We show that for systems with broken time-reversal symmetry the maximum efficiency and the efficiency at maximum power are both determined by two parameters: a "figure of merit" and an asymmetry parameter. In contrast to the time-symmetric case, the figure of merit is bounded from above; nevertheless the Carnot efficiency can be reached at lower and lower values of the figure of merit and far from the so-called strong coupling condition as the asymmetry parameter increases. Moreover, the Curzon-Ahlborn limit for efficiency at maximum power can be overcome within linear response. Finally, always within linear response, it is allowed to have simultaneously Carnot efficiency and non-zero power.
We study the minimally nonlinear irreversible heat engines in which the time-reversal symmetry for the systems may b e broken. The expressions for the power and the efficiency are derived, in which the effects of the nonlinear terms due to dissipations are included. We show that, as within the linear responses, the minimally nonlinear irreversible heat engines enable attainment of Carnot efficiency at positive power. We also find that the Curzon-Ahlborn limit imposed on the efficiency at maximum power can be overcomed if the time-reversal symmetry is broken.
We show that when non-unitary noise effects are taken into account the thermopower is in general asymmetric under magnetic field reversal, even for non-interacting systems. Our findings are illustrated in the example of a three-dot ring structure pierced by an Aharonov-Bohm flux.
The thermodynamic uncertainty relation gives a lower bound on the amount of dissipation in a mesoscopic system. By considering the fluctuations in the hysteresis of the current -- the sum of the currents in the time-forward and time-reversed processes -- we extend this relation to systems with broken time-reversal symmetry, either due to the presence of odd state variables, odd driving field or due to explicit time-dependent driving that is time-reversal asymmetric. We illustrate our predictions on a dilute, weakly-interacting gas driven out of equilibrium by the slow compression of a piston a…
We consider heat transport through systems with broken time-reversal symmetry. We apply strong magnetic fields to weakly charged particle systems, where the dynamics are dominated by the Lorentz force and spring forces. The standard momentum conservation is not satisfied and the sound wave disappears depending on the charge structure. We introduce an exactly solvable model and demonstrate the appearance of a new universality class. The absence of sound waves affects the relation between equilibrium correlation and the diverging thermal conductivity in the open system.
We study the performance of a three-terminal thermoelectric device such as heat engine and refrigerator with broken time-reversal symmetry by applying the unified trade-off figure of merit ($\dotΩ$ criterion) which accounts for both useful energy and losses. For heat engine, we find that a thermoelectric device working under the maximum $\dotΩ$ criterion gives a significantly better performance than a device working at maximum power output. Within the framework of linear irreversible thermodynamics such a direct comparison is not possible for refrigerators, however, our study indicates that, f…
For a generic class of machines with broken time-reversal symmetry we show that in the linear response regime the relative fluctuation of the sum of output currents for time-forward and time-reversed processes is always lower bounded by the corresponding relative fluctuation of the sum of input currents. This bound is received when the same operating condition, for example, engine, refrigerator or pump, is imposed in both the forward and the reversed processes. As a consequence, universal upper and lower bounds for the ratio of fluctuations between the output and the input current is obtained.…
We characterize a system of hard spheres with a simple collision rule that breaks time reversal symmetry, but conserves energy. The collisions lead to an a-chiral, isotropic, and homogeneous stationary state, whose properties are determined in simulations and compared to an approximate theory originally developed for elastic hard spheres. In the nonequilibrium fluid state, velocities are correlated, a phenomenon known from other nonequilibrium stationary states. The correlations are long-ranged decaying like $1/r^d$ in $d$ dimensions. Such correlations are expected on general grounds far from …
We provide numerical evidence that the Onsager symmetry remains valid for systems subject to a spatially dependent magnetic field, in spite of the broken time-reversal symmetry. In addition, for the simplest case in which the field strength varies only in one direction, we analytically derive the result. For the generic case, a qualitative explanation is provided.
Universal properties of the statistics of stochastic efficiency for mesoscopic time-reversal symmetry broken energy transducers are revealed in the Gaussian approximation. We also discuss how the second law of thermodynamics restricts the statistics of stochastic efficiency. The tight-coupling (reversible) limit becomes unfavorable, characterized by an infinitely broad distribution of efficiency at {\em all times}, when time-reversal symmetry breaking leads to an asymmetric Onsager response matrix. The underlying physics is demonstrated through the integer quantum Hall effect and further elabo…
A system's invariance under Galilean transformation implies three locally conserved densities. Including them as variables, the thermodynamics is rendered explicitly frame independent, dissipative mass currents are shown to vanish, and spontaneously broken Galilean symmetry becomes a sensible concept in condensed systems.
We introduce a continuous time-reversal operation which connects the time-forward and time-reversed trajectories in the steady state of an irreversible Markovian dynamics via a continuous family of stochastic dynamics. This continuous time-reversal allows us to derive a tighter version of the thermodynamic uncertainty relation (TUR) involving observables evaluated relative to their local mean value. Moreover, the family of dynamics realizing the continuous time-reversal contains an equilibrium dynamics halfway between the time-forward and time-reversed dynamics. We show that this equilibrium d…
Superconductivity is associated with spontaneously broken gauge symmetry. In some exotic superconductors the time-reversal symmetry is broken as well, accompanied with internal magnetic field. A time-reversal symmetry broken (TRSB) superconductivity without internal magnetic field involved can be induced by frustrated inter-component couplings, which becomes a realistic issue recently due to the discovery of iron-pnictide superconductors. Here we derive stability condition for this novel TRSB state using the Ginzburg-Landau (GL) theory. We find that there are multiple divergent coherence lengt…
Strong-coupling statistical thermodynamics is formulated as Hamiltonian dynamics of an observed system interacting with another unobserved system (a bath). It is shown that the entropy production functional of stochastic thermodynamics, defined as the log-ratio of forward and backward system path probabilities, is in one-to-one relation with the log-ratios of joint initial conditions of the system and the bath. A version of strong-coupling statistical thermodynamics where the system-bath interaction vanishes at the beginning and the end of a process is, as is also weak-coupling stochastic ther…
We study the entropy production in non-equilibrium quantum systems without dissipation, which is generated exclusively by the spontaneous breaking of time-reversal invariance. Systems which preserve the total energy and particle number and are in contact with two heat reservoirs are analysed. Focussing on point-like interactions, we derive the probability distribution induced by the entropy production operator. We show that all its moments are positive in the zero frequency limit. The analysis covers both Fermi and Bose statistics.
The hamiltonian of an asymmetric diffusion process with injection and ejection of particles at the ends of a chain of finite length is known to be relevant to that of the spin-1/2 XXZ chain with integrable boundary terms. However, the inclusion of boundary sources and sinks of particles breaks the arrow-reversal symmetry necessary for solution via the usual Bethe Ansatz approach. Developments in solving the model in the absence of arrow-reversal symmetry are discussed.
We present an effective field theory for the nonlinear fluctuating hydrodynamics of a single conserved charge with or without time-reversal symmetry, based on the Martin-Siggia-Rose formalism. Applying this formalism to fluids with only charge and multipole conservation, and with broken time-reversal symmetry, we predict infinitely many new dynamical universality classes, including some with arbitrarily large upper critical dimensions. Using large scale simulations of classical Markov chains, we find numerical evidence for a breakdown of hydrodynamics in quadrupole-conserving models with broke…
Fluctuation-dissipation relations (FDRs) and time-reversal symmetry (TRS), two pillars of statistical mechanics, are both broken in generic driven-dissipative systems. These systems rather lead to non-equilibrium steady states far from thermal equilibrium. Driven-dissipative Ising-type models, however, are widely believed to exhibit effective thermal critical behavior near their phase transitions. Contrary to this picture, we show that both the FDR and TRS are broken even macroscopically at, or near, criticality. This is shown by inspecting different observables, both even and odd operators un…
We present an extensive experimental study of the distributions of the real and imaginary parts of the off-diagonal elements of the scattering matrix $\hat S$ and the Wigner's reaction $\hat K$-matrix for open microwave networks with broken time ($T$) reversal invariance. Microwave Faraday circulators were applied in order to break $T$-invariance. The experimental distributions of the real and imaginary parts of the off-diagonal entries of the scattering matrix $\hat S$ are compared with the theoretical predictions from the supersymmetry random matrix theory [A. Nock, S. Kumar, H.-J. Sommers, …
We experimentally demonstrate that highly structured distributions of work emerge during even the simple task of erasing a single bit. These are signatures of a refined suite of time-reversal symmetries in distinct functional classes of microscopic trajectories. As a consequence, we introduce a broad family of conditional fluctuation theorems that the component work distributions must satisfy. Since they identify entropy production, the component work distributions encode both the frequency of various mechanisms of success and failure during computing, as well giving improved estimates of the …
