Abstract
Maximum-entropy ensembles are key primitives in statistical mechanics. Several approaches have been developed in order to justify the use of these ensembles in statistical descriptions. However, there is still no full consensus on the precise reasoning justifying the use of such ensembles. In this work, we provide an approach to derive maximum-entropy ensembles, taking a strictly operational perspective. We investigate the set of possible transitions that a system can undergo together with an environment, when one only has partial information about the system and its environment. The set of these transitions encodes thermodynamic laws and limitations on thermodynamic tasks as particular cases. Our main result is that the possible transitions are exactly those that are possible if both system and environment are assigned the maximum-entropy state compatible with the partial information. This justifies the overwhelming success of such ensembles and provides a derivation independent of typicality or information-theoretic measures.
Highlights
Maximum-entropy ensembles are key primitives in statistical mechanics
Given some partial information about a system, a vast set of predictions about its behaviour can be derived by assigning to the system that statistical ensemble which maximises the entropy compatible with the partial information
Our main result is that, for any initial state, the possible state transitions on such a system under partial information coincide exactly with those possible if the system and the environment were initially in the maximum-entropy ensemble state compatible with the partial information. This justifies the use of the canonical ensemble to represent a system under partial information, it allows one to derive the building blocks of phenomenological thermodynamics without assuming systems to be represented by this ensemble
Summary
Maximum-entropy ensembles are key primitives in statistical mechanics. Several approaches have been developed in order to justify the use of these ensembles in statistical descriptions. Our main result is that the possible transitions are exactly those that are possible if both system and environment are assigned the maximum-entropy state compatible with the partial information This justifies the overwhelming success of such ensembles and provides a derivation independent of typicality or information-theoretic measures. 2,3 for a review on this approach and its conceptual problems), or based on the notion of typicality The latter is the observation that the volume of pure quantum states (compatible with the information) that behave like a maximum-entropy ensemble is close to unity, with respect to a relevant measure on state space[4,5,6]. Our results hold for small, individual quantum systems
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