|
Nonequilibrium Partition Identity
The nonequilibrium partition identity (NPI) is a remarkably simple and elegant consequence of the fluctuation theorem previously known as the Kawasaki identity: : \left\langle \right\rangle = 1,\quad \forall t (Carberry et al. 2004). Thus in spite of the second law inequality which might lead one to expect that the average would decay exponentially with time, the exponential probability ratio given by the FT ''exactly'' cancels the negative exponential in the average above leading to an average which is unity for all time. The first derivation of the nonequilibrium partition identity for Hamiltonian systems was by Yamada and Kawasaki in 1967. For thermostatted deterministic systems the first derivation was by Morriss and Evans in 1985. Bibliography * * * * See also * Fluctuation theorem – Provides an equality that quantifies fluctuations in time averaged entropy production in a wide variety of nonequilibrium systems * Crooks fluctuation theorem – Provides a fluctuatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fluctuation Theorem
The fluctuation theorem (FT), which originated from statistical mechanics, deals with the relative probability that the entropy of a system which is currently away from thermodynamic equilibrium (i.e., maximum entropy) will increase or decrease over a given amount of time. While the second law of thermodynamics predicts that the entropy of an isolated system should tend to increase until it reaches equilibrium, it became apparent after the discovery of statistical mechanics that the second law is only a statistical one, suggesting that there should always be some nonzero probability that the entropy of an isolated system might spontaneously ''decrease''; the fluctuation theorem precisely quantifies this probability. Statement Roughly, the fluctuation theorem relates to the probability distribution of the time-averaged irreversible entropy production, denoted \overline_t. The theorem states that, in systems away from equilibrium over a finite time ''t'', the ratio between the probab ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fluctuation Theorem
The fluctuation theorem (FT), which originated from statistical mechanics, deals with the relative probability that the entropy of a system which is currently away from thermodynamic equilibrium (i.e., maximum entropy) will increase or decrease over a given amount of time. While the second law of thermodynamics predicts that the entropy of an isolated system should tend to increase until it reaches equilibrium, it became apparent after the discovery of statistical mechanics that the second law is only a statistical one, suggesting that there should always be some nonzero probability that the entropy of an isolated system might spontaneously ''decrease''; the fluctuation theorem precisely quantifies this probability. Statement Roughly, the fluctuation theorem relates to the probability distribution of the time-averaged irreversible entropy production, denoted \overline_t. The theorem states that, in systems away from equilibrium over a finite time ''t'', the ratio between the probab ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Entropy Production
Entropy production (or generation) is the amount of entropy which is produced in any irreversible processes such as heat and mass transfer processes including motion of bodies, heat exchange, fluid flow, substances expanding or mixing, anelastic deformation of solids, and any irreversible thermodynamic cycle, including thermal machines such as power plants, heat engines, refrigerators, heat pumps, and air conditioners. In the dual representation entropy–exergy for accounting the second law of thermodynamics it can be expressed in equivalent terms of exergy disruption. Short history Entropy is produced in irreversible processes. The importance of avoiding irreversible processes (hence reducing the entropy production) was recognized as early as 1824 by Carnot. In 1865 Rudolf Clausius expanded his previous work from 1854 on the concept of "unkompensierte Verwandlungen" (uncompensated transformations), which, in our modern nomenclature, would be called the entropy production. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Crooks Fluctuation Theorem
The Crooks fluctuation theorem (CFT), sometimes known as the Crooks equation, is an equation in statistical mechanics that relates the work done on a system during a non-equilibrium transformation to the free energy difference between the final and the initial state of the transformation. During the non-equilibrium transformation the system is at constant volume and in contact with a heat reservoir. The CFT is named after the chemist Gavin E. Crooks (then at University of California, Berkeley) who discovered it in 1998. The most general statement of the CFT relates the probability of a space-time trajectory x(t) to the time-reversal of the trajectory \tilde(t). The theorem says if the dynamics of the system satisfies microscopic reversibility, then the forward time trajectory is exponentially more likely than the reverse, given that it produces entropy, : \frac = e^. If one defines a generic reaction coordinate of the system as a function of the Cartesian coordinates of the c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jarzynski Equality
The Jarzynski equality (JE) is an equation in statistical mechanics that relates free energy differences between two states and the irreversible work along an ensemble of trajectories joining the same states. It is named after the physicist Christopher Jarzynski (then at the University of Washington and Los Alamos National Laboratory, currently at the University of Maryland) who derived it in 1996. Fundamentally, the Jarzynski equality points to the fact that the fluctuations in the work satisfy certain constraints separately from the average value of the work that occurs in some process. Overview In thermodynamics, the free energy difference \Delta F = F_B - F_A between two states ''A'' and ''B'' is connected to the work ''W'' done on the system through the ''inequality'': : \Delta F \leq W , with equality holding only in the case of a quasistatic process, i.e. when one takes the system from ''A'' to ''B'' infinitely slowly (such that all intermediate states are in thermody ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Mechanics
In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. It does not assume or postulate any natural laws, but explains the macroscopic behavior of nature from the behavior of such ensembles. Statistical mechanics arose out of the development of classical thermodynamics, a field for which it was successful in explaining macroscopic physical properties—such as temperature, pressure, and heat capacity—in terms of microscopic parameters that fluctuate about average values and are characterized by probability distributions. This established the fields of statistical thermodynamics and statistical physics. The founding of the field of statistical mechanics is generally credited to three physicists: *Ludwig Boltzmann, who developed the fundamental interpretation of entropy in terms of a collection of microstates *James Clerk Maxwell, who developed models of probability distr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Non-equilibrium Thermodynamics
Non-equilibrium thermodynamics is a branch of thermodynamics that deals with physical systems that are not in thermodynamic equilibrium but can be described in terms of macroscopic quantities (non-equilibrium state variables) that represent an extrapolation of the variables used to specify the system in thermodynamic equilibrium. Non-equilibrium thermodynamics is concerned with transport processes and with the rates of chemical reactions. Almost all systems found in nature are not in thermodynamic equilibrium, for they are changing or can be triggered to change over time, and are continuously and discontinuously subject to flux of matter and energy to and from other systems and to chemical reactions. Some systems and processes are, however, in a useful sense, near enough to thermodynamic equilibrium to allow description with useful accuracy by currently known non-equilibrium thermodynamics. Nevertheless, many natural systems and processes will always remain far beyond the scope o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
