Generic far-away-from-equilibrium many-body dynamics involve entropy production and hence is thermodynamically irreversible. Near quantum critical points, an emergent conformal symmetry can impose strong constraints on entropy production rates and in some cases can completely forbid entropy production, which usually occurs for systems that deviate from quantum critical points. In this article, we illustrate how the vanishing entropy production near a quantum critical point results in reversible far-away-from-equilibrium dynamics at finite temperatures that is otherwise irreversible. Away from the quantum critical point, the quantum dynamics is damped, and our analysis directly relates the thermalization timescale to the hydrodynamic viscosity near quantum critical points with the dynamical critical exponent $z=2$. We demonstrate how both controllable reversible and irreversible dynamics can be potentially studied in cold gas experiments using Feshbach resonances.
Generic far-away-from-equilibrium many-body dynamics involve entropy production and hence is thermodynamically irreversible. Near quantum critical points, an emergent conformal symmetry can impose strong constraints on entropy production rates and in some cases can completely forbid entropy production, which usually occurs for systems that deviate from quantum critical points. In this article, we illustrate how the vanishing entropy production near a quantum critical point results in reversible far-away-from-equilibrium dynamics at finite temperatures that is otherwise irreversible. Away from the quantum critical point, the quantum dynamics is damped, and our analysis directly relates the thermalization timescale to the hydrodynamic viscosity near quantum critical points with the dynamical critical exponent z=2. We demonstrate how both controllable reversible and irreversible dynamics can be potentially studied in cold gas experiments using Feshbach resonances.
In this article we study the quench dynamics of Galilean and scale-invariant many-body systems which can be prepared using interacting atomic gases. The far-from-equilibrium dynamics is investigated by employing m-body density matrices, which are most conveniently defined in terms of a special basis, the conformal tower states. We explicitly illustrate that, although during the initial stage of the dynamics all symmetries can be broken and absent in the unitary evolution because of the initialization of the state, there is always an emergent conformal symmetry in the long-time limit. The emergence of this dynamic conformal symmetry is robust and always occurs, even when scale and other symmetries (such as rotational symmetry) are still fully broken in the many-body states; it uniquely defines the characteristics of the asymptotic dynamics near a scale-invariant strong-coupling fixed point. As an immediate application of the asymptotic dynamics of the microscopic density matrices, we focus on the effects of this emergent conformal symmetry on two observables: the moment of inertia tensor Iij(t),i,j=x,y,z, and the entropy density field S(r,t) in the hydrodynamic flow of strongly interacting particles. We show that the long-time behavior of these observables is completely set by conformal symmetry, while the leading long-time corrections depend on interference effects between different conformal tower states. The emergent conformal symmetry naturally leads to entropy conservation and conformal cooling, an energy-conserving cooling of a strongly interacting gas during free expansion. When the interaction Hamiltonian breaks the scale symmetry, we further demonstrate that there is a direct cause-effect relation between conformal symmetry breaking in the long-time limit and a nonvanishing entropy production. This suggests that the entropy production rate is a natural parameter for categorizing the breaking of conformal symmetry.
Conformal symmetry heavily constrains the dynamics of nonrelativistic quantum gases tuned to a nearby quantum critical point. One important consequence of this symmetry is that entropy production can be absent in far-away-from-equilibrium dynamics of strongly interacting three-dimensional (3D) and one-dimensional (1D) quantum gases placed inside an adjustable harmonic trapping potential. This can lead to an oscillatory fully revivable many-body dynamic state, which is reflected in many physical observables. In this article we further investigate the consequences of conformal symmetry on (a) the zero-temperature autocorrelation function, (b) the Wigner distribution function, and (c) the von Neumann entanglement entropy. A direct calculation of these quantities for generic strongly interacting systems is usually extremely difficult. However, we have derived the general structures of these functions in the nonequilibrium dynamics when their dynamics are constrained by conformal symmetry. We obtain our results for (a) by utilizing an operator-state correspondence which connects the imaginary time evolution of primary operators to different initial states of harmonically trapped gases, while the dynamics of the functions in (b) and (c) are derived from conformal invariant density matrices.
Quantum phase transitions occur strictly at zero temperature and are accessed by varying a physical parameter such as a magnetic field or chemical potential. While these transitions themselves are experimentally inaccessible, the existence of a zero temperature quantum critical point has remarkable effects on the dynamical properties of interacting quantum many-body systems at finite temperatures. In this thesis, we study dynamics in four strongly interacting many-body systems near quantum critical points in the context of NMR relaxation, quantum quenches, many-body quantum chaos, and charge diffusion. In chapter 1, we begin by revisiting the issue of NMR relaxation in the quantum disordered phase of Ising spin chains. We find that the imaginary part of the spin susceptibility at low frequences is dominated by rare quantum processes which leads to an NMR relaxation rate that scales as 1/T1∼exp(−T2Δ) near the quantum critical point rather than the previously conjectured 1/T1∼exp(−TΔ). These results resolve certain discrepancies between the energy scales measured with different experimental probes in the quantum disordered paramagnetic phase of the Ising chain system CoNb2O6. In chapter 2, we study the non-equilibrium dynamics of Sachdev-Ye-Kitaev (SYK) models with q body interactions after a quantum quench, considering a quench protocol which drives the system from an initial state with long-lived quasiparticle excitations to a final state lacking any long-lived quasiparticle excitations. For q=4, we find that the timescale for the system to locally thermalize τeq∼kBTℏ and for q→∞ we find that the system thermalizes instantaneously. In chapter 3, we study the real time dynamics of quantum electrodynamics in 2+1 dimensions with Nf flavors of fermions. We focus on thermalization and the onset of many-body quantum chaos and compute the quantum Lyapunov exponent in a Nf1 expansion. We briefly comment on chaos, locality, and gauge invariance. Finally, in Chapter 4 we consider whether the butterfly velocity - a speed at which quantum information propagates - may provide a fundamental bound on diffusion constants in dirty incoherent metals by computing the charge diffusion constant and the butterfly velocity in charge-neutral holographic matter with long wavelength ``hydrodynamic" disorder. In this limit, we find that the butterfly velocity does not set a sharp lower bound for the charge diffusion constant.
Phase transitions represent fundamental transformations of matter, characterized by abrupt changes in macroscopic properties and often associated with singular behavior at critical points. While equilibrium aspects of phase transitions, particularly universal critical exponents and scaling laws, are well-understood, the non-equilibrium processes occurring near criticality, especially the production of entropy, remain a rich area of investigation. This paper explores the intricate relationship between critical entropy production and the emergence of scaling laws in systems undergoing phase transitions. We delve into how the rate of entropy production diverges or exhibits anomalous scaling near critical points, reflecting the system's attempts to dissipate energy and respond to external perturbations as it approaches a state of macroscopic change. By integrating concepts from non-equilibrium thermodynamics, statistical mechanics, and renormalization group theory, we aim to elucidate the underlying mechanisms that govern entropy generation in these critical regimes. We discuss theoretical frameworks that predict universal scaling behaviors for entropy production rates, analogous to those observed for equilibrium order parameters and susceptibilities. The implications of these scaling laws extend beyond theoretical physics, offering insights into complex systems, far-from-equilibrium dynamics, and the efficiency of energy conversion processes in critical environments. Our analysis highlights the critical entropy production as a unique signature of non-equilibrium dynamics during phase transitions, providing a deeper understanding of the interplay between fluctuations, dissipation, and universality near points of instability.
We consider the temporal evolution of an isolated system of particles from a non-equilibrium state of entropy S = S′ to the equilibrium state of maximum entropy S = S max, S′ ≤ S max. The application of usual density matrix theory to the temporal development of S leads us to the unexpected result P = dS/dt = 0. The entropy does not change in time. This result is valid in case of the equilibrium state. However it is wrong for a non-equilibrium state, which could not irreversibly change from S′ to S max by entropy production P > 0. This contradicts the second law of thermodynamics. The paradoxial result can be traced back to the Liouville theorem. To overcome this difficulty, we introduce the t–P space. The time t and the entropy production P are observables in quantum thermodynamics. They are defined by the eigenvalue equations t|t〉 = t|t〉 and P|P〉 = P|P〉. The operators t and P do not commute. We have a non-vanishing commutator, [t,P] = ik, and consequently a t–P uncertainty relation, ΔtΔP ≥ k/2. The Boltzmann constant k is characteristic of quantum thermodynamics and represents the atomic entropy unit. — The time evolution operator U(τ) = exp[−(i/k)τP] shifts the time t by τ, U(τ)|t〉 = |t + τ〉. The generator of τ is the operator P of entropy production. Then the eigenvector |P〉 is also an eigenket of U(t), and it follows with progressing time τ ≥ 0 that τP ≥ 0 and hence P = dS/dt ≥ 0. This is the second law of thermodynamics, which is correctly reproduced in quantum thermodynamics. — Exchanging −τ for +τ replaces the equations of forward time +τ by the equations of backward time −τ. Independent of the direction of the arrow of time, the entropy of the system always increases or remains constant in the limit of the equilibrium state, dS ≥ 0. This is characteristic of irreversibility, for the system does not return to its initial state on time reversal. — The t–P uncertainty relation allows to discuss the temporal evolution of the expectation value 〈P〉 of entropy production and the lifetime Δt of the transient states, the system passes through on approaching the equilibrium state. In case of a non-equilibrium state 〈P〉, ΔP, and Δt are finite. On approaching the equilibrium state, 〈P〉 and ΔP decrease, consequently Δt increases. Finally, in the case of equilibrium (eq), we have 〈P〉eq = 0, ΔP eq = 0, and Δt eq → ∞. The lifetime of the equilibrium state is unlimited, because the entropy production 〈P〉 and the uncertainty of entropy production ΔP exactly vanish. The temporal evolution of the system can be described by means of a phenomenological equation.
Symmetries play a central role in both equilibrium and nonequilibrium phase transitions, yet their quantitative characterization in dynamical quantum phase transitions (DQPTs) remains an open challenge. In this work, we establish a direct connection between symmetry properties of a many-body model and measures of quantum asymmetry, showing that asymmetry monotones provide a robust and physically transparent indicator of dynamical quantum criticality. Focusing on the quenched Lipkin-Meshkov-Glick model, we demonstrate that asymmetry measures associated with collective spin generators faithfully capture the onset of DQPTs, reflecting the dynamical restoration or breaking of underlying symmetries. Remarkably, the time-averaged asymmetry exhibits clear signatures of the dynamical critical point, in close correspondence with both the dynamical order parameter and the behavior of entropy production. We further uncover a quantitative link between asymmetry generation and thermodynamic irreversibility, showing that peaks in asymmetry coincide with maximal entropy production across the transition. Our results position asymmetry as a unifying concept bridging symmetry, information-theoretic quantifiers, and nonequilibrium thermodynamics in dynamical quantum phase transitions, providing a powerful framework for understanding critical dynamics beyond traditional order parameters.