We establish an end-to-end theoretical framework and numerical validation for the dissipation of metastable bound energy states, connecting empirical engineering lifetime forecasting of primary chemical cells to fundamental non-equilibrium quantum-informational thermodynamics. We prove that the irreversible relaxation of stored free energy Delta F into a thermal reservoir at temperature T is governed by the Planckian dissipation timescale tau_P = hbar / (k_B T) and the dimensionless Landauer information capacity Phi_0 = Delta F / (k_B T). Utilizing stochastic Langevin integration across a saddle-node bifurcation normal form, we uncover a universal power-law divergence of voltage noise variance prior to system collapse with critical exponent gamma = 1/2: Var(V, t) ~ (t_death - t)^(-1/2), offering an exact, non-invasive early-warning precursor for catastrophic failure. Furthermore, by numerically solving the exact unitary Schrodinger equation for an 8-qubit non-integrable chaotic Heisenberg spin chain via the Loschmidt Echo protocol, we demonstrate that macroscopic thermodynamic irreversibility emerges from many-body quantum information scrambling (reaching 72.1% of the Page thermalization entropy), wherein a microscopic 5% Hamiltonian perturbation collapses time-reversal fidelity to 19.74%. The universal master equation is validated across 52 orders of magnitude in energy, spanning intracellular ATP metabolic pools, galvanic cells, and degenerate cooling white dwarfs.
We establish an end-to-end theoretical framework and numerical validation for the dissipation of metastable bound energy states, connecting empirical engineering lifetime forecasting of primary chemical cells to fundamental non-equilibrium quantum-informational thermodynamics. We prove that the irreversible relaxation of stored free energy Delta F into a thermal reservoir at temperature T is governed by the Planckian dissipation timescale tau_P = hbar / (k_B T) and the dimensionless Landauer information capacity Phi_0 = Delta F / (k_B T). Utilizing stochastic Langevin integration across a saddle-node bifurcation normal form, we uncover a universal power-law divergence of voltage noise variance prior to system collapse with critical exponent gamma = 1/2: Var(V, t) ~ (t_death - t)^(-1/2), offering an exact, non-invasive early-warning precursor for catastrophic failure. Furthermore, by numerically solving the exact unitary Schrodinger equation for an 8-qubit non-integrable chaotic Heisenberg spin chain via the Loschmidt Echo protocol, we demonstrate that macroscopic thermodynamic irreversibility emerges from many-body quantum information scrambling (reaching 72.1% of the Page thermalization entropy), wherein a microscopic 5% Hamiltonian perturbation collapses time-reversal fidelity to 19.74%. The universal master equation is validated across 52 orders of magnitude in energy, spanning intracellular ATP metabolic pools, galvanic cells, and degenerate cooling white dwarfs.
Quantum reservoir computing provides a framework for processing complex temporal data, yet its fundamental computational and energetic limits remain unresolved. Here, we establish a non-equilibrium thermodynamic framework that links the macroscopic predictive performance of driven open quantum systems to their microscopic energetic costs. By mapping Holevo capacities onto the Bogoliubov-Kubo-Mori geometric manifold, we analytically prove that the computational peak within the quantum critical region originates from a spectral resonance: the closing of the intrinsic energy gap forces the reservoir's internal transition frequencies to align with the chaotic drive. To evaluate the associated thermodynamic costs, we introduce quantum informational dissipation to quantify the non-predictive historical data retained by the reservoir. This allows us to derive a generalized Landauer bound for continuous temporal processing, which reveals a fundamental thermodynamic trade-off: the critical resonance that maximizes predictive capacity simultaneously maximizes informational dissipation and the irreversible work required for environmental erasure. Furthermore, coherence decomposition demonstrates that quantum coherences amplify predictive capacity without demanding additional mechanical work. These findings establish the fundamental energetic limits of quantum learning devices, providing theoretical principles for designing energy-efficient quantum neuromorphic hardware.
The emergence of irreversibility in physical processes, despite the fundamentally reversible nature of quantum mechanics, remains an open question in physics. This thesis explores the intricate relationship between quantum mechanics and thermodynamics, with a particular focus on minimizing entropy production in finite-time processes. By employing tools from quantum information theory and geometric thermodynamics, we tackle the challenge of deriving irreversible thermodynamic behavior from the reversible microscopic framework of quantum mechanics. We begin with a comprehensive review of the laws of thermodynamics, setting the stage for the subsequent analyses. We introduce novel developments in quantum thermodynamics through a generalized framework for geometric thermodynamics, which enables the derivation of finite-time corrections beyond the Markovian regime. Building on this foundation, we extend Landauer's principle by incorporating a finite-time correction that highlights the necessity of strong coupling for optimal information erasure processes. This result underscores the emergence of Planckian time as a fundamental speed limit to thermalization. Additionally, we explore how collective effects can be harnessed to reduce energy dissipation in thermodynamic operations, revealing that classical correlations between systems can significantly mitigate dissipation, though this may pose new questions regarding the third law of thermodynamics. Finally, we optimize thermodynamic processes in mesoscopic systems, including quantum dot engines and information engines. These findings not only enhance our understanding of the fundamental limits of irreversibility but also open new avenues for research. Future works will focus on fully exploiting collective effects, aligning these with the third law of thermodynamics, and understanding the thermodynamic consistency of master equations.
Observer-information entropy production quantifies the loss of recoverable information about a physical source when an already formed observation undergoes source-independent irreversible degradation. The statistical second-law statement Σobs[s,t]=I(X;Rs)−I(X;Rt)=I(X;Rs∣Rt)≥0 follows from data processing, but by itself it does not identify a physical energetic or thermodynamic cost. This paper establishes such a connection within an explicit and deliberately restricted stochastic-thermodynamic regime. We consider a finite observer memory Rt coupled to a single heat bath at temperature T. A source label X is fixed during the passive relaxation, the transition generator of Rt is independent of X, and the memory dynamics satisfies detailed balance with respect to a strictly positive equilibrium law q. For the joint source--memory ensemble and for the unconditioned memory marginal, we define the standard stochastic-thermodynamic entropy-production rates. Using the relative-entropy chain rule and the detailed-balance H-theorem, we prove the exact correlation-dissipation decomposition kBS˙totXR=σobs+kBS˙totR. Consequently, S˙totXR≥kBσobs,ΔStotXR[s,t]≥kBΣobs[s,t]. At fixed temperature the same result is an excess-free-energy dissipation bound, \[ \Fex_{XR}(s)-\Fex_{XR}(t) \ge k_BT\Sigma_{\mathrm{obs}}[s,t]. \] Equality holds when the memory marginal remains at equilibrium, in which case all thermodynamic irreversibility is attributable to the destruction of source--record correlation. A symmetric two-state memory provides an exactly solvable saturation example. The result is not a universal Landauer principle. It constrains total entropy production and loss of nonequilibrium free energy during passive decorrelation; it does not assert a universal heat or work cost for arbitrary information loss. Driven memories, source-dependent transition rates, active measurement, feedback, multiple reservoirs, and nonequilibrium steady states require the broader information-thermodynamic bookkeeping developed in stochastic thermodynamics. We then place the thermodynamic result beside two Fisher--Shannon bridges. Under Gaussian observation heat flow Yt=X+Bt, observer-information dissipation obeys the exact identity σobs(t)=21(td−J(Yt))=2t21mmse(X∣Yt), while pairwise statistical distinguishability obeys \[ \frac{d}{dt}\KL(p_t\|q_t) =-\frac12\Jrel(p_t\|q_t). \] Recent temporal-Fisher speed-limit results provide a complementary route from physical entropy production to the speed of probability evolution. Together these results separate three objects that are often conflated: thermodynamic irreversibility, Shannon information loss about the physical source, and Fisher-geometric statistical motion. The paper thereby supplies a physical-cost layer for observer information theory without identifying information with energy or thermodynamic entropy.
Abstract The quantum measurement problem arises from the coexistence of unitary Schr¨odinger evolution with the apparent nonunitary collapse of quantum states during observation. Despite extensive theoretical development, no consensus has been reached on a microscopic physical mechanism for state reduction within standard quantum theory. In this work, we present a complete dynamical theory of quantum measurement in which wavefunction collapse emerges from irreversible information transfer and entropy production in realistic system–detector–environment interactions. Starting from microscopic Hamiltonian models, we derive a stochastic nonlinear evolution equation for conditioned quantum states without introducing additional axioms or phenomenological parameters. We demonstrate that the effective collapse rate is uniquely determined by environmental entropy production and remains well-defined in thermal, non-Markovian, chaotic, and zero-temperature regimes. Using stochastic calculus and martingale theory, we establish the dynamical emergence of the Born probability rule and prove almost-sure convergence of measurement trajectories to definite outcomes. The theory exhibits robust many-body amplification, universal behavior in nonlinear detectors, and mathematical well-posedness in both finite- and infinite-dimensional settings. Compatibility with algebraic quantum field theory, renormalization theory, and stochastic semiclassical gravity is established, ensuring consistency with relativistic and high-energy physics. Extensive numerical simulations confirm analytical predictions, and a comprehensive experimental program is proposed, together with rigorous validation and replication protocols. Logical analysis demonstrates compatibility with Bell nonlocality, resolution of Wigner’s friend and Frauchiger–Renner paradoxes, and compliance with information-theoretic constraints. These results provide a unified physical explanation of quantum measurement as an emergent nonequilibrium process governed by universal thermodynamic and informational principles, integrating state reduction into the standard dynamical framework of physics.
Autonomous quantum thermal machines have recently been proposed as physics-based computing substrates where logical inputs and outputs are encoded in temperature gradients. While such ``thermodynamic neurons'' exhibit a clear trade-off between computational fidelity and heat dissipation, the fundamental information-theoretic limits of temperature-encoded computation remain uncharacterized. Here, we derive rigorous bounds linking average error probability, channel capacity, and entropy production for finite-capacity thermal reservoirs operating far from equilibrium. We prove that the minimal dissipation required to achieve a target average error probability ⟨ξ⟩ diverges as ⟨ξ⟩ approaches a fundamental minimum error floor $\epsMin$ imposed by finite-reservoir thermal fluctuations. We further establish a thermodynamic channel capacity that saturates at high dissipation, and quantify the minimal dissipation required for cascaded networks to maintain target fidelity. We demonstrate that the required dissipation grows linearly O(L) with network depth for shallow networks, but diverges as the network depth L approaches a fundamental maximum limit $L_{\max} = \epsNet/\epsMin$ imposed by the minimum error floor. Furthermore, under strong noise amplification conditions, the required dissipation can grow up to O(L3). Our framework bridges stochastic thermodynamics, finite-time information theory, and autonomous computation, providing rigorous design principles for energy-efficient analog thermodynamic hardware.
Based on the "Interface Projection Realism" framework, this paper rigorously derives the universal formula for internal dissipation power and the microscopic expression for the energy distribution ratio f from first principles. We treat the qubit (Q), the interfacial defect network (D), and the bulk dissipation channel (B) as a self-contained total system, no longer presupposing any part of it as an external environment. By applying the Born-Markov approximation to the degrees of freedom of D and B, we obtain the reduced master equation for Q, and subsequently calculate the net energy flow rate from Q to the incoherent degrees of freedom—the internal dissipation power R_internal. The result is: R_internal = ħω_q [Γ↓ ⟨n⟩ - Γ↑ (1-⟨n⟩)], where Γ↓ and Γ↑ are transition rates determined by the Q-D coupling and the internal structure of D, and ⟨n⟩ is the excited state population of Q. This formula does not rely on any thermal equilibrium assumptions and is applicable to arbitrary Markovian non-equilibrium steady states. Building on this, we define the total effective power absorbed by the system as R_total = ⟨∂H_drive/∂t⟩ and introduce the system's stored energy E_stored = ⟨H_Q⟩. Under periodic averaging, the energy conservation equation reads dE_stored/dt = R_total - R_internal, where the overline denotes time average. The energy distribution ratio f = R_internal / R_total satisfies f = 1 in the periodic steady state where dE_stored/dt = 0; during transients, f can deviate from 1, its specific expression depending on microscopic parameters, reflecting the degree of deviation from the steady state. We further demonstrate that when D and B are in thermal equilibrium, the above formula reduces to the traditional fluctuation-dissipation theorem. This paper proves that the universal formula for internal dissipation power naturally contains the fluctuation-dissipation theorem under thermal equilibrium conditions, while its validity in non-equilibrium states constitutes a non-equilibrium generalization of the traditional theorem, providing a unified theoretical foundation for understanding the energetic origin of quantum decoherence.