The generalized setup of comprehensive thermodynamic theory of stability of irreversible processes (CTTSIP) and a few illustrative applications

Department of Chemistry, Nagpur University, Amravati Road Campus, Nagpur-440 033, India
E-mail : anabha@hotmail.com
Manuscript received 5 October 2004

A generalized setup of the recently developed comprehensive thermodynamic theory of stability of irreversible processes
(CTTSIP) has been described. In the first place, it involves expressing thermodynamic Lyapunov function, L_s (defined in
the perturbation space) and the entropy source strength, σs, corresponding to the perturbed trajectory as the Taylor expansion
about their values on the real (unperturbed) trajectory whose thermodynamic stability is under investigation. In this way
all quantities are obtained that are tenable within the thermodynamic perturbation space and hence one is led to the autonomous mathematical description. Yet another advantage is that in a single setup there is now available an apparatus to determine thermodynamic stability against uni- and bilateral perturbations and correspondingly first and higher order stability considerations are also dealt with as the case may be. Of course, all cases are handled with the fabric of celebrated Lyapunov's second (direct) method of stability of motion. A few representative examples have been described to illustrate how this generalized setup of CTTSIP works. The conclusions about the stability, asymptotic stability, stability against the constantly acting small disturbances and instability are drawn using Lyapunov and Malkin theorems.