Kiyavash Irankhah, Soheil Asadimehr, Behzad Kiani, Jamshid Jamali, Reza Rezvani, Seyyed Reza Sobhani
Investigating the role of the built environment, socio-economic status, and lifestyle factors in the prevalence of chronic diseases in Mashhad: PLS-SEM model
Frontiers in public health
chapter 12 opens ehrenfest classification phase transitions first order discontinuities first derivative gibbs free energy w r intensive variables second order discontinuities second derivatives followed analysis helmholtz free energy van der waals gas although van der waals equation satisfy stability conditions entire range many conclusions applicable real systems example point pt coexistence liquidvapor diagram would vs vs v diagram exhibit two minima one liquid volume one gaseous volume curve connecting two minima must go maximum unstable due fluctuations system finds maximum system unstable split two phases minima get shallower closer system critical point eventually merge one minimum resulting large fluctuations pointed fluctuations normally ignored macroscopic thermodynamics appear play vital role critical region discussion sets stage treatment statistical mechanics next chapters