The vapor-liquid critical behavior of intrinsically asymmetric fluids is studied in finite systems of linear dimensions, $L$, focusing on periodic boundary conditions, as appropriate for simulations. The recently propounded ``complete'' thermodynamic $(L\to\infty)$ scaling theory incorporating pressure mixing in the scaling fields as well as corrections to scaling ${ [arXiv:cond-mat/0212145]}$, is extended to finite $L$, initially in a grand canonical representation. The theory allows for a Yang-Yang anomaly in which, when $L\to\infty$, the second temperature derivative, $(d^{ 2}\mu_{ \sigma}/dT^{ 2})$, of the chemical potential along the phase boundary, $\mu_{ \sigma}(T)$, diverges when $T\to\Tc -$. The finite-size behavior of various special { \em critical loci} in the temperature-density or $(T,\rho)$ plane, in particular, the $k$-inflection susceptibility loci and the $Q$-maximal loci -- derived from $Q_{ L}(T,<\rho>_{ L}) \equiv < m^{ 2}>^{ 2}_{ L}/< m^{ 4}>_{ L}$ where $m \equiv \rho - <\rho>_{ L}$ -- is carefully elucidated and shown to be of value in estimating $\Tc$ and $\rhoc$. Concrete illustrations are presented for the hard-core square-well fluid and for the restricted primitive model electrolyte including an estimate of the correlation exponent $\nu$ that confirms Ising-type character. The treatment is extended to the canonical representation where further complications appear.
Categories: cond-mat.stat-mech