We derive an operationally defined lower bound on the physical time \( \Delta t \)required to execute any information-processing task, based on the total entropy produced \( \Delta\Sigma \). The central result, \( \Delta t \geq \tau_{\Sigma} \Delta\Sigma \), introduces the Process-Dependent Dissipation Timescale \( \tau_{\Sigma} \equiv 1/\langle \dot{\Sigma} \rangle_{\text{max}} \), which quantifies the maximum achievable entropy production rate for a given physical platform. We derive \( \tau_{\Sigma} \) from microscopic system-bath models and validate our framework against experimental data from superconducting qubit platforms. Crucially, we obtain a Measurement Entropic Time Bound:\( \Delta t_{\text{meas}} \geq \tau_{\Sigma} k_{\text{B}}[H(P) - S(\rho)] \), relating measurement time to information gained. Comparison with IBM and Google quantum processors shows agreement within experimental uncertainties. This framework provides a thermodynamic interpretation of quantum advantage as reduced entropy production per logical inference and suggests concrete optimization strategies for quantum hardware design.
We derive an operationally defined lower bound on the physical time ( \Delta t )required to execute any information-processing task, based on the total entropy produced ( \Delta\Sigma ). The central result, ( \Delta t \geq \tau_{\Sigma} \Delta\Sigma ), introduces the Process-Dependent Dissipation Timescale ( \tau_{\Sigma} \equiv 1/\langle \dot{\Sigma} \rangle_{\text{max}} ), which quantifies the maximum achievable entropy production rate for a given physical platform. We derive ( \tau_{\Sigma} ) from microscopic system-bath models and validate our framework against experimental data from superconducting qubit platforms. Crucially, we obtain a Measurement Entropic Time Bound:( \Delta t_{\text{meas}} \geq \tau_{\Sigma} k_{\text{B}}[H(P) - S(\rho)] ), relating measurement time to information gained. Comparison with IBM and Google quantum processors shows agreement within experimental uncertainties. This framework provides a thermodynamic interpretation of quantum advantage as reduced entropy production per logical inference and suggests concrete optimization strategies for quantum hardware design.
Quantum information reset is an intrinsically irreversible process constrained by the second law of thermodynamics. In contemporary superconducting processors, dissipation during qubit reset is frequently dominated not only by quantum limits but by a classical energy floor on the order of 10^{-21} J. In contrast, the entropic bound T \Delta S at dilution refrigerator temperatures (\sim 15 mK) corresponds to a lower energy scale of approximately 10^{-23} J, establishing entropy production as the organizing physical principle that limits both the efficiency and the speed of reset operations. We introduce an entropy-limited efficiency estimator, \eta_S = 1 - (T \Delta S / W_{\rm diss}), which quantifies the thermodynamic distance from the entropic (Landauer) limit. By construction, \eta_S = 0 corresponds to the saturation of the entropy production limit, while \eta_S \to 1 indicates dissipation dominated by non-entropic (classical) contributions. Maximizing \eta_S is equivalent to a constrained variational problem in which dissipated work is minimized subject to the second law of thermodynamics. For typical superconducting qubits (\omega_q/2\pi \sim 5 GHz, T_1 \sim 50–100 \mus, T \sim 15 mK), the entropic bound T \Delta S \sim 10^{-23} J lies two orders of magnitude below the experimentally observed classical dissipation floor W_{\rm floor} \sim 10^{-21} J. Figures 1 and 2 were generated using the provided scripts_generate_figures.py script, using parameters: \omega_q/2\pi = 5 GHz, T_1 = 80 \mus, and T = 15 mK.
Dissipation is vital to any cyclic process in realistic systems. Recent research focus on nonequilibrium processes in stochastic systems has revealed a fundamental trade-off, called dissipation-time uncertainty relation, that entropy production rate associated with dissipation bounds the evolution pace of physical processes [Phys. Rev. Lett. 125, 120604 (2020)PRLTAO0031-900710.1103/PhysRevLett.125.120604]. Following the dissipative two-level model exemplified in the same Letter, we experimentally verify this fundamental trade-off in a single trapped ultracold ^{40}Ca^{+} ion using elaborately designed dissipative channels, along with a postprocessing method developed in the data analysis, to build the effective nonequilibrium stochastic evolutions for the energy transfer between two heat baths mediated by a qubit. Since the dissipation-time uncertainty relation imposes a constraint on the quantum speed regarding entropy flux, our observation provides the first experimental evidence confirming such a speed restriction from thermodynamics on quantum operations due to dissipation, which helps us further understand the role of thermodynamical characteristics played in quantum information processing.
Given a fixed physical process, we consider the entropy production (EP) incurred by some initial state ρ, additional to the minimal EP incurred by the least-dissipative state φ. We show that this additional EP has a universal information-theoretic form, given by the contraction of the relative entropy between ρ and φ over time. This result holds for total integrated EP, instantaneous EP rate, and fluctuating EP. We derive novel bounds on EP, analyze the thermodynamics of quantum error correction, and propose a thermodynamically-motivated measure of the logical irreversibility of a channel.
We derive a fundamental uncertainty principle relating entropy change and time: for any quantum system coupled to a thermal environment, the entropy change ΔS and the characteristic timescale Δt satisfy ΔS·Δt ≥ kᴪ/2. We call this the Parker Relation. The derivation proceeds from the quantum Thermodynamic Uncertainty Relation (quantum TUR) of Hasegawa and Van Vu [Phys. Rev. E 99, 062126 (2019)], which holds for all quantum channels without restriction to quasi-static or equilibrium processes. We provide a second independent derivation from the canonical commutation relations of the entropy field operator Ś = ∫Φ√(-g) d³x, which yields the same bound through the Robertson inequality. Four immediate consequences are derived with explicit numerical predictions: (1) a minimum information erasure time of 18.4 femtoseconds at 300 K, establishing a fundamental floor on computational switching speed beyond any engineering constraint; (2) a minimum decoherence time of 53 nanoseconds for a 5 GHz superconducting transmon qubit at 20 mK; (3) an exponential suppression of high-frequency vacuum modes that removes 119 orders of magnitude from the cosmological constant ultraviolet divergence; and (4) a characteristic thermodynamic timescale of ~15 ms for living cells at physiological metabolic rates, coinciding with observed neural and cellular signaling timescales. The Parker Relation is interpretation-independent: it holds in Copenhagen, many-worlds, and objective collapse frameworks equally. It is the temporal complement of Landauer’s principle and the thermodynamic analog of the Heisenberg energy-time uncertainty relation.
This research establishes an operational lower bound on entropy production induced by mass gaps in quantum systems. Using completely positive trace-preserving (CPTP) dynamics, the study demonstrates that any physical reset of a system with a minimal spectral gap \delta_{min}=mc^{2} incurs a minimum entropy production defined by the relation \Sigma\ge mc^{2}/T. Unlike Landauer's principle, this bound follows purely from thermodynamic admissibility and spectral structure rather than logical irreversibility or information-theoretic arguments. Key Features of the Study: ELQR Framework: The research utilizes the Entropy-Limited Quantum Reset (ELQR) framework to model reset as a constrained CPTP control problem. Reinforcement Learning Validation: Optimization using RL agents (specifically PPO) shows that the theoretical bound emerges as a robust dynamical attractor under unconstrained control optimization. Hawking Emission Application: When applied to black-hole horizons, the bound implies a minimal entropic cost for Hawking emission per particle of mass m that is independent of information loss or Page-curve considerations. Many-Body Systems: Validated through tensor-network simulations (TeNPy) of short Heisenberg chains, confirming that the operational bound is robust even in correlated systems. Non-Markovian Extensions: Preliminary simulations of qubits coupled to memory show that while transient backflow occurs, the envelope remains consistent with the mass-induced limit.
Quantum thermodynamic uncertainty relations establish fundamental trade-offs between the precision achievable in quantum systems and associated thermodynamic quantities such as entropy production or dynamical activity. While foundational, empirical demonstrations have thus far been confined to specific cases, either assuming time-reversal symmetry or involving particular measurement types, leaving the verification of their universal validity unrealized. This work leverages a quantum computer to present the first empirical verification of a general quantum thermodynamic uncertainty relation, valid for arbitrary dynamics and observables. We theoretically derive the relation, identifying survival activity as the pivotal thermodynamic quantity governing the precision bound. The verification is demonstrated on IBM's cloud-based quantum processor, which is treated as a real thermodynamic system. To achieve accurate results despite substantial device errors, we introduce a generic protocol for measuring survival activity and employ circuit reduction techniques based on the relation's properties. This strategy allows us to empirically measure survival activity for the first time and confirm the derived relation. Furthermore, the quantum computer's versatility enables the implementation of optimal observables, leading to the saturation of the relation and demonstrating the sharpness of our bound on a physical device. The method's broad applicability is further illustrated by verifying the trade-off for quantum time correlators. Our findings establish quantum computers as effective platforms for investigating fundamental thermodynamic trade-off relations.