The concept of maximum entropy production (MEP) is closely linked to the second law of thermodynamics, which explains spontaneous processes in the universe. In geophysics, studies have argued that planetary atmospheres and various subsystems of Earth also operate at maximum dissipation through MEP. One of the debates, however, has concerned the degree of empirical support. This article extends the topic by considering measurements from a high-altitude, cold glacier in the tropical atmosphere and a numerical model, which represents the open and nonequilibrium system of glacier-air exchanges. Results reveal that several sensitive system parameters, which are mainly tied to the shortwave radiation budget, cause MEP states at values that coincide closely with the in situ observations. Parameters that set up the forcing of the whole system, however, do not show this pattern. Empirical support for the detection of MEP states, therefore, is limited to parameters that regulate the internal efficiency of energy flow in the glacier. System constraints are shown to affect the solutions, yet not critically in the case of the two most sensitive parameters. In terms of MEP and geophysical fluids, the results suggest that the local atmosphere-glacier system might be of relevance in the further discussion. For practical purposes, the results hold promise for using MEP in single or multiparameter optimization for process-based mass balance models of glaciers.