Search Results (43)

We revisit the question of the existence of a potential function, the Cole–Hopf transform of the stationary measure, for nonequilibrium steady states, in particular those found in active matter systems. This has been the subject of ongoing research for more than fifty years, but continues to be relevant. In particular, we want to make a connection to some recent work on the theory of Helmholtz–Hodge decompositions and address the recently suggested notion of typical trajectories in such systems. Full article

Modeling the evolution of a system using stochastic dynamics typically implies increasing subjective uncertainty in the adopted state of the system and its environment as time progresses, and stochastic entropy production has been developed as a measure of this change. In some situations, the evolution of stochastic entropy production can be described using an Itô process, but mathematical difficulties can emerge if diffusion in the system phase space happens to be restricted to a subspace of a lower dimension. This situation can arise if there are constants of the motion, for example, or more generally when there are functions of the coordinates that evolve without noise. More simply, difficulties can emerge if there are more coordinates than there are independent noises. We show how the problem of computing the stochastic entropy production in such a situation can be overcome. We illustrate the approach using a simple case of diffusion on an ellipse. We go on to consider an open three-level quantum system modeled within a framework of Markovian quantum state diffusion. We show how a nonequilibrium stationary state of the system, with a constant mean rate of stochastic entropy production, can be established under suitable environmental couplings. Full article

We consider three different systems in a heat flow: an ideal gas, a van der Waals gas, and a binary mixture of ideal gases. We divide each system internally into two subsystems by a movable wall. We show that the direction of the motion of the wall, after release, under constant boundary conditions, is determined by the same inequality as in equilibrium thermodynamics $\mathrm{d}U-đQ\le 0$. The only difference between the equilibrium and non-equilibrium laws is the dependence of the net heat change, $đQ$, on the state parameters of the system. We show that the same inequality is valid when introducing the gravitational field in the case of both the ideal gas and the van der Waals gas in the heat flow. It remains true when we consider a thick wall permeable to gas particles and derive Archimedes’ principle in the heat flow. Finally, we consider the Couette (shear) flow of the ideal gas. In this system, the direction of the motion of the internal wall follows from the inequality $\mathrm{d}E-đQ-đW_s\le 0$, where $\mathrm{d}E$ is the infinitesimal change in total energy (internal plus kinetic) and $đW_s$ is the infinitesimal work exchanged with the environment due to the shear force imposed on the flowing gas. Ultimately, we synthesize all these cases within a general framework of the second law of non-equilibrium thermodynamics. Full article

We consider two different time fractional telegrapher’s equations under stochastic resetting. Using the integral decomposition method, we found the probability density functions and the mean squared displacements. In the long-time limit, the system approaches non-equilibrium stationary states, while the mean squared displacement saturates due to the resetting mechanism. We also obtain the fractional telegraph process as a subordinated telegraph process by introducing operational time such that the physical time is considered as a Lévy stable process whose characteristic function is the Lévy stable distribution. We also analyzed the survival probability for the first-passage time problem and found the optimal resetting rate for which the corresponding mean first-passage time is minimal. Full article

The fluctuation relation stands as a fundamental result in nonequilibrium statistical physics. Its derivation, particularly in the stationary state, places stringent conditions on the physical systems of interest. On the other hand, numerical analyses usually do not directly reveal any specific connection with such physical properties. This study proposes an investigation of such a connection with the fundamental ingredients of the derivation of the fluctuation relation for the dissipation, which includes the decay of correlations, in the case of heat transport in one-dimensional systems. The role of the heat baths in connection with the system’s inherent properties is then highlighted. A crucial discovery of our research is that different lattice models obeying the steady-state fluctuation relation may do so through fundamentally different mechanisms, characterizing their intrinsic nature. Systems with normal heat conduction, such as the lattice ${\varphi }^4$ model, comply with the theorem after surpassing a certain observational time window, irrespective of lattice size. In contrast, systems characterized by anomalous heat conduction, such as Fermi–Pasta–Ulam–Tsingou-$\beta$ and harmonic oscillator chains, require extended observation periods for theoretical alignment, particularly as the lattice size increases. In these systems, the heat bath’s fluctuations significantly influence the entire lattice, linking the system’s fluctuations with those of the bath. Here, the current autocorrelation function allows us to discern the varying conditions under which different systems satisfy with the fluctuation relation. Our findings significantly expand the understanding of the stationary fluctuation relation and its broader implications in the field of nonequilibrium phenomena. Full article

Molecular switches based on functionalized graphene nanoribbons (GNRs) are of great interest in the development of nanoelectronics. In experiment, it was found that a significant difference in the conductance of an anthraquinone derivative can be achieved by altering the pH value of the environment. Building on this, in this work we investigate the underlying mechanism behind this effect and propose a general design principle for a pH based GNR-based switch. The electronic structure of the investigated systems is calculated using density functional theory and the transport properties at the quasi-stationary limit are described using nonequilibrium Green’s function and the Landauer formalism. This approach enables the examination of the local and the global transport through the system. The electrons are shown to flow along the edges of the GNRs. The central carbonyl groups allow for tunable transport through control of the oxidation state via the pH environment. Finally, we also test different types of GNRs (zigzag vs. armchair) to determine which platform provides the best transport switchability. Full article

Using a single-site mean-field approximation (MFA) and Monte Carlo simulations, we examine Ising-like models on directed regular random graphs. The models are directed-network implementations of the Ising model, Ising model with absorbing states, and majority voter models. When these nonequilibrium models are driven by the heat-bath dynamics, their stationary characteristics, such as magnetization, are correctly reproduced by MFA as confirmed by Monte Carlo simulations. It turns out that MFA reproduces the same result as the generating functional analysis that is expected to provide the exact description of such models. We argue that on directed regular random graphs, the neighbors of a given vertex are typically uncorrelated, and that is why MFA for models with heat-bath dynamics provides their exact description. For models with Metropolis dynamics, certain additional correlations become relevant, and MFA, which neglects these correlations, is less accurate. Models with heat-bath dynamics undergo continuous phase transition, and at the critical point, the power-law time decay of the order parameter exhibits the behavior of the Ising mean-field universality class. Analogous phase transitions for models with Metropolis dynamics are discontinuous. Full article

In this paper, we formulate the first law of global thermodynamics for stationary states of the binary ideal gas mixture subjected to heat flow. We map the non-uniform system onto the uniform one and show that the internal energy $U(S^{*},V,N_1,N_2,f_1^{*},f_2^{*})$ is the function of the following parameters of state: a non-equilibrium entropy $S^{*}$, volume V, number of particles of the first component, $N_1$, number of particles of the second component $N_2$ and the renormalized degrees of freedom. The parameters $f_1^{*},f_2^{*}$, $N_1,N_2$ satisfy the relation $(N_1/(N_1+N_2))f_1^{*}/f_1+(N_2/(N_1+N_2))f_2^{*}/f_2=1$ ($f_1$ and $f_2$ are the degrees of freedom for each component respectively). Thus, only 5 parameters of state describe the non-equilibrium state of the binary mixture in the heat flow. We calculate the non-equilibrium entropy $S^{*}$ and new thermodynamic parameters of state $f_1^{*},f_2^{*}$ explicitly. The latter are responsible for heat generation due to the concentration gradients. The theory reduces to equilibrium thermodynamics, when the heat flux goes to zero. As in equilibrium thermodynamics, the steady-state fundamental equation also leads to the thermodynamic Maxwell relations for measurable steady-state properties. Full article

We formulate the first law of global thermodynamics for stationary states of the ideal gas in the gravitational field subjected to heat flow. We map the non-uniform system (described by profiles of the density and temperature) onto the uniform one and show that the total internal energy $U(S^{*},V,N,L,M^{*})$ is the function of the following parameters of state: the non-equilibrium entropy $S^{*}$, volume V, number of particles, N, height of the column L along the gravitational force, and renormalized mass of a particle $M^{*}$. Each parameter corresponds to a different way of energy exchange with the environment. The parameter $M^{*}$ changes internal energy due to the shift of the centre of mass induced by the heat flux. We give analytical expressions for the non-equilibrium entropy $S^{*}$ and effective mass $M^{*}$. When the heat flow goes to zero, $S^{*}$ approaches equilibrium entropy. Additionally, when the gravitational field vanishes, our fundamental relation reduces to the fundamental relation at equilibrium. Full article

The Ornstein–Uhlenbeck (O-U) process with resetting is considered as the anomalous transport taking place on a three-dimensional comb. The three-dimensional comb is a comb inside a comb structure, consisting of backbones and fingers in the following geometrical correspondence x–backbone →y–fingers–backbone →z–fingers. Realisation of the O-U process on the three-dimensional comb leads to anomalous (non-Markovian) diffusion. This specific anomalous transport in the presence of resets results in non-equilibrium stationary states. Explicit analytical expressions for the mean values and the mean squared displacements along all three directions of the comb are obtained and verified numerically. The marginal probability density functions for each direction are obtained numerically by Monte Carlo simulation of a random transport described by a system of coupled Langevin equations for the comb geometry. Full article

We performed a theoretical study of the dephasing dynamics of a quantum two-state system under the influences of a non-equilibrium fluctuating environment. The effect of the environmental non-equilibrium fluctuations on the quantum system is described by a generalized random telegraph noise (RTN) process, of which the statistical properties are both non-stationary and non-Markovian. Due to the time-homogeneous property in the master equations for the multi-time probability distribution, the decoherence factor induced by the generalized RTN with a modulatable-type memory kernel can be exactly derived by means of a closed fourth-order differential equation with respect to time. In some special limit cases, the decoherence factor recovers to the expression of the previous ones. We analyzed in detail the environmental effect of memory modulation in the dynamical dephasing in four types of dynamics regimes. The results showed that the dynamical dephasing of the quantum system and the conversion between the Markovian and non-Markovian characters in the dephasing dynamics under the influence of the generalized RTN can be effectively modulated via the environmental memory kernel. Full article

Information Geometry is a useful tool to study and compare the solutions of a Stochastic Differential Equations (SDEs) for non-equilibrium systems. As an alternative method to solving the Fokker–Planck equation, we propose a new method to calculate time-dependent probability density functions (PDFs) and to study Information Geometry using Monte Carlo (MC) simulation of SDEs. Specifically, we develop a new MC SDE method to overcome the challenges in calculating a time-dependent PDF and information geometric diagnostics and to speed up simulations by utilizing GPU computing. Using MC SDE simulations, we reproduce Information Geometric scaling relations found from the Fokker–Planck method for the case of a stochastic process with linear and cubic damping terms. We showcase the advantage of MC SDE simulation over FPE solvers by calculating unequal time joint PDFs. For the linear process with a linear damping force, joint PDF is found to be a Gaussian. In contrast, for the cubic process with a cubic damping force, joint PDF exhibits a bimodal structure, even in a stationary state. This suggests a finite memory time induced by a nonlinear force. Furthermore, several power-law scalings in the characteristics of bimodal PDFs are identified and investigated. Full article

This review is devoted to the universal algebraic and geometric properties of the non-relativistic quantum current algebra symmetry and to their representations subject to applications in describing geometrical and analytical properties of quantum and classical integrable Hamiltonian systems of theoretical and mathematical physics. The Fock space, the non-relativistic quantum current algebra symmetry and its cyclic representations on separable Hilbert spaces are reviewed and described in detail. The unitary current algebra family of operators and generating functional equations are described. A generating functional method to constructing irreducible current algebra representations is reviewed, and the ergodicity of the corresponding representation Hilbert space measure is mentioned. The algebraic properties of the so called coherent states are also reviewed, generated by cyclic representations of the Heisenberg algebra on Hilbert spaces. Unbelievable and impressive applications of coherent states to the theory of nonlinear dynamical systems on Hilbert spaces are described, along with their linearization and integrability. Moreover, we present a further development of these results within the modern Lie-algebraic approach to nonlinear dynamical systems on Poissonian functional manifolds, which proved to be both unexpected and important for the classification of integrable Hamiltonian flows on Hilbert spaces. The quantum current Lie algebra symmetry properties and their functional representations, interpreted as a universal algebraic structure of symmetries of completely integrable nonlinear dynamical systems of theoretical and mathematical physics on functional manifolds, are analyzed in detail. Based on the current algebra symmetry structure and their functional representations, an effective integrability criterion is formulated for a wide class of completely integrable Hamiltonian systems on functional manifolds. The related algebraic structure of the Poissonian operators and an effective algorithm of their analytical construction are described. The current algebra representations in separable Hilbert spaces and the factorized structure of quantum integrable many-particle Hamiltonian systems are reviewed. The related current algebra-based Hamiltonian reconstruction of the many-particle oscillatory and Calogero–Moser–Sutherland quantum models are reviewed and discussed in detail. The related quasi-classical quantum current algebra density representations and the collective variable approach in equilibrium statistical physics are reviewed. In addition, the classical Wigner type current algebra representation and its application to non-equilibrium classical statistical mechanics are described, and the construction of the Lie–Poisson structure on the phase space of the infinite hierarchy of distribution functions is presented. The related Boltzmann–Bogolubov type kinetic equation for the generating functional of many-particle distribution functions is constructed, and the invariant reduction scheme, compatible with imposed correlation functions constraints, is suggested and analyzed in detail. We also review current algebra functional representations and their geometric structure subject to the analytical description of quasi-stationary hydrodynamic flows and their magneto-hydrodynamic generalizations. A unified geometric description of the ideal idiabatic liquid dynamics is presented, and its Hamiltonian structure is analyzed. A special chapter of the review is devoted to recent results on the description of modified current Lie algebra symmetries on torus and their Lie-algebraic structures, related to integrable so-called heavenly type spatially many-dimensional dynamical systems on functional manifolds. Full article

The Markovian time evolution of the entropy production rate is studied as a measure of irreversibility generated in a bipartite quantum system consisting of two coupled bosonic modes immersed in a common thermal environment. The dynamics of the system is described in the framework of the formalism of the theory of open quantum systems based on completely positive quantum dynamical semigroups, for initial two-mode squeezed thermal states, squeezed vacuum states, thermal states and coherent states. We show that the rate of the entropy production of the initial state and nonequilibrium stationary state, and the time evolution of the rate of entropy production, strongly depend on the parameters of the initial Gaussian state (squeezing parameter and average thermal photon numbers), frequencies of modes, parameters characterising the thermal environment (temperature and dissipation coefficient), and the strength of coupling between the two modes. We also provide a comparison of the behaviour of entropy production rate and Rényi-2 mutual information present in the considered system. Full article

The RNA world is one of the principal hypotheses to explain the emergence of living systems on the prebiotic Earth. It posits that RNA oligonucleotides acted as both carriers of information as well as catalytic molecules, promoting their own replication. However, it does not explain the origin of the catalytic RNA molecules. How could the transition from a pre-RNA to an RNA world occur? A starting point to answer this question is to analyze the dynamics in sequence space on the lowest level, where mononucleotide and short oligonucleotides come together and collectively evolve into larger molecules. To this end, we study the sequence-dependent self-assembly of polymers from a random initial pool of short building blocks via templated ligation. Templated ligation requires two strands that are hybridized adjacently on a third strand. The thermodynamic stability of such a configuration crucially depends on the sequence context and, therefore, significantly influences the ligation probability. However, the sequence context also has a kinetic effect, since non-complementary nucleotide pairs in the vicinity of the ligation site stall the ligation reaction. These sequence-dependent thermodynamic and kinetic effects are explicitly included in our stochastic model. Using this model, we investigate the system-level dynamics inside a non-equilibrium ‘RNA reactor’ enabling a fast chemical activation of the termini of interacting oligomers. Moreover, the RNA reactor subjects the oligomer pool to periodic temperature changes inducing the reshuffling of the system. The binding stability of strands typically grows with the number of complementary nucleotides forming the hybridization site. While shorter strands unbind spontaneously during the cold phase, larger complexes only disassemble during the temperature peaks. Inside the RNA reactor, strand growth is balanced by cleavage via hydrolysis, such that the oligomer pool eventually reaches a non-equilibrium stationary state characterized by its length and sequence distribution. How do motif-dependent energy and stalling parameters affect the sequence composition of the pool of long strands? As a critical factor for self-enhancing sequence selection, we identify kinetic stalling due to non-complementary base pairs at the ligation site. Kinetic stalling enables cascades of self-amplification that result in a strong reduction of occupied states in sequence space. Moreover, we discuss the significance of the symmetry breaking for the transition from a pre-RNA to an RNA world. Full article