We show the validity of some results of finite-time thermodynamics, also within the quasi-static framework of classical thermodynamics. First, we consider the efficiency at maximum work (EMW) from finite source and sink modelled as identical thermodynamic systems. The near-equilibrium regime is characterized by expanding the internal energy upto second order (i.e. upto linear response) in the difference of initial entropies of the source and the sink. It is shown that the efficiency is given by a universal expression 2η C /(4 − η C ), where η C is the Carnot efficiency. Then, different sizes of source and sink are treated, by combining different numbers of copies of the same thermodynamic system. The efficiency of this process is found to be η 0 = η C /(2 − γη C ), where the parameter γ depends only on the relative size of the source and the sink. This implies that within the linear response theory, EMW is bounded as η C /2 ≤ η 0 ≤ η C /(2 − η C ), where the upper (lower) bound is obtained with a sink much larger (smaller) in size than the source. We also remark on the behavior of the efficiency beyond linear response.

No abstract

A nonextensive thermostatic approach to chaotic dynamical systems is developed by expressing generalized Tsallis distribution as escort distribution. We explicitly show the thermodynamic limit and also derive the Legendre Transform structure. As an application, bit variance is calculated for ergodic logistic map. Consistency of the formalism demands a relation between box size (ǫ) and degree of nonextensivity, given as (1 − q) ∼ −1/ln ǫ. This relation is numerically verified for the case of bit variance as well as using basic definition of Tsallis entropy. 05.45.+b, 05.70.Ce

No abstract

No abstract