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.
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.
We derive a thermodynamic quantum speed limit for irreversible processes: (kB ∆Σ)·τ ≥ ■/(2T), where ∆Σ is the entropy produced in units of kB , τ is the process duration, T is the temperature, and ■ is thereduced Planck constant. We call this the Parker Relation. It is derived by two routes for thermalLindblad channels in the weak-coupling limit (γ/ω ■ 1): (1) the Deffner–Lutz quantum speed limit foropen systems applied to the amplitude damping channel, with a Hilbert–Schmidt norm bound on theLindblad generator rigorous to leading order in γ/ω; and (2) the open-system Margolus–Levitin bound,where the effective driving energy T × kB × ∆Σ follows from the free energy budget of a Markovianthermal channel with no external work. We establish explicitly when the relation is novel versus when itreduces to existing bounds. For thermal relaxation (∆Σ = ■ω/kB T) the Parker bound reproduces thestandard Mandelstam–Tamm result τ ≥ 1/(2ω) — a consistency check. For Landauer logical erasure (∆Σ= ln 2) the bound is independent of existing quantum speed limits. The classical bridge is established viathe incoherent limit of the quantum amplitude damping channel, which reduces exactly to the classicaltwo-state master equation governing bistable erasure devices. ■ appears in the classical bound becauseevery thermal bath has a quantum mechanical substrate; the classical Fisher–Rao speed limit combinedwith the quantum-limited attempt frequency ν0~ kBT/■ gives τmin ~ ■/(2kB T) to within a numericalprefactor of order unity (see Appendix A). The primary novel prediction is the minimum time forirreversible bit erasure at 300 K: τ min = ■/(2kB T ln 2) = 18.4 femtoseconds — a quantum-derivedfoundational floor that real CMOS devices exceed by 8 orders of magnitude. For a 5 GHz transmon at20 mK the bound gives τ min ≈ 16 ns — 60 000× below current best T2 values, a consistency check not anovel prediction. Four open questions are identified: tightening the generator norm bound numericallyvia QuTiP; completing the Route 2 formal connection to del Campo–Funo; extending beyond thermalLindblad channels; and completing the classical bridge via Nicholson et al. or Dechant. The relation isconjectured to hold generally for all irreversible processes at temperature T.
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.
The Landauer's principle, a cornerstone of information thermodynamics, provides a fundamental lower bound on the energetic cost of information erasure in terms of the information content change. However, its traditional formulation is largely confined to systems exchanging solely energy with an ideal thermal bath. In this work, we derive general information-cost trade-off relations that go beyond the scope of Landauer's principle by developing a thermodynamic inference approach based on the maximum entropy principle. These relations require only information about the system and are applicable to complex quantum scenarios involving multiple conserved charges and non-thermal environments. Specifically, we present two key results: (i) In scenarios where only the mean values of observables are accessible, we derive an information-content-informed upper bound on the thermodynamic cost which complements an existing generalized Landauer lower bound. (ii) When second-order fluctuations can also be measured, we obtain an information-content-informed lower bound on the change in variances of observables, thereby extending the Landauer's principle to constrain higher-order fluctuation costs. We numerically validate our information-cost trade-off relations using a coupled-qubit system exchanging energy and excitations, a driven qubit implementing an information erasure process, and a driven double quantum dot system that can operate as an inelastic heat engine. Our results underscore the broad utility of maximum-entropy inference in constraining thermodynamic costs for generic finite-time quantum processes, with direct relevance to quantum information processing and quantum thermodynamic applications.
The thermodynamic uncertainty relation (TUR) imposes a fundamental constraint between current fluctuations and entropy production, providing a refined formulation of the second law for micro- and nanoscale systems. Quantum violations of the classical TUR reveal genuinely quantum thermodynamic effects, which are essential for improving performance and enabling optimization in quantum technologies. In this work, we analyze the TUR in a class of paradigmatic quantum thermal-machine models whose operation is enabled by coherent coupling between two energy levels forming a virtual qubit. Steady-state coherences are confined to this virtual-qubit subspace, while in the absence of coherent coupling the system satisfies detailed balance with the thermal reservoirs and supports no steady-state heat currents. We show that the steady-state currents and entropy production can be fully reproduced by an effective classical Markov process, whereas current fluctuations acquire an additional purely quantum correction originating from coherence. As a result, the thermodynamic uncertainty naturally decomposes into a classical (diagonal) contribution and a coherent contribution. The latter becomes negative under resonant conditions and reaches its minimum at the coupling strength that maximizes steady-state coherence. We further identify the conditions for minimizing the thermodynamic uncertainty, and the criteria for surpassing the classical TUR bound in the vicinity of the reversible limit.
The Constant Δ𝐻 Principle: Quantized Potential Differences as the Origin of Time, Matter,and Observable FieldsWe propose the Constant Δ𝐻𝑓𝑖𝑒𝑙𝑑 Principle: that all physical systems must possess a non-zerominimum energy difference Δ𝐻𝑓𝑖𝑒𝑙𝑑 = 𝐸𝑏𝑎𝑟𝑟𝑖𝑒𝑟 − 𝐸0 between two resolvable states. We showthat the Heisenberg Uncertainty Principle, Δ𝐸 ⋅ Δ𝑡 ≥ℏ2, emerges geometrically from theboundedness of this interval. Macroscopic entropy is shown to arise statistically from theensemble of microstate Δ𝐻 − 𝑓𝑙𝑖𝑝𝑠, unifying information theory 𝐼 = − ∑ 𝑝𝑖𝑙𝑜𝑔𝑝𝑖 withthermodynamics 𝑆 = 𝑘𝐵 ln𝛺. We present three falsifiable predictions: 1. A minimum energygap in all systems, 2. A frequency cutoff for interactions, and 3. The origin of 1/𝑓 noise inunresolved Δ𝐻 flips. Applications are discussed for quantum computing, where decoherenceis an unwanted Δ𝐻 flip; for cosmology, where Dark Energy is the sum of vacuum Δ𝐻; and formaterials, where band engineering is Δ𝐻 engineering. This work reframes physics from thestudy of "what is" to the study of "the difference between". It suggests that reality, time, andinformation are consequences of a fundamental, conserved interval.Keywords: Uncertainty Principle, Quantum Foundations, Information Theory, Entropy,Decoherence, Dark Energy
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.