Related papers: Gouy-Stodola Theorem as a variational principle fo…
The Energy-Dissipation Principle provides a variational tool for the analysis of parabolic evolution problems: solutions are characterized as so-called null-minimizers of a global functional on entire trajectories. This variational…
It exists a large class of systems for which the traditional notion of extensivity breaks down. From experimental examples we induce two general hypothesis concerning such systems. In the first the existence of an internal coordinate system…
For configurational changes of soft matter systems affected or caused by external hydrodynamic flow, we identify applied work, exchanged heat, and entropy change on the level of a single trajectory. These expressions guarantee invariance of…
This paper presents the notion of a variation entropy. This concept is an entropy framework for the gradient of the solution of a conservation law instead of on the solution itself. It appears that all semi-norms are admissible variation…
The second law of nonequilibrium thermodynamics within the open system paradigm (a small system coupled to one or multiple baths) is derived. This is done by showing positivity of entropy production for arbitrary Hamiltonian dynamics for a…
Hamilton variational principle for special type of statistical ensemble of deterministic dynamical systems is derived. Thie form of variational principle allows one to describe the statistical ensemble in terms of wave functions and…
Based on the recently proposed framework of general relativistic stochastic mechanics [{\em J. Stat. Phys.}, 190:193, 2023; {\em J. Stat. Phys.}, 190:181, 2023] and stochastic thermodynamics [{\em SciPost Physics Core} 7, 082, 2024] at the…
The maximum entropy principle determines the values of thermodynamic variables in thermally isolated equilibrium systems. This paper extends the principle to a variational principle that applies to liquid-gas coexistence in heat conduction.…
We propose a variational formulation for the nonequilibrium thermodynamics of discrete open systems, i.e., discrete systems which can exchange mass and heat with the exterior. Our approach is based on a general variational formulation for…
We show that the naive application of the maximum entropy principle can yield answers which depend on the level of description, i.e. the result is not invariant under coarse-graining. We demonstrate that the correct approach, even for…
Starting from the most general formulation of stochastic thermodynamics---i.e. a thermodynamically consistent nonautonomous stochastic dynamics describing systems in contact with several reservoirs---, we define a procedure to identify the…
The laws of thermodynamics apply to biophysical systems on the nanoscale as described by the framework of stochastic thermodynamics. This theory provides universal, exact relations for quantities like work, which have been verified in…
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…
Work fluctuation and total entropy production play crucial roles in small thermodynamic systems subject to large thermal fluctuations. We investigate a trade-off relation between them in a nonequilibrium situation in which a system starts…
Different notions of entropy play a fundamental role in the classical theory of dynamical systems. Unlike many other concepts used to analyze autonomous dynamics, both measure-theoretic and topological entropy can be extended quite…
Thermodynamics plays an important role in gravitational theories. It is a principle independent of the gravitational dynamics, and there is still no rigorous proof to show that it is consistent with the dynamical principle. We consider a…
This is the first part in a series in which sofic entropy theory is generalized to class-bijective extensions of sofic groupoids. Here we define topological and measure entropy and prove invariance. We also establish the variational…
A variational principle is derived for two-dimensional incompressible rotational fluid flow with a free surface in a moving vessel when both the vessel and fluid motion are to be determined. The fluid is represented by a stream function and…
We develop the stochastic approach to thermodynamics based on the stochastic dynamics, which can be discrete (master equation) continuous (Fokker-Planck equation), and on two assumptions concerning entropy. The first is the definition of…
The criteria determining the sign of entropy change in the open system are formulated. The concepts of entrostat, degree of openness, critical level of ordering are entered. The opportunity of occurrence of entropy oscillations in a…