(t)=Φinfo(t)−ΔS(t),\dot{\kappa}(t) = \Phi_{\text{info}}(t) - \Delta S(t),κ˙(t)=Φinfo(t)−ΔS(t), where κ(t)=S(ρdiag)−S(ρ)\kappa(t) = S(\rho_{\text{diag}}) - S(\rho)κ(t)=S(ρdiag)−S(ρ) is the entropy-valued coherence, Φinfo(t)=−ddtS(ρt∥ν)\Phi_{\text{info}}(t) = -\frac{d}{dt} S(\rho_t \Vert \nu)Φinfo(t)=−dtdS(ρt∥ν) is the information flux relative to a canonical maximum-entropy reference state ν\nuν, and ΔS(t)=Tr[L(ρt)(logρt−logσ)]≥0\Delta S(t) = \text{Tr}[ \mathcal{L}(\rho_t)(\log \rho_t - \log \sigma)] \ge 0ΔS(t)=Tr[L(ρt)(logρt−logσ)]≥0 is the Spohn entropy production rate. The result establishes an exact entropy-balance identity connecting quantum coherence, thermodynamic irreversibility, and information flow — all expressed in consistent entropy-per-time units.Operational protocols are provided for experimental validation using modern quantum platforms (e.g., superconducting qubits, trapped ions, or cavity QED).A residual test, R(t)=κ˙−Φinfo+ΔSR(t) = \dot{\kappa} - \Phi_{\text{info}} + \Delta SR(t)=κ˙−Φinfo+ΔS, offers a falsifiable criterion for detecting non-Markovianity or hidden memory flux. The framework unifies information geometry, resource-theoretic coherence, and nonequilibrium thermodynamics into a single experimentally testable law, illuminating how quantum structure can be sustained only when information inflow compensates entropy production. Keywords:Quantum thermodynamics, information theory, open quantum systems, coherence, entropy production, relative entropy, Lindblad dynamics, irreversibility, information geometry.
SCQG paper 15 of 28 This paper follows the energy and entropy changes involved in creating, retaining, reading, using and resetting quantum records. It treats the pointers, memories, controllers, work stores and reservoirs as physical systems and counts each energy transfer once. Forward actionability means resolving uncertainty into a distinction that a later operation can use. Local grounding depends on that action making the resolved distinction available. The paper derives exact balances for finite quantum interactions, reset with and without retained side information, and autonomous control. It connects record lifetime and decoding accuracy to the information available for later use, and identifies the instrument-dependent information that enters feedback-work bounds. It also develops capacity-proportional selection, in which an outcome’s probability is proportional to the physical capacity available for that outcome. For nonconstant outcome probabilities, respecting ordinary mixtures of preparations forces this selection law to have positive-operator-valued measure (POVM) form. Agreement with the Born rule then requires the normalized capacity operators to equal the measurement’s outcome effects. The paper gives first-arrival, stationary and quantum-jump realizations and states their no-signalling conditions. The Stoney action equals αℏ, giving the uncertainty bound ΔX ΔP ≥ 1/(2α). Further results relate screen fluctuations, measurement precision, trajectory probabilities and entropy export. The complete physical construction keeps its reservoirs and work sources within their own reciprocal branch and supplies the defined stress interface used by the gravitational papers.
Microscopic unitary dynamics preserves all fine information, yet an isolated finite system can show a robust thermodynamic window in which the entropy associated with a restricted record rises. We ask why information hidden from the current record usually fails to rebuild a low-entropy macrostate. For a fixed projective record, every finite step separates exactly into the evolution predicted from the record alone and an exact correction carried by unresolved microscopic structure. The record-only contribution starts only at second order in time, so all instantaneous change of the record comes from hidden currents between macrostates. We derive the exact entropy rate, separate entropy-spreading from return-oriented currents, and resolve those currents into energy-gap amplitudes. Transitions with the same gap add coherently, revealing how the Hamiltonian and the microscopic state organize hidden information for return. In interacting mixing dynamics the current power is spread over many frequencies; free and deliberately commensurate controls progressively concentrate it, and the engineered dynamics reconstructs a low-entropy macrostate. An independent distribution-level test separates hidden dynamical activity from finite-step return, and an exact classical measure-preserving counterpart shows which parts of the construction are not uniquely quantum. Within the specified record and observation window, irreversibility is therefore not loss of microscopic information, but the failure of that information to organize currents that restore macroscopic order.
Physical–Observation Dual-Axis (PODA) theory retains the physical state and the objective state of record formation as distinct responsibilities. We develop a thermodynamic formulation on their admissible joint histories, starting from a common energy, an explicitly specified thermal closure and a declared physical time reversal. For a finite-state realization with channel-resolved local detailed balance, the full trajectory entropy production obeys the usual integral fluctuation relation. We prove an exact decomposition of its mean into the relative entropy visible in a declared record and a nonnegative conditional contribution from the unrecorded joint history. Equality holds precisely when the forward and reverse conditional history laws coincide. An exact recovery theorem identifies preservation of the observation section, marked history laws, energy exchanges and reverse protocol. A separate sufficiency criterion determines whether a record captures all entropy production. The finite-state section recovers the first and second laws, Gibbs equilibrium and isothermal free-energy dissipation of the reduced system. Two analytic models distinguish correlation loss from heat release and demonstrate positive joint entropy production with stationary equilibrium marginals. A regular perturbation formula expresses the leading hidden entropy production through conditional score mismatch. The results give conditional, exact criteria for thermodynamic recovery within PODA and identify the dynamical quantities required for departures from a fixed observation description.
A consistent theory of non-equilibrium thermodynamics for Markovian open quantum systems has been developed in the late seventies in analogy with Classical Irreversible Thermodynamics. The time-evolution of these open systems is usually described by means of effective master equations in Lindblad form, that turn out to be reliable when there is a separation of time-scales between system and environment, such that memory effects are negligible and the so-called Markovian approximation is justified. In this framework, the variations of energy and entropy in the system are consistently described, distinguishing between heat and work contributions and providing a statement of the second law of thermodynamics as positivity of the entropy production.\nHowever, there is empirical evidence that many physical systems like photosynthetic complexes,\nopto-mechanical resonators and superconducting qubits, just to mention a few, experience more general non-Markovian dynamics. The formulation of the laws of thermodynamics in a non-Markovian setting is matter of current research and represents the main topic of the present work. As a first step, we show that the entropy production defined as in the Markovian case can be negative for a class of non-Markovian dynamics. We argue that this outcome should not be interpreted as a violation of the second law of thermodynamics because the environment must be explicitly taken into account in the balance of entropy in the non-Markovian setting. In order to justify this claim we adopt a more general point of view, studying a closed bipartite quantum system, such that each of the two subsystems plays the role of a finite environment out of equilibrium for the other one. We concentrate on the balance of energy first and construct an effective Hamiltonian for each subsystem using physically reasonable requirements; then we define heat and work as in the standard Markovian treatment, with the effective Hamiltonian replacing the free Hamiltonian. It turns out that, in our framework, the work power is perfectly balanced between subsystems, while the correlations can store a part of energy locally inaccessible and exchange it with both subsystems in the form of heat.\nConcerning the balance of entropy, a quite general formulation of the second law of thermodynamics can be given as follows: under the assumption of a factorized initial state for the compound system, the sum of the total variations of the entropies in the two subsystems is always nonnegative. We show with an explicit example that this general formulation does not correspond to the statement presented in the framework of Markovian master equations, which should not be considered a priori the second law of thermodynamics.\nIn the last part of the thesis we concentrate of the so-called fluctuation relations, that are results extending the thermodynamic formalism beyond the behavior of average quantities. After reviewing the main theoretical outcomes, such as the Jarzynski equality and the Crooks fluctuation theorem, we describe a proposal to access experimentally the work performed on an ensemble of diatomic molecules by a time-dependent electric field coupled with their vibrational degree of freedom. This procedure could then be used to test the quantum Jarzynski equality. With respect to the results so far appeared in the literature, in which the left-hand side of the equality is inferred from an experiment and the right-hand side is computed according to a model, in our proposed setting we should be able to estimate from the experiment both the left-hand side and the right-hand side of the equality, independently.
The same position need not imply the same future: observing an address may discard information about past events, active memory, and records. This work determines the data needed to reconstruct a temporal law and reconcile its spatial, coherent, and record readouts. Admissible extensions of a history define a graded generator of actualization; marked event rates specify its dynamics in physical time. We establish separate criteria for recovering the event count from an address and for the predictive sufficiency of that address. A distinguishing future test yields a sharp lower bound on the error of a purely spatial description. On a finite strongly connected state space, marked cycle probabilities classify strictly positive laws up to local changes of clock. For factorized first-event records, outcome fractions form a complete metric invariant after a common reparametrization of age has been factored out. On a finite irreducible state space, zero configurational entropy production characterizes the unitary continuation of the same temporal form. Its invariant complex sectors realize all finite-dimensional autonomous Hamiltonian dynamics, up to a global phase. Preparation, probabilistic readout, and retention of a sector require separate operational conditions. The zero-support condition for address jumps acquires the precise meaning of preserving the admissible state space, provided that the continuous evolution is also checked. For a phase-pure QND writer, an independently calibrated rate of record discrimination predicts transition suppression and a sufficient event-count budget on a finite interval. The joint pressure of transport and recording distinguishes realizations with identical separate marginals. Marked irreversibility may persist even when the configurational dynamics is reversible. These results define a testable sequence: reconstruct the event law, determine its sufficient readouts, and compare predictions across instruments. Equilibrium event algebras, protected phase constructions, and local clocks for infinite systems extend this sequence under explicitly stated assumptions. This preprint develops the temporal sector of the Theory of Structural Articulation (TSA).