What are the cognitive and neurological bases for apathy? Apathy, or effectively the feeling of "not caring" or putting it colloquially, "not giving a rats", is something that most of us get sometime or another in varying degrees.

My question is, what are the cognitive and neurological bases for apathy?  Why is it that some experience it far stronger and more often than others?
Assuming the original poster (now departed) was considering apathy as a distinct phenomena from depression, then current evidence points to the current neurological basis of apathy being connectivity in the pre-motor brain systems according to "Individual Differences in Premotor Brain Systems Underlie Behavioral Apathy" by Bonelle et al. (2016):


  The results demonstrate that behavioral apathy is associated with
  increased effort sensitivity as well as greater recruitment of neural
  systems involved in action anticipation: supplementary motor area
  (SMA) and cingulate motor zones. In addition, decreased structural and
  functional connectivity between anterior cingulate cortex (ACC) and
  SMA were associated with increased behavioral apathy. These findings
  reveal that effort sensitivity and translation of intentions into
  actions might make a critical contribution to behavioral apathy. We
  propose a mechanism whereby inefficient communication between ACC and
  SMA might lead to increased physiological cost—and greater effort
  sensitivity—for action initiation in more apathetic people.


Note that the authors of the paper controlled for depression using questionnaires:


  Self-reports of apathy traits were obtained using a modified, extended
  version of the original Lille Apathy Rating Scale (LARS-e), available
  online in Bonnelle et al. (2014) (see Supplementary Material for more
  details). The LARS-e uses subscales that allow assessment of apathy
  traits along several domains reflecting the distinct component of
  apathy (behavioral, cognitive, and emotional). We used the “Action
  Initiation” (AI) subscale of the LARS-e, which measures every-day
  productivity and initiative and is an index of behavioral apathy
  (Sockeel et al. 2006). This subscale was previously found specifically
  to relate to the willingness to engage in an effort response in order
  to obtain a reward on our paradigm (Bonnelle et al. 2014). In
  addition, to control for a potential confound of depression and
  anhedonia, we also used the Depression, Anxiety, Stress Scales (DASS)
  (Lovibond and Lovibond 1995), a questionnaire developed in nonclinical
  populations to measure depression, and the Snaith–Hamilton Pleasure
  Scale (Snaith et al. 1995), which assesses anhedonia.


The authors assessed patients according to their willingness to complete a task while stakes (a combination of expected reward and expected effort) were manipulated. They found a high correlation between sensitivity to effort and behavioural apathy as assessed via the questionnaires in the previous quote. They then examined connectivity via fMRI of the patients completing the task and determined certain areas were more connected in patients with lower behavioural apathy. Specifically, the pre-motor brain systems were better connected in non-apathetic individuals.

It's unclear what this means cognitively, but the authors hypothesize, based on other activation, that this: "might be due to higher 'subjective experience' of effort cost in individuals who are more apathetic".