Related papers: Mesoscopic and Macroscopic Entropy Balance Equatio…
The entropy production is one of the most essential features for systems operating out of equilibrium. The formulation for discrete-state systems goes back to the celebrated Schnakenberg's work and hitherto can be carried out when for each…
It is shown how the macroscopic non-equilibrium dynamics of a class of systems whose microscopic stochastic dynamics involves disordered and frustrated but range-free interactions can be well described by closed deterministic flow…
Active matter systems operate far from equilibrium due to the continuous energy injection at the scale of constituent particles. At larger scales, described by coarse-grained models, the global entropy production rate S quantifies the…
Using the stochastic thermodynamics, we determine the entropy production and the dynamic heat capacity of systems subject to a sinusoidally time dependent temperature, in which case the systems are permanently out of thermodynamic…
Entropy notions for $\varepsilon$-incremental practical stability and incremental stability of deterministic nonlinear systems under disturbances are introduced. The entropy notions are constructed via a set of points in state space which…
A quantum statistical expression for the entropy of a nonequilibrium system is defined so as to be consistent with Gibbs' relation, and is shown to corresponds to dynamical variable by introducing analogous to the Heisenberg picture in…
To illustrate Boltzmann's construction of an entropy function that is defined for a microstate of a macroscopic system, we present here the simple example of the free expansion of a one dimensional gas of non-interacting point particles.…
Entropy is useful in statistical problems as a measure of irreversibility, randomness, mixing, dispersion, and number of microstates. However, there remains ambiguity over the precise mathematical formulation of entropy, generalized beyond…
For stochastic non-equilibrium dynamics like a Langevin equation for a colloidal particle or a master equation for discrete states, entropy production along a single trajectory is studied. It involves both genuine particle entropy and…
The difference diffusion model with two equilibrium states is given by a stochastic equation with two components: the predicted one, which is determined by the regression function of increments with two equilibriums, and the stochastic one,…
We derive the expression for the entropy production for stochastic dynamics defined on a continuous space of states containing unidirectional transitions. The expression is derived by taking the continuous limit of a stochastic dynamics on…
We investigate the decomposition of the total entropy production in continuous stochastic dynamics when there are odd-parity variables that change their signs under time reversal. The first component of the entropy production, which…
We consider a generic class of stochastic particle-based models whose state at an instant in time is described by a set of continuous degrees of freedom (e.g. positions), and the length of this set changes stochastically in time due to…
The postulates of thermodynamics were originally formulated for macroscopic systems. They lead to the definition of the entropy, which, for a homogeneous system, is a homogeneous function of order one in the extensive variables and is…
This work contains two single-letter upper bounds on the entropy rate of a discrete-valued stationary stochastic process, which only depend on second-order statistics, and are primarily suitable for models which consist of relatively large…
Entropy in thermodynamics is an extensive quantity, whereas standard methods in statistical mechanics give rise to a non-extensive expression for the entropy. This discrepancy is often seen as a sign that basic formulas of statistical…
A change in a stochastic system has three representations: Probabilistic, statistical, and informational: (i) is based on random variable $u(\omega)\to\tilde{u}(\omega)$; this induces (ii) the probability distributions $F_u(x)\to…
We study non-equilibrium statistical mechanics of a Gaussian dynamical system and compute in closed form the large deviation functionals describing the fluctuations of the entropy production observable with respect to the reference state…
`Entropy' appears as driving force in many different evolution equations, both deterministic and stochastic, and in these equations this `entropy' also takes different forms. We show how all these examples can be understood as different…
Employing the stochastic wave function method, we study quantum features of stochastic entropy production in nonequilibrium processes of open systems. It is demonstarted that continuous measurements on the environment introduce an…