Fluctuation-dissipation theoremThe fluctuation–dissipation theorem (FDT) or fluctuation–dissipation relation (FDR) is a powerful tool in statistical physics for predicting the behavior of systems that obey detailed balance. Given that a system obeys detailed balance, the theorem is a proof that thermodynamic fluctuations in a physical variable predict the response quantified by the admittance or impedance (to be intended in their general sense, not only in electromagnetic terms) of the same physical variable (like voltage, temperature difference, etc.
Gay-Lussac's lawGay-Lussac's law usually refers to Joseph-Louis Gay-Lussac's law of combining volumes of gases, discovered in 1808 and published in 1809. However, it sometimes refers to the proportionality of the volume of a gas to its absolute temperature at constant pressure. The latter law was published by Gay-Lussac in 1802, but in the article in which he described his work, he cited earlier unpublished work from the 1780s by Jacques Charles. Consequently, the volume-temperature proportionality is usually known as Charles's Law.
Crooks fluctuation theoremThe 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.
Glauber dynamicsIn statistical physics, Glauber dynamics is a way to simulate the Ising model (a model of magnetism) on a computer. It is a type of Markov Chain Monte Carlo algorithm. In the Ising model, we have say N particles that can spin up (+1) or down (-1). Say the particles are on a 2D grid. We label each with an x and y coordinate. Glauber's algorithm becomes: Choose a particle at random. Sum its four neighboring spins. . Compute the change in energy if the spin x, y were to flip. This is (see the Hamiltonian for the Ising model).
Energy-based modelAn energy-based model (EBM) is a form of generative model (GM) imported directly from statistical physics to learning. GMs learn an underlying data distribution by analyzing a sample dataset. Once trained, a GM can produce other datasets that also match the data distribution. EBMs provide a unified framework for many probabilistic and non-probabilistic approaches to such learning, particularly for training graphical and other structured models. An EBM learns the characteristics of a target dataset and generates a similar but larger dataset.
RothalpyRothalpy (or trothalpy) , a short name of rotational stagnation enthalpy, is a fluid mechanical property of importance in the study of flow within rotating systems. Consider we have an inertial frame of reference and a rotating frame of reference which both are sharing common origin . Assume that frame is rotating around a fixed axis with angular velocity .
Random energy modelIn the statistical physics of disordered systems, the random energy model is a toy model of a system with quenched disorder, such as a spin glass, having a first-order phase transition. It concerns the statistics of a collection of spins (i.e. degrees of freedom that can take one of two possible values ) so that the number of possible states for the system is . The energies of such states are independent and identically distributed Gaussian random variables with zero mean and a variance of .
Thermodynamic databases for pure substancesThermodynamic databases contain information about thermodynamic properties for substances, the most important being enthalpy, entropy, and Gibbs free energy. Numerical values of these thermodynamic properties are collected as tables or are calculated from thermodynamic datafiles. Data is expressed as temperature-dependent values for one mole of substance at the standard pressure of 101.325 kPa (1 atm), or 100 kPa (1 bar). Both of these definitions for the standard condition for pressure are in use.
GranularityGranularity (also called graininess) is the degree to which a material or system is composed of distinguishable pieces, "granules" or "grains" (metaphorically). It can either refer to the extent to which a larger entity is subdivided, or the extent to which groups of smaller indistinguishable entities have joined together to become larger distinguishable entities. Coarse-grained materials or systems have fewer, larger discrete components than fine-grained materials or systems.
Master equationIn physics, chemistry, and related fields, master equations are used to describe the time evolution of a system that can be modeled as being in a probabilistic combination of states at any given time, and the switching between states is determined by a transition rate matrix. The equations are a set of differential equations – over time – of the probabilities that the system occupies each of the different states. The name was proposed in 1940.
