Equilibrium, canonical based expressions of entropy are known to exhibit non-local effects that can complicate statistical mechanical formulations and applications. Here, we demonstrate proper normalization the underlying probability density functions remove in entropy. Our analysis is carried out through third order function expansions lead results consistent with macroscopic thermodynamics, a...

In the frame work of Palatini approach to modified f(R) theories gravity, we attempt investigate thermodynamic behavior time-dependent wormhole geometries. By considering an evolving spacetime, find field equations in gravity. The energy density and pressure are redefined order satisfy continuity equation. To discuss behavior, expression for variation total entropy is obtained. Then, extend our...

Self-propulsion allows living systems to display self-organization and unusual phase behavior. Unlike passive systems in thermal equilibrium, active matter systems are not constrained by conventional thermodynamic laws. A question arises, however, as to what extent, if any, can concepts from classical thermodynamics be applied to nonequilibrium systems like active matter. Here we use the new sw...