Generalized Clausius relation and power dissipation in nonequilibrium stochastic systems

Abstract

In the framework of the stochastic dynamics of open Markov systems, we derive an extension of the Clausius inequality for transitions between states of the system. We give a formula for the power produced when the system is in its stationary state and relate it to the dissipation of energy needed to maintain the system out of equilibrium. We deduce that, near equilibrium, maximal power production requires an energy dissipation of the same order of magnitude as the power production.

Efficiency of a thermodynamic motor at maximum power

“…We recover, with different notations, the main result of Ref. [13], as well as the following conclusions. g C is a decreasing function of K 1 /K 2 .…”

“…In practical cases, a typical value of C V is of the order of 2.5 R and T 1 /T 2 ranges between 2 and 3 (see Refs. [4,13] 3. Entropy production in a generalized motor.…”

“…Thus the Carnot limit is not appropriate for an actual motor, which must have a finite power production. Many authors over the years [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] have considered the Carnot efficiency of a bi-thermal motor when it produces its maximum power either for macroscopic motors, or for microscopic systems. Clearly, this maximum depends on the parameters which are supposed to be varied, and different responses can be found in different conditions.…”

“…The hypotheses used for deriving this formula became more and more sophisticated, and it was extended to broader situations [18][19][20][21]. Recently, a new energetic efficiency, called the sustainable efficiency g S , was proposed for stationary systems in the framework of stochastic thermodynamics [13][14][15]. According to this definition, which applies for an arbitrary number of temperature sources, g S is the ratio of the power produced over the maximum power which could be produced if the power dissipation could vanish.…”

Entropy Production in Nonequilibrium Systems at Stationary States

“…an expression that has been considered by several authors [10][11][12][13][14][15][16][17][18][19][20][21][22] and has a close relationship with the fluctuation theorems of Gallavotti and Cohen [23] and with the Jarzynski equality [24,25]. It is nonnegative because each term in the summation is of the form ðx À yÞ lnðx=yÞ and vanishes in equilibrium, that is, when microscopic reversibility or detailed balance condition is obeyed.…”