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The foundations of the Boltzmann-Gibbs (BG) distributions for describing equilibrium statistical mechanics of systems are examined. Broadly, they fall into: (i) probabilistic paaroaches based on the principle of equal a priori probability…
Multistable non-equilibrium systems are abundant outcomes of nonlinear dynamics with feedback but still relatively little is known about what determines the stability of the steady states and their switching rates in terms of entropy and…
The applicability of stochastic differential equations to thermodynamics is considered and a new form, different from the classical Ito and Stratonovich forms, is introduced. It is shown that the new presentation is more appropriate for the…
Exergy represents the maximum useful work possible when a system at a specific state reaches equilibrium with the environmental dead state at temperature To. Correspondingly, the exergy difference between two states is the maximum work…
We study the entropy production of a system with a finite number of states connected by random transition rates. The stationary entropy production, driven out of equilibrium both by asymmetric transition rates and by an external probability…
In this article, I give a definition of topological entropy for random dynamical systems associated to an infinite countable discrete amenable group action. I obtain a variational principle between the topological entropy and measurable…
Entropy is one of the key thermodynamic variables reflecting changes in the state of matter. Unlike other thermodynamic variables, it is well-defined also for nonequilibrium steady states through its relation to information. Applying this…
In traditional thermodynamical and statistical-mechanical approaches one has (some) detailed knowledge of the principles governing the microdynamics of a system. However in many instances we may not have a Hamiltonian or good information…
Thermodynamics is commonly presented as a theory of macroscopic systems in stable equilibrium, built upon assumptions of extensivity and scaling with system size. In this paper, we present a universal formulation of the elementary…
Statistical physics aims to describe properties of macroscale systems in terms of distributions of their microscale agents. Its central tool is the maximization of entropy, a variational principle. We review the history of this principle,…
The backbone of nonequilibrium thermodynamics is the stability structure, where entropy is related to a Lyapunov function of thermodynamic equilibrium. Stability is the background of natural selection: unstable systems are temporary, and…
The paper deals with the variational principles for evaluation of the spectral radii of transfer and weighted shift operators associated with a dynamical system. These variational principles have been the matter of numerous investigations…
We show that systems driven by an external force and described by Nose-Hoover dynamics allow for a consistent nonequilibrium thermodynamics description when the thermostatted variable is initially assumed in a state of canonical…
Based on trajectory dependent path probability formalism in state space, we derive generalized entropy production fluctuation relations for a quantum system in the presence of measurement and feedback. We have obtained these results for…
The variational principle for a thin dust shell in General Relativity is constructed. The principle is compatible with the boundary-value problem of the corresponding Euler-Lagrange equations, and leads to ``natural boundary conditions'' on…
We introduce from an experimental point of view the main concepts of fluctuation theorems for work, heat and entropy production in out of equilibrium systems. We will discuss the important difference between the applications of these…
The entropy production rate is a key quantity in non-equilibrium thermodynamics of both classical and quantum processes. No universal theory of entropy production is available to date, which hinders progress towards its full grasping. By…
Spearheaded by the recent efforts to derive stochastic geophysical fluid dynamics models, we present a generic framework for introducing stochasticity into variational principles through the concept of a semi-martingale driven variational…
A generalised notion of exponential families is introduced. It is based on the variational principle, borrowed from statistical physics. It is shown that inequivalent generalised entropy functions lead to distinct generalised exponential…
In a series of previous articles by the author, it was shown that one could effectively give a variational formulation to non-conservative mechanical systems, as well as ones that subject to non-holonomic constraints by starting with the…