Using the scaling relation of the ground state quantum fidelity, we propose the most generic scaling relations of the irreversible work (the residual energy) of a closed quantum system at absolute zero temperature when one of the parameters of its Hamiltonian is suddenly changed; we consider two extreme limits namely, the heat susceptibility limit and the thermodynamic limit. It is then argued that the irreversible entropy generated for a thermal quench at low enough temperature when the system is initially in a Gibbs state, is likely to show a similar scaling behavior. To illustrate this proposition, we consider zero-temperature and thermal quenches in one and two-dimensional Dirac Hamiltonians where the exact estimation of the irreversible work and the irreversible entropy is indeed possible. Exploiting these exact results, we then establish: (i) the irreversible work at zero temperature indeed shows an appropriate scaling in the thermodynamic limit; (ii) the scaling of the irreversible work in the 1D Dirac model at zero-temperature shows logarithmic corrections to the scaling which is a signature of a marginal situation. (iii) Furthermore, remarkably the logarithmic corrections do indeed appear in the scaling of the entropy generated if temperature is low enough while disappears for high temperatures. For the 2D model, no such logarithmic correction is found to appear.
In the framework of irreversible thermodynamics, we study autonomous systems of reaction-diffusion equations to show how the entropy and free energy of an open and irreversible reactor depend on concentrations. To do this, we find a Lyapunov function that depends directly on the eigenvalues and eigenvectors of the linearized problem valid for linear and asymptotically stable systems. By suggesting the role of this Lyapunov function as internal free energy, we were able to reflect the properties of the dynamical system directly into the second law of thermodynamics making a redefinition of the …
Linear, irreversible thermodynamics predicts that the entropy production rate can become negative. We demonstrate this prediction for metals under AC-driving whose conductivity is well-described by the Drude-Sommerfeld model. We then show that these negative rates are fully compatible with stochastic thermodynamics, namely, that the entropy production does fulfill a fluctuation theorem. The analysis is concluded with the observation that the stochastic entropy production as defined by the surprisal or ignorance of the Shannon information does not agree with the phenomenological approach.
The irreversible work during a driving protocol constitutes one of the most widely studied measures in non-equilibrium thermodynamics, as it constitutes a proxy for entropy production. In quantum systems, it has been shown that the irreversible work has an additional, genuinely quantum mechanical contribution, due to coherence produced by the driving protocol. The goal of this paper is to explore this contribution in systems that undergo a quantum phase transition. Substantial effort has been dedicated in recent years to understand the role of quantum criticality in work protocols. However, pr…
This work presents the thermodynamical analysis of the ballistic heat equation from the viewpoint of two approaches: Classical Irreversible Thermodynamics (CIT) and Extended Irreversible Thermodynamics (EIT). A formula for calculation of the entropy within the framework of EIT for the ballistic heat equation is derived in this work. Entropy is calculated for a sinusoidal initial temperature perturbation by using both approaches. The results obtained from CIT show that the entropy is a non-monotonic function and the entropy production can be negative. The results obtained with EIT show that the…
By considering an explicit nonequilibrium model, we analyze the statistics of the irreversible work, $w_{\rm irr}$, and irreversible entropy production, $Δ_i s$, within the stochastic energetics framework. Restating the second law of thermodynamics as a function of $w_{\rm irr}$, we introduce the explicit probability of violating the canonical form of that second law for a different set of parameters and initial conditions of the model. Moreover, we study the irreversible entropy production along the same lines, since it can be cast as a generalization of the irreversible work. From an informa…
Entropy production is a key quantity in any finite-time thermodynamic process. It is intimately tied with the fundamental laws of thermodynamics, embodying a tool to extend thermodynamic considerations all the way to non-equilibrium processes. It is also often used in attempts to provide the quantitative characterization of logical and thermodynamic irreversibility, stemming from processes in physics, chemistry and biology. Notwithstanding its fundamental character, a unifying theory of entropy production valid for general processes, both classical and quantum, has not yet been formulated. Dev…
In the present paper, a new model of the collision term, of the Boltzmann Kinetic equation dealing with binary gas mixture affected by a centrifugal field, is introduced. The new model is representing a modification of the BGK (Bhatnagar-Gross-Krook) model of the Boltzmann kinetic equation to be suitable for studying the influence of centrifugal field affected on gases mixture. The scientific achievement of the new model is that it is a very simple model without any mathematical complexity; but without any loss of generality. We shed light upon that the new model is satisfied the conservation …
Steepest-Entropy-Ascent and Maximal-Entropy-Production Dynamical Models of Irreversible Relaxation to Stable Equilibrium from Any Non-Equilibrium State. Unified Treatment for Six Non-Equilibrium Frameworks
The stochastic thermodynamics provides a framework for the description of systems that are out of thermodynamic equilibrium. It is based on the assumption that the elementary constituents are acted by random forces that generate a stochastic dynamics, which is here represented by a Fokker-Planck-Kramers equation. We emphasize the role of the irreversible probability current, the vanishing of which characterizes the thermodynamic equilibrium and yields a special relation between fluctuation and dissipation. The connection to thermodynamics is obtained by the definition of the energy function an…
A formidable perspective in understanding quantum criticality of a given many-body system is through its entanglement contents. Until now, most progress are only limited to the disorder-free case. Here, we develop an efficient scheme to compute the entanglement entropy of $(2+1)$-dimensional quantum critical points with randomness, from a conceptually novel angle where the quenched disorder can be considered as dimensionally reducible interactions. As a concrete example, we reveal novel entanglement signatures of $(2+1)$-dimensional Dirac fermion exposed to a random magnetic field, which hosts…
This work considers entropy generation and relaxation in quantum quenches in the Ising and $3$-state Potts spin chains. In the absence of explicit symmetry breaking we find universal ratios involving Rényi entropy growth rates and magnetisation relaxation for small quenches. We also demonstrate that the magnetisation relaxation rate provides an observable signature for the "dynamical Gibbs effect" which is a recently discovered characteristic non-monotonous behaviour of entropy growth linked to changes in the quasi-particle spectrum.
In this paper we construct time-dependent solutions of three-dimensional gravity in AdS space dual to systems with boundaries (BCFTs), following the AdS/BCFT prescription. Such solutions can be discussed in the context of the dynamics of first order phase transitions, or more generally, in the description of quantum quenches. As an example, we apply the holographic model to calculate the dynamics of the entanglement entropy of a local quench corresponding to a nucleation of a Euclidean bubble. As in the known 1+1 CFT examples of local cut and glue quenches, the holographic entanglement entropy…
We study the time evolution of the entanglement entropy after quantum quenches in Lifshitz free scalar theories, with the dynamical exponent $z>1$, by using the correlator method. For quantum quenches we consider two types of time-dependent mass functions: end-critical-protocol (ECP) and cis-critical-protocol (CCP). In both cases, at early times the entanglement entropy is independent of the subsystem size. After a critical time ($t_c$), the entanglement entropy starts depending on the subsystem size significantly. This critical time $t_c$ for $z = 1$ in the fast ECP and CCP has been explained…
