We derive detailed and intergral fluctuation relations as well as a thermodynamic uncertainty relation constraining the exchange statistics of an arbitrary number of noncommuting conserved quantities among two quantum systems in transport setups arbitrary far from equilibrium. These universal relations, valid without the need of any efficacy parameter, extend the well-known heat exchange fluctuation theorems for energy and particle transport to the case of non-Abelian quantum transport, where the noncommutativity of the charges allows going beyond standard thermodynamic behavior. In particular, we show that this can lead to enhanced precision in the current fluctuations, and it allows for the inversion of all currents against their affinity biases.
We derive detailed and intergral fluctuation relations as well as a thermodynamic uncertainty relation constraining the exchange statistics of an arbitrary number of noncommuting conserved quantities among two quantum systems in transport setups arbitrary far from equilibrium. These universal relations, valid without the need of any efficacy parameter, extend the well-known heat exchange fluctuation theorems for energy and particle transport to the case of non-Abelian quantum transport, where the noncommutativity of the charges allows going beyond standard thermodynamic behavior. In particular, we show that this can lead to enhanced precision in the current fluctuations, and it allows for the inversion of all currents against their affinity biases.
Noncommutativity of observables is a defining feature of quantum physics. It plays a fundamental role in the formulation of the uncertainty principle for complementary variables and strongly affects the thermodynamic behavior of systems with noncommuting, that is, non-Abelian, conserved quantities. We here derive extensions of the first and second laws of thermodynamics, including nonequilibrium fluctuation relations, for driven quantum systems. We identify an additional non-Abelian contribution to the energy and entropy balances, without which these relations would be violated. This contribution can be harnessed to enhance both work extraction and nonequilibrium currents compared to what is achieved in commuting thermodynamics. These results demonstrate that noncommutativity is a potentially valuable thermodynamic resource.
Thermodynamic uncertainty relations (TURs) bound the precision of currents by entropy production, but quantum transport of noncommuting (non-Abelian) charges challenges standard formulations because different charge components cannot be monitored within a single classical frame. We derive a process-level matrix TUR starting from the operational entropy production Σ=D(ρSE′∥ρS′⊗ρE). Isolating the experimentally accessible bath divergence Dbath=D(ρE′∥ρE), we prove a fully nonlinear, saturable lower bound valid for arbitrary current vectors Δq: Dbath≥B(Δq,V,V′), where the bound depends only on the transported-charge signal Δq and the pre/post collision covariance matrices V and V′. In the small-fluctuation regime Dbath≥21ΔqTV−1Δq+O(∥Δq∥4), while beyond linear response it remains accurate. Numerical strong-coupling qubit collisions illustrate the bound and demonstrate near-saturation across broad parameter ranges using only local measurements on the bath probe.
We extend entropy production to a deeply quantum regime involving noncommuting conserved quantities. Consider a unitary transporting conserved quantities (“charges”) between two systems initialized in thermal states. Three common formulas model the entropy produced. They respectively cast entropy as an extensive thermodynamic variable, as an information-theoretic uncertainty measure, and as a quantifier of irreversibility. Often, the charges are assumed to commute with each other (e.g., energy and particle number). Yet quantum charges can fail to commute. Noncommutation invites generalizations, which we posit and justify, of the three formulas. The noncommutation of charges, we find, breaks the equivalence of the formulas. Furthermore, different formulas quantify different physical effects of the noncommutation of charges on entropy production. For instance, entropy production can signal contextuality—true nonclassicality—by becoming nonreal. This work opens up stochastic thermodynamics to noncommuting—and so particularly quantum—charges. Published by the American Physical Society 2024
Thermodynamic uncertainty relations (TURs) bound current precision by entropy production, but transport of noncommuting (non-Abelian) charges lacks a single joint classical record of all current components. We derive an operational, process-level matrix TUR for this setting from the entropy production Σ=D(ρ_{SE}^{'}∥ρ_{S}^{'}⊗ρ_{E}). Isolating the bath divergence D_{bath}=D(ρ_{E}^{'}∥ρ_{E}), we prove a fully nonlinear, saturable lower bound valid for arbitrary current vectors Δq: D_{bath}≥B(Δq,V,V^{'}), where the bound depends only on the transported-charge signal Δq and on the pre- and postcollision covariance matrices V and V^{'} reconstructed from separate probe measurement settings. In the small-fluctuation regime D_{bath}≥1/2Δq^{T}V^{-1}Δq+O(∥Δq∥^{4}), while beyond linear response the full integral bound remains valid. Numerical strong-coupling qubit collisions illustrate the bound and its near-saturation using only local measurements on the bath probe.
Abstract We study the fluctuations of generic currents in multi-terminal, multi-channel coherent quantum transport settings. In the quantum regime, these fluctuations and the resulting precision differ strongly depending on whether the device is of fermionic or bosonic nature. Using scattering theory, we show that the precision is bounded by constraints set by the entropy production and by the activity in the spirit of thermodynamic or kinetic uncertainty relations, valid for fermionic and bosonic quantum systems also in the absence of time-reversal symmetry. Furthermore, we derive a combined thermodynamic kinetic uncertainty relation, which is tight over a wide range of parameters and can hence predict the reachable precision of a device. Since these constraints can be expressed in terms of observables accessible in transport measurements, such as currents and bandwidth, we foresee that the tight thermodynamic kinetic uncertainty-like bounds are also useful as an inference tool: they can be exploited to estimate entropy production from transport observables, such as the charge current and its noise, which are more easily accessible in experiment.
Temperature uncertainty of a quantum system in canonical ensemble is inversely determined by its energy fluctuation, which is known as the temperature-energy uncertainty relation. No such uncertainty relation was discovered for a non-equilibrium open quantum system. In this article, we derive a universal temperature uncertainty relation for general non-equilibrium processes. We find that it is the fluctuation of heat, which is defined as the change in bath energy, determines the temperature uncertainty in non-equilibrium case. Specifically, the heat is divided into trajectory heat and backaction heat, which are associated with the system's trajectory of evolution and the backaction of partial measurement on system, respectively. Based on this decomposition, we reveal that both correlations between system and bath's process function and state function are the resources for enhancing temperature precision. Our findings are conductive to design ultrahigh sensitive quantum thermometer.