The resource-theoretic approach to quantum thermodynamics assumes complete knowledge of the thermal equilibrium against which thermodynamic resources are defined. In practice, however, this state is determined by the system Hamiltonian and the bath temperature, neither of which is known with perfect precision. We develop a framework in which the equilibrium reference is specified by a set of candidate states reflecting this uncertainty. Under a generic geometric condition, we prove a no-go theorem that sharply limits athermality ``purification'': conversion from an uncertain athermality resource to a definite target is either trivial or impossible, with no room for tradeoff. We then introduce two complementary battery models: a clean battery with a precisely known equilibrium state and a dirty battery with an uncertain one. For both models, we derive exact one-shot entropic characterizations of work extraction and work of formation in terms of standard min- and max-relative entropies and new subspace-constrained variants. In the asymptotic regime, both models exhibit a strong form of thermodynamic irreversibility. In particular, we give a simple and explicit example in which, in the clean-battery model, work is required to form a state but no work can be extracted from it, in direct analogy with bound entanglement, whereas in the dirty-battery model, work can be extracted but formation requires infinite work cost. These phenomena persist even under arbitrarily small uncertainty, showing that equilibrium uncertainty is not a minor perturbation of the standard theory but a qualitatively new ingredient that reshapes the fundamental limits of thermodynamic resource interconversion.

翻译：资源论方法在量子热力学中假定对热力学资源所定义的热平衡态具有完全认知。然而实际中，该状态由系统哈密顿量与热库温度共同决定，而两者均无法达到完美精确。我们建立了一个理论框架，其中平衡参考态由一组反映这种不确定性的候选状态来表征。在通用几何条件下，我们证明了一个无go定理，严格限制了非热性的"纯化"过程：将不确定的非热资源转化为确定目标态要么平凡可实现，要么完全不可能，不存在任何权衡空间。随后我们引入两类互补电池模型：精确已知平衡态的清电池和平衡态不确定的污电池。针对两个模型，我们基于标准最小/最大相对熵及其新提出的子空间约束变体，推导了功提取与态生成精确单发熵特征量。在渐近区域中，两类模型均展现出强热力学不可逆性。特别地，我们给出一个简明显式示例：清电池模型中，态生成需要消耗功却无法从中提取功（直接类比束缚纠缠）；而在污电池模型中，可提取功但生成需无限功成本。上述现象即使在任意小的不确定性下依然存在，表明平衡态不确定性绝非标准理论的微扰修正，而是重塑热力学资源相互转换基本极限的全新构成要素。