Future output of a system with memory depends on future input and a number of state variables, such as values of the input or output at various times in the past.
Linearity implies that operation of a system can be scaled to arbitrarily large magnitudes, which is not possible.
By definition of time-invariance, it is violated by aging effects that can change the outputs of analog systems over time (usually years or even decades).
Thermal noise and other random phenomena ensure that the operation of any analog system will have some degree of stochastic behavior.
A lumped LTI system is specified by a finite number of parameters, be it the zeros and poles of its transfer function, or the coefficients of its differential equation, whereas specification of a distributed LTI system requires a complete function, or partial differential equations.