Crook's Fluctuation Theorem and Jarzynski equality are immensely powerful tools in obtaining equilibrium properties through non-equilibrium transition between two equilibrium states. In this letter, we propose an extension to the Crook's fluctuation theorem for transition between two non-equilibrium steady states (NESS). Using the proposed theorem, we show that it is possible to obtain free energy differences of multiple equilibrium states from a single set of data obtained from the transition between two NESS. The results are verified using numerical simulations by employing Nose-Hoover dynamics and a single dimensional $ϕ^4$ chain. The equations are cast in a manner that makes it possible to do experimental verification. The proposed method can provide free-energy difference for a range of temperature, and consequently is much faster than either the Jarzynski equality or the Crooks's fluctuation theorem.
A view on the physical meaning of the so called ergodic hypothesis: its role on the foundations of equilibrium statistical mechanics in mid '800, its interpretations and hints at its relevance for modern nonequilibrium statistical mechanics. Followed by appendices with detailed comments on the original papers.
Extracting equilibrium information from nonequilibrium measurements is a challenge task of great importance in understanding the thermodynamic properties of physical, chemical, and biological systems. The discovery of the Jarzynski equality illumines the way to estimate the equilibrium free energy difference from the work performed in nonequilibrium driving processes. However, the nonlinear (exponential) relation causes the poor convergence of the Jarzynski equality. Here, we propose a concise method to estimate the free energy difference through a linear nonequilibrium equality which inherent…
Near equilibrium, Green-Kubo relations provide microscopic expressions for macroscopic transport coefficients in terms of equilibrium correlation functions. At their core, they are based on the intimate relationship between response and fluctuations as embodied by the equilibrium fluctuation-dissipation theorem, a connection generically broken far from equilibrium. In this work, we identify a class of perturbations whose response around far-from-equilibrium steady states is linked to steady-state correlation functions via an equilibrium-like fluctuation-response equality. We then utilize this …
We relate progress in statistical mechanics, both at and far from equilibrium, to advances in the theory of dynamical systems. We consider computer simulations of time-reversible deterministic chaos in small systems with three- and four-dimensional phase spaces. These models provide us with a basis for understanding equilibration and thermodynamic irreversibility in terms of Lyapunov instability, fractal distributions, and thermal constraints
Estimating equilibrium ensemble averages using multiple time slices from driven nonequilibrium processes: theory and application to free energies, moments, and thermodynamic length in single-molecule pulling experiments
While the Ising model belongs to the realm of equilibrium statistical mechanics, the voter model is an example of a nonequilibrium system. We examine an opinion formation model, which is a mixture of Ising and voter agents with concentrations $p$ and $1-p$, respectively. Although in our model for $p<1$ a detailed balance is violated, on a complete graph the average magnetization in the stationary state for any $p>0$ is shown to satisfy the same equation as for the pure Ising model ($p=1$). Numerical simulations confirm such a behavior, but the equivalence with the pure Ising model apparently h…
In the absence of external driving, a system exposed to thermal fluctuations will relax to equilibrium. However, the constant input of work makes it possible to counteract this relaxation, and maintain the system in a nonequilibrium steady state. In this Article, we use the stochastic thermodynamics of Markov jump processes to compute the minimum rate at which energy must be supplied and dissipated to maintain an arbitrary nonequilibrium distribution in a given energy landscape. This lower bound depends on two factors: the undriven probability current in the equilibrium state, and the distance…
We consider stationary driven systems in contact with a thermal equilibrium bath. There is a constant (Joule) heat dissipated from the steady system to the environment as long as all parameters are unchanged. As a natural generalization from equilibrium thermodynamics, the nonequilibrium heat capacity measures the excess in that dissipated heat when the temperature of the thermal bath is changed. To improve experimental accessibility we show how the heat capacity can also be obtained from the response of the instantaneous heat flux to small periodic temperature variations.
Aspects of the modern dynamical systems approach to thermodynamics of stationary states out of equilibrium with attention to the original conceptions which arose at the beginnings of Statistical Mechanics
Nonequilibrium statistical physics is concerned with a fundamental problem in physics, the phenomenon of irreversibility, which is not rigorously solved yet. Different approaches to the statistical mechanics of nonequilibrium processes are based on empirical assumptions but a rigorous, first principle theory is missing. An important contribution to describe irreversible behavior starting from reversible Hamiltonian dynamics was given by Zubarev who invented the method of the nonequilibrium statistical operator (NSO). We discuss this approach, in particular the extended von Neumann equation and…
Microreversibility rules the fluctuations of the currents flowing across open systems in nonequilibrium (or equilibrium) steady states. As a consequence, the statistical cumulants of the currents and their response coefficients at arbitrary orders in the deviations from equilibrium obey time-reversal symmetry relations. It is shown that these relations allow us to systematically reduce the amount of independent quantities that need to be measured experimentally or computed theoretically in order to fully characterize the linear and nonlinear transport properties of general open systems. This r…
Recent years have witnessed major advances in our understanding of nonequilibrium processes. The Jarzynski equality, for example, provides a link between equilibrium free energy differences and finite-time, nonequilibrium dynamics. We propose a generalization of this relation to non-Hamiltonian dynamics, relevant for active matter systems, continuous feedback, and computer simulation. Surprisingly, this relation allows us to calculate the free energy difference between the desired initial and final equilibrium states using arbitrary dynamics. As a practical matter, this dissociation between th…
There are many functional contexts where it is desirable to maintain a mesoscopic system in a nonequilibrium state. However, such control requires an inherent energy dissipation. In this article, we unify and extend a number of works on the minimum energetic cost to maintain a mesoscopic system in a prescribed nonequilibrium distribution using ancillary control. For a variety of control mechanisms, we find that the minimum amount of energy dissipation necessary can be cast as an information-theoretic measure of distinguishability between the target nonequilibrium state and the underlying equil…
Equilibrium is characterized by its fundamental properties such as the detailed balance, the fluctuation-dissipation relation, and no heat dissipation. Based on the stochastic thermodynamics, we show that these three properties are equivalent to each other in conventional Langevin thermal systems with microscopic reversibility. Thus, a conventional steady state has either all three properties (equilibrium) or none of them (nonequilibrium). In contrast, with velocity-dependent forces breaking the microscopic reversibility, we prove that the detailed balance and the fluctuation-dissipation relat…
