This paper presents a generalized maximum entropy principle for quantum many-body systems, applicable to both temporal and projected ensembles of states. The principle states that ensembles of pure states, formed by either the temporal trajectory of a quantum state under unitary evolution or by partial projective measurements on subsystems, maximize their entropy under constraints such as energy conservation and thermalization. These ensembles are characterized by their statistical moments, which are shown to be universal and independent of the specific details of the initial state or system dynamics. The results demonstrate that such ensembles exhibit properties of Hilbert-space ergodicity and deep thermalization, with the former referring to the uniform exploration of Hilbert space by quantum states and the latter to the thermalization of both local and non-local observables. The paper also discusses the information-theoretic implications of these results, showing that the ensembles have maximal information content while being maximally difficult to interrogate, thus scrambling information as strongly as possible. The findings generalize the concepts of Hilbert-space ergodicity and deep thermalization to time-independent Hamiltonian dynamics and finite effective temperatures. The work provides new perspectives on characterizing and understanding universal behaviors of quantum dynamics using statistical and information-theoretic tools. The results are supported by numerical verification and have implications for quantum communication, information theory, and the study of many-body systems.This paper presents a generalized maximum entropy principle for quantum many-body systems, applicable to both temporal and projected ensembles of states. The principle states that ensembles of pure states, formed by either the temporal trajectory of a quantum state under unitary evolution or by partial projective measurements on subsystems, maximize their entropy under constraints such as energy conservation and thermalization. These ensembles are characterized by their statistical moments, which are shown to be universal and independent of the specific details of the initial state or system dynamics. The results demonstrate that such ensembles exhibit properties of Hilbert-space ergodicity and deep thermalization, with the former referring to the uniform exploration of Hilbert space by quantum states and the latter to the thermalization of both local and non-local observables. The paper also discusses the information-theoretic implications of these results, showing that the ensembles have maximal information content while being maximally difficult to interrogate, thus scrambling information as strongly as possible. The findings generalize the concepts of Hilbert-space ergodicity and deep thermalization to time-independent Hamiltonian dynamics and finite effective temperatures. The work provides new perspectives on characterizing and understanding universal behaviors of quantum dynamics using statistical and information-theoretic tools. The results are supported by numerical verification and have implications for quantum communication, information theory, and the study of many-body systems.