It is conventionally believed that there are no self-sustained thermoacoustit oscillations in the absence of acoustic modes in combustors. However, such oscillations (also known as intrinsic thermoacoustic instability) are recently found to occur in a premixed combustor with a mean flow present but no acoustic eigenmodes involved. Practical combustors are associated with entropy waves, pressure jump and mean flow, which are ignored in previous studies without justification. In this work, an entropy involved energy measure is defined and used to study the stability behaviors of intrinsic thermoacoustic modes. The concepts and methods are exemplified with the classical time-delay n-tau unsteady heat release model. The intrinsic thermoacoustic eigenmodes are found to be related to not only a flame transfer/describing function but also the acoustic impedance at the flame, which is boundary-dependent. It is shown that the predicted frequency omega(r)(f) of the intrinsic modes and the critical gain n(c) depend on the ratio (T) over bar (2)/(T) over bar (1) between the after- and before-combustion temperatures and the inlet mean flow Mach number (M) over bar1. Comparison is then made between the present results and those available in literature. Good agreement is obtained for omega(r)(f). Furthermore, the predicted stability of intrinsic modes based on calculated tie is found to agree well with direct numerical simulations (DNS). It is also interesting to show that as (T) over bar (2)/(T) over bar (1) -> 1, the critical gain as predicted from the previous models is n(c) -> +infinity, which means that all intrinsic eigenmodes are stable. However, the present works shows that n(c) -> 1.0. Further illustration is then performed by conducting case studies of measured flame transfer and describing functions in premixed combustors. The present work opens up an alternative but more applicable way to study intrinsic thermoacoustic oscillations via the entropy-involved energy measure. (C) 2016 Elsevier Ltd. All rights reserved.