Interesting thoughts from Jones here - certain viscosity effects result in systems with time-dependent net energies - and negative hysteresis losses would indeed be OU, since the "induced" B field would be automatically changing under zero applied H field, and a freely-alternating (time-varying) field is a free energy gradient. The automatic flipping of the remanant flux against its own coercivity would provide hefty gains per cycle.
It is clear however that negative hysteresis appears to be fundamentally contrary to the nature of ferromagnetism and remanance / retentivity, so further speculation on the matter seems of little value in the present context. It does however throw a quick spotlight on the relationship between time-varying forces and the conservation of energy, and this area is right up our street.. Noether's theorem is often rather crassly summarised as demonstrating that the conservation laws are time-invariant. But of course this is a perfectly trite statement - the CoE laws are the same today as yesterday, big whoop... and entirely missing the real lesson, which is not so trivial.. The more salient point becomes apparent in applying the concept to an interaction, comprising discrete input vs output (ie. inbound vs outbound) force times displacement integrals (classical work); if the force in question is time-variant, then the balance of energy between our two integrals is a function of our applied displacement velocities in relation to the field's own finite rates of change. In symmetrical / non-time varying interactions, force variations can be treated as propogating at C, effectively instantaneously, thus ensuring energy symmetry regardless of any variation in input vs output velocities (ie. mass & gravity are mediated at C so asymmetric gravitational interactions are impossible). However in material or aggregagte systems, effective field propogation rates can be finite (per "slow light" phenomena), opening up this arena of passively time-varying systems, with time-dependent net energies... In other words, any passively time-varying system is an open thermodynamic system - it may or may not have constant energy, but cannot be thermodynamically closed. Hysteresis losses are an example of extra work that must be performed against the field - an excess of input work for a corresponding output integral. In other words, hysteresis losses are inherently non-dissipative - the additional input work required, by definition, is a function of ordinary force and displacement - the extra workload is principally magnetic. Non-dissipative loss mechanisms are the corollary, inverse phenomena of thermodynamic gains - it's exactly the same form of asymmetry, with the direction reversed. But the same animal nonetheless. However hysteresis losses are normally only encountered, and hence their implications considered, in terms of their effects on conventional EM systems such as motors and transformers, in which case they result in an additional load upon the power supply - more current is needed to produce a stronger applied field, incurring higher resistance losses from the coils and net circuit, and thus a dissipative loss mechanism. And at this juncture, something with profound implications has been cast by the wayside.. But suppose for a moment that we had passively-superconducting circuits (not in itself prohibited) - we'd still have to perform more input work to raise the current and flux density, but we could then recoup that investment coming back down the other side, when the domains are aligning in their preferential direction, and we'll have incurred no such incidental heating costs. The net sum's still zero, but we haven't lost anything either. Another example would be entropy viscosity (Sv) as investigated by Rutherford in his first paper (c. 1886) - normally an engineering obstacle, since a motor or transformer pulsed faster than the response frequency of its magnetic cores cannot induce any more flux with rising current, hence the only remaining workload beyond an Sv-restricted max speed would again be resistance losses. As such, Sv is usually dismissed as dissipative when it, too, is not - resistance losses are surely dissipative, but incidental to the nature of Sv losses which are intrinsically time-variant. As an example, suppose a magnet is allowed to attract itself across some small distance, to a lump of rough iron. Due to the diversity of the iron's internal domain structures, different regions have varying remanance and coercivities, some domains are pinned harder than others and so its magnetisation curve is non-linear and laggy - holdout domains are still popping into alignment, even some time after the magnets have joined together and stopped moving. So the induced field is increasing, ambiently, of its own accord. If we then separate the magnet from the core, we'll have to input more mechanical effort to prise them apart, than they originally exerted when attracting together. Again, the actual "form" of the additional input work required is conventional F*d. We've simply input more energy to the field, than it has output into our mechanical (thermodynamic) realm - the crucial point being that we haven't incurred any additional heating mechanism... ie. our loss here is non-dissipative. They attract together against a low force. Then the force rises of its own accord. Then we have to separate them agasint this higher force, inputting more F over a given d - a closed-loop mechanical loss. To really drive home the implications of this, we could, in principle, dump ANY amount of energy into such an interaction, over any number of cycles, without raising the temperature of the closed system (ie. calorimetry shows total loss of energy). The energy has thus, to all intents and purposes, disappeared from the classical, thermodynamic, domain. This energy isn't really "lost" - we know it was input against magnetic force, in an asymmetric exchange of mechanical to magnetic work (negatively-signed ambient momentum transfered by virtual photon flux)... yet as far as classical concepts are concerned, this energy has been destroyed..! So excuse the sermon, but this seemed an apposite opportunity to expound on this often under-appreciated issue. TL;DR: ______ Noether's theorem and the classical conservations laws are as much prescriptive as proscriptive - telling us what IS possible, as much as what isn't.... The "X" marking the treasure is surely the fact that wherever force is a passive function of time over a given displacement, so, potentially, is net energy.. and we already know of such examples, that effectively violate the classical first law. Strictly, the only remaining controversy concerns the direction of the asymmetry.. but the fate of such "destroyed" energy is precisely the same conversation as the provenance of any prospective gains - ask me where it comes from, and i'll ask you where it goes..
