|
Frenesy (physics)
Frenesy is a concept in statistical physics that measures the Dynamical system, dynamical activity of a system's microscopic trajectories under Non-equilibrium thermodynamics, non-equilibrium conditions. It complements the notion of entropy production, which measures T-symmetry, time-antisymmetric aspects associated with irreversibility. Frenesy reflects how frequently states are visited or how many transitions occur over time and how busy the system's trajectories are. It relates to reactivities, escape rates and Residence time (statistics), residence times of a physical state. Origin and context The notion of frenesy was introduced in 2006 in the study of Non-equilibrium thermodynamics, non-equilibrium processes by Christian Maes and collaborators, and has been discussed in various studies since then. In systems described by trajectory ensembles or path-space measures (e.g. originating in ''Markov processes'' or ''Langevin equation, Langevin dynamics''), frenesy is associated w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Physics
In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. Sometimes called statistical physics or statistical thermodynamics, its applications include many problems in a wide variety of fields such as biology, neuroscience, computer science, information theory and sociology. Its main purpose is to clarify the properties of matter in aggregate, in terms of physical laws governing atomic motion. 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. While classical thermodynamics is primarily concerned with thermodynamic equilibrium, statistical mechanics has been applied in non-equilibrium stat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kubo Formula
The Kubo formula, named for Ryogo Kubo who first presented the formula in 1957, is an equation which expresses the linear response of an observable quantity due to a time-dependent perturbation. Among numerous applications of the Kubo formula, one can calculate the charge and spin susceptibilities of systems of electrons in response to applied electric and magnetic fields. Responses to external mechanical forces and vibrations can be calculated as well. General Kubo formula Consider a quantum system described by the (time independent) Hamiltonian H_0. The expectation value of a physical quantity at equilibrium temperature T, described by the operator \hat, can be evaluated as: :\left\langle\hat\right\rangle = \operatorname\,\left hat\hat\right= \sum_n \left\langle n \left, \hat \ n \right\rangle e^, where \beta=1/k_T is the thermodynamic beta, \hat_0 is density operator, given by :\hat = e^ = \sum_n , n \rangle\langle n , e^ and Z_0 = \operatorname\,\left hat\rho_0\right/ ... [...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 (statistical thermodynamics), 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 fi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stochastic Thermodynamics
Overview When a microscopic machine (e.g. a Microelectromechanical systems, MEM) performs useful work it generates heat and entropy as a byproduct of the process, however it is also predicted that this machine will operate in "reverse" or "backwards" over appreciable short periods. That is, heat energy from the surroundings will be converted into useful work. For larger engines, this would be described as a violation of the second law of thermodynamics, as entropy is consumed rather than generated. Loschmidt's paradox states that in a time reversible system, for every trajectory there exists a time-reversed anti-trajectory. As the entropy production of a trajectory and its equal anti-trajectory are of identical magnitude but opposite sign, then, so the argument goes, one cannot prove that entropy production is positive. For a long time, exact results in thermodynamics were only possible in linear systems capable of reaching equilibrium, leaving other questions like the Loschmidt p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heartbeat
Heartbeat, heart beat or heartbeats may refer to: Science and technology * Heartbeat (biology), one cardiac cycle of the heart * Heartbeat (computing), a periodic signal to indicate normal operation or to synchronize parts of a system ** Heartbeat (software), clustering software from the Linux-HA project Arts and entertainment Films * ''Heartbeat'' (1938 film), a French comedy * ''Heartbeat'' (1946 film), an American film by Sam Wood, starring Ginger Rogers * ''La Chamade'' (film) (English title: ''Heartbeat''), a 1968 French film by Alain Cavalier * ''Heart Beat'' (film), a 1980 American film about the love triangle between Jack Kerouac, Carolyn Cassady and Neal Cassady * ''Dhadkan'' (2000 film) (English title: ''Heartbeat''), a 2000 Indian Hindi-language film by Dharmesh Darshan * ''Heart Beats'' (film), a 2007 Indian Malayalam-language film * ''Heartbeats'' (2010 film), a Canadian French–English film by Xavier Dolan * ''Heartbeat'' (2010 film), a South Korean film abo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Non-linear Amplification
In mathematics and science, a nonlinear system (or a non-linear system) is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathematicians, and many other scientists since most systems are inherently nonlinear in nature. Nonlinear dynamical systems, describing changes in variables over time, may appear chaotic, unpredictable, or counterintuitive, contrasting with much simpler linear systems. Typically, the behavior of a nonlinear system is described in mathematics by a nonlinear system of equations, which is a set of simultaneous equations in which the unknowns (or the unknown functions in the case of differential equations) appear as variables of a polynomial of degree higher than one or in the argument of a function which is not a polynomial of degree one. In other words, in a nonlinear system of equations, the equation(s) to be solved cannot be written as a linea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Van Der Pol Oscillator
In the study of dynamical systems, the van der Pol oscillator (named for Dutch physicist Balthasar van der Pol) is a non-Conservative force, conservative, oscillating system with non-linear damping. It evolves in time according to the second-order differential equation - \mu(1-x^2) + x = 0, where is the position coordinate system, coordinate—which is a function (mathematics), function of the time —and is a scalar (mathematics), scalar parameter indicating the nonlinearity and the strength of the damping. History The Van der Pol oscillator was originally proposed by the Dutch electrical engineering, electrical engineer and physicist Balthasar van der Pol while he was working at Philips. Van der Pol found stable oscillations, which he subsequently called relaxation oscillator, relaxation-oscillations and are now known as a type of limit cycle, in electrical circuits employing vacuum tubes. When these circuits are driven near the limit cycle, they become entrainment (phys ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thermal Noise
A thermal column (or thermal) is a rising mass of buoyant air, a convective current in the atmosphere, that transfers heat energy vertically. Thermals are created by the uneven heating of Earth's surface from solar radiation, and are an example of convection, specifically atmospheric convection. Thermals on Earth The Sun warms the ground, which in turn warms the air directly above. The warm air near the surface expands, becoming less dense than the surrounding air. The lighter air rises and cools due to its expansion in the lower pressure at higher altitudes. It stops rising when it has cooled to the same temperature, thus density, as the surrounding air. Associated with a thermal is a downward flow surrounding the thermal column. The downward-moving exterior is caused by colder air being displaced at the top of the thermal. The size and strength of thermals are influenced by the properties of the lower atmosphere (the ''troposphere''). When the air is cold, bubbles of w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Friction
Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. Types of friction include dry, fluid, lubricated, skin, and internal -- an incomplete list. The study of the processes involved is called tribology, and has a history of more than 2000 years. Friction can have dramatic consequences, as illustrated by the use of friction created by rubbing pieces of wood together to start a fire. Another important consequence of many types of friction can be wear, which may lead to performance degradation or damage to components. It is known that frictional energy losses account for about 20% of the total energy expenditure of the world. As briefly discussed later, there are many different contributors to the retarding force in friction, ranging from asperity deformation to the generation of charges and changes in local structure. When two bodies in contact move relative to each other, due to these variou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Negative Differential Resistance
In electronics, negative resistance (NR) is a property of some electrical circuits and devices in which an increase in voltage across the device's terminals results in a decrease in electric current through it. This is in contrast to an ordinary resistor, in which an increase in applied voltage causes a proportional increase in current in accordance with Ohm's law, resulting in a positive resistance. Under certain conditions, negative resistance can increase the power of an electrical signal, amplifying it. Negative resistance is an uncommon property which occurs in a few nonlinear electronic components. In a nonlinear device, two types of resistance can be defined: 'static' or 'absolute resistance', the ratio of voltage to current v / i, and ''differential resistance'', the ratio of a change in voltage to the resulting change in current \Delta v/\Delta i. The term negative resistance means negative differential resistance (NDR), \Delta v / \Delta i < 0. In general, a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Diffusion
Diffusion is the net movement of anything (for example, atoms, ions, molecules, energy) generally from a region of higher concentration to a region of lower concentration. Diffusion is driven by a gradient in Gibbs free energy or chemical potential. It is possible to diffuse "uphill" from a region of lower concentration to a region of higher concentration, as in spinodal decomposition. Diffusion is a stochastic process due to the inherent randomness of the diffusing entity and can be used to model many real-life stochastic scenarios. Therefore, diffusion and the corresponding mathematical models are used in several fields beyond physics, such as statistics, probability theory, information theory, neural networks, finance, and marketing. The concept of diffusion is widely used in many fields, including physics (Molecular diffusion, particle diffusion), chemistry, biology, sociology, economics, statistics, data science, and finance (diffusion of people, ideas, data and price v ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Einstein Relation (kinetic Theory)
In physics (specifically, the kinetic theory of gases), the Einstein relation is a previously unexpected connection revealed independently by William Sutherland in 1904, Albert Einstein in 1905, and by Marian Smoluchowski in 1906 in their works on Brownian motion. The more general form of the equation in the classical case is D = \mu \, k_\text T, where * is the diffusion coefficient; * is the "mobility", or the ratio of the particle's terminal drift velocity to an applied force, ; * is the Boltzmann constant; * is the absolute temperature. This equation is an early example of a fluctuation-dissipation relation. Note that the equation above describes the classical case and should be modified when quantum effects are relevant. Two frequently used important special forms of the relation are: * Einstein–Smoluchowski equation, for diffusion of charged particles: D = \frac * Stokes–Einstein–Sutherland equation, for diffusion of spherical particles through a li ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
