Related papers: Statistical mechanics of dissipative systems
Based on the concept of ensemble, it is proved in the manuscript that the probability amplitude function can also been used to describe the classical statistical system. The motion equations of probability amplitude functions of classical…
We define a thermostatic system to be a convex space of states together with a concave function sending each state to its entropy, which is an extended real number. This definition applies to classical thermodynamics, classical statistical…
The methods of statistical mechanics are applied to two-dimensional foams under macroscopic agitation. A new variable -- the total cell curvature -- is introduced, which plays the role of energy in conventional statistical thermodynamics.…
We examine the fundamental aspects of statistical mechanics, dividing the problem into a discussion purely about probability, which we analyse from a Bayesian standpoint. We argue that the existence of a unique maximising probability…
The path probability of stochastic motion of non dissipative or quasi-Hamiltonian systems is investigated by numerical experiment. The simulation model generates ideal one-dimensional motion of particles subject only to conservative forces…
We study the behavior of an assembly of $N$ granular particles contained in two compartments within a simple kinetic approach. The particles belonging to each compartment collide inelastically with each other and are driven by a stochastic…
The typicality approach and the Hilbert space averaging method as its technical manifestation are important concepts of quantum statistical mechanics. Extensively used for expectation values we extend them in this paper to transition…
In a physical system, changing parameters such as temperature can induce a phase transition: an abrupt change from one state of matter to another. Analogous phenomena have recently been observed in large language models. Typically, the task…
This work is an analytical calculation of the path probability for random dynamics of mechanical system described by Langevin equation with Gaussian noise. The result shows an exponential dependence of the probability on the action. In the…
We develop the theory of canonical-dissipative systems, based on the assumption that both the conservative and the dissipative elements of the dynamics are determined by invariants of motion. In this case, known solutions for conservative…
Quantum statistical mechanics is formulated as an integral over classical phase space. Some details of the commutation function for averages are discussed, as is the factorization of the symmetrization function used for the grand potential…
To describe the nonequilibrium states of a system we introduce a new thermodynamic parameter - the lifetime (the first passage time) of a system. The statistical distributions that can be obtained out of the mesoscopic description…
Strong-coupling statistical thermodynamics is formulated as Hamiltonian dynamics of an observed system interacting with another unobserved system (a bath). It is shown that the entropy production functional of stochastic thermodynamics,…
We describe some general results that constrain the dynamical fluctuations that can occur in non-equilibrium steady states, with a focus on molecular dynamics. That is, we consider Hamiltonian systems, coupled to external heat baths, and…
Exact generalized stochastic representation of deterministic interaction between two dynamical (quantum or classical) systems is derived which helps when considering one of them to replace another by equivalent commutative ($c$-number…
We use the phase space position-velocity ($x,v$) to deal with the statistical properties of velocity dependent dynamical systems, like dissipative ones. Within this approach, we study the statistical properties of an ensemble of harmonic…
Current fluctuations in a dissipative two-state system have been studied using a novel quantum dynamics simulation method. After a transformation of the path integrals, the tunneling dynamics is computed by deterministic integration over…
For a Markov and stationary stochastic process described by the well-known classical master equation, we introduce complex transition rates instead of real transition rates to study the pre-thermal oscillatory behaviour in complex…
Heat fluctuations are studied in a dissipative system with both mechanical and stochastic components for a simple model: a Brownian particle dragged through water by a moving potential. An extended stationary state fluctuation theorem is…
We identify the conditions under which a stochastic driving inducing energy changes on a system coupled to a thermal bath can be treated as a work source. When these conditions are met, the work statistics satisfies the Crooks fluctuation…